classroom discourse and the space of learning
TRANSCRIPT
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Classroom Discourse
and the Space of Learning
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Classroom Discourse
and the Space of L earning
Ference
Marton, Goteborg Universi ty
Am y B. M. Tsui,
The
Un iversity
of
Ho n g K o n g
With
Pakey P. M .
Chik
PoYukKo
M un Ling 33Lo
Ida
A . C. Mok
Dorothy F . P. Ng
M i n g F ai Pang
Wing Yan Pong
Ulla Runesson
IEA
1
•
LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS
2004 Mahwah, New Jersey London
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C o p y r ig h t ©
2004
b y L awren ce E r lbau m A s s oc ia t es , I n c .
A ll
r i g h t s
reserved.
No part o f th i s book m ay be rep roduced in
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m eans ,
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10
In dus t r i a l Avenue
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Jersey
07430
Cover des ign by John Leung
Library
of Congress
C a t a l o g i n g - i n - P u b l i c a t io n D a t a
Marlon , Ference .
Class room d iscourse and the
space
o f l ea rn ing / Ference Mar ton ,
A m y B . M .
Ts u i w i t h Pakey
P . M.
C h i k
. . . [et
al . ] .
p. cm.
I nc l ude s
b ib l i o g rap h i ca l r e f e ren ces
a nd
i n d ex .
I S B N
0-8058-4008-7 (c lo th :
alk . paper)
I S B N
0-8058-4009-5
( pbk . : a lk . paper )
1 .
C o m m u n i c a t i o n
in
ed u ca t i o n .
2.
L e a r n i n g .
3.
Class room
envi ronment .
I . Ts u i , Am y . II . Ti t l e .
L B 1 0 3 3 . 5 . M 2 6 5
2003
371.102'2^c21
2003047019
C I P
Books publ ished
by
L awrence Erlb aum Associates
are
printed
on
acid-
free paper, and their bindings are chosen for strength and durabili ty.
Pr in ted in the Un i ted S ta tes o f A m er ica
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C o n t e n t s
Contributors v ii
P re f a c e ix
Part
I O n
Learning
and
Language
1 The
Space
of
Learning
3
Ference M arlon , Ulla Runesson, and Amy B. M. Tsui
Part II O n Learning
2
Vanation
and the Secret of the
Virtuoso
43
Po Yuk Ko and Ference Marlon
3
Discernment
and the
Question, "What
Can Be
Learned?"
63
Ulla Runesson and Ida A. C. Mok
4 Simultaneity and the Enacted Object of Learning 89
Pakey P. M. Chik and Mun Ling Lo
Part
III O n Language
5
Questions
and the
Space
of
Learning
113
Amy B . M.
Tsui, Ference Marlon ,
Ida A. C. Mok,
and Dorothy F. P. Ng
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V I
CONTENTS
6 The Semant ic E nr ichm ent of the Space of Learning 1 39
A m y B . M .
Tsui
7 The
Shared Space
of
L earning
1 65
Amy B. M.
Tsui
Part IV O n Improving Learning
8 Toward a Pedagogy of Learning 1 89
M un Ling
Lo , Ference Marlon , Ming F ai Pang ,
and
Wing
Y an
Pong
Epilogue
227
References 233
Au thor Index 239
Subject Index 241
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Contr ibutors
Ference
M arton, Professor of Educat ion, Facul ty of Educat ion, Goteborg
Universi ty,
Sweden ,
and
Honorary Professor , Facul ty
o f
Educa t i on ,
T he
U nivers ity of Hon g K ong.
Am y B . M . Tsui , Chair Professor , Facul ty of Ed ucat ion, The Un ivers i ty of
Hong Kong .
Pakey P . M . C hik , S tuden t, Degree
of
M as ter
o f
Phi losophy, Facu l ty
of Ed-
ucat ion ,
The U nivers ity of Hong Kong.
Po Yuk Ko, Lec turer , Department
of
C urr icu lum
and
Ins t ruct ion,
The
H o n g
Kong Ins t i tu te o f Educat ion .
M u n L i n g L o , Head, Centre
for
Development
of
School Partnership
and
Field
Ex perience, The Hon g Kong Ins t itu te of Ed uca t ion.
Ida A. C.
Mok, A ssis tant Professor , Fac ul ty
o f
E duca t ion ,
Th e
Un ivers i ty
of Hong Kong .
D or ot h y F. P. N g, Teaching Fellow, Fa culty of
Educat ion ,
The U nivers ity of
Hong Kong .
M ing Fa i Pang, A ssistant Professor , Fa cul ty of Educ at ion, The Un ivers ity
of Hong Kong.
W in g Y a n P on g ,
Principal , Hong Kong Management Associat ion, David
Li
K w o k
Po
Col lege.
Ulla Runesson, Postdoctoral Fellow, Senior Lecturer, Faculty
of
E du c a -
t ion,
Goteborg Universi ty, Sweden.
V I I
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Preface
This book
is
abou t learning
in
schools ,
and the
role
of
language
in
learning.
W e have tr ied to capture i ts tw o m ain ideas in the t i t le . Co ntained w ithin the
first idea is the
p rem ise
that wh atever you are trying to learn, there are cer-
tain
necessary condi t ions for succeeding. Al thou gh you cannot be sure tha t
learning w il l take place when those co ndit ions are m et , you can be sure that
no
learning w il l take place
if
they
are
not .
T he
l imits
o f
w h a t
is
possible
to
learn, w e call " the space o f learning." T he second premise is tha t langu age
p l a y s a cen tra l role in learning : that i t does not m erely convey m eaning, it
also creates
m e a n in g .
A n
understanding
of how the
space
of
learning
i s
l in-
gui s t i ca l ly co nst i tute d in the c lassroom is best achieved through invest igat-
ing "classroom discourse ," wh ich
is
w h a t
w e a im to do
here .
A teach er can never ensure that the intended learning wi l l ac tual ly take
p lace , but a teacher should try to ensure that i t
i s
possible for the studen ts to
learn
w ha t is inte nd ed. That is, the teacher sho uld ensure that the space of
learning
a l lows
for the
intended learning
to
take place .
F or
every educa-
t ional
aim, for every single thing that students are expected to learn, there
are
specif ic
c ondit ions necessary fo r that learning. In our view, f inding ou t
w h a t
these condition s are, and br inging them about , should be the teacher 's
pr imary p rofess iona l task .
A
p rerequisi te
fo r
f inding
ou t
these condit ions
is
the
rea l iza tion tha t
one's
ow n w ay o f teaching is not the only w ay. Such a re-
al izat ion can only be achieved by co nfron ting different way s of teaching the
same th ing , by exam ining how the different w ays are actual ly played out in
the c lassroom and by com paring w hat is intended with wh at is enac ted. A nd
invest igat ing
the discourse in which the teacher and the s tudents are en-
gaged
in the
classroom
is an
essential par t
of
this endeavor.
It is,
there fore ,
fundamenta l ly important that teachers—an d student teachers , for that mat-
ter— are given opportuni t ies
to
observe different teachers teaching
the
same
ix
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X
P R E F A C E
th ing ,
and to analyze and ref lec t on how the c lass room d iscourse in w hic h
they
a re
engaged w i th
th e
s tuden t s m ax im izes
o r
m in im izes oppor tun it ie s
for
learning.
This book
is organized in
four
par ts . In Par t I , "On Learning and Lan-
guage," w e
p resen t
the
theo r e t i ca l backg r ound , namely
th e
theor ies tha t
wh atever you are t rying to learn, there are cer tain necessary co ndi t io ns for
succ eeding , and that langu ag e play s a central role in lea rnin g. Par t II , "On
Learning,"
com prises
three chap ters , each
o f
w hich e labora tes
on one of the
three core
e l emen t s
of our
view
o f
learn ing : va r ia t ion , d i scernm ent ,
and si-
m ultanei ty . Part I I I , "O n Language," comprises three chapters a s w e l l , each
of
which deals wi th
one of the
three aspects
of the
role
o f
la n g u a g e
in
class-
room
learn ing :
th e
role
of
quest ions
in
c ons t i t u t ing
the
space
o f
l ea r n ing ,
the
semant ic n a ture o f the space of learn ing , and the jo i n t con s t i tu t io n of tha t
space. In Par t IV, "On Improving Learning," we give three examples of
teachers
w orking
together a nd
using
the
very the oretical tools presented
in
the previous chapters .
Three
fea tures o f th i s book d is t inguish it f rom s im i lar books about learn-
ing in
schools. First ,
it is a
book about both theory
an d
p rac t ice .
I t
con ta in s
a
detai led ex pl icat ion of the theory of learnin g that m otivated the ana lyse s of
classroom teach ing in the res t of the book. I t presents deta i led an aly ses of
classroom teach ing that were dr iven by classroom discourse data in a nu m -
ber of authe nt ic cases of learn ing in school, and w h i c h w i l l be of p r ac t i ca l
relevance to teachers .
Second, th is book is m ore cul tura l ly s i tuated than most othe r books about
learning
in
schools . M ost
o f the
studie s reported
in
th is book have been ca r-
ried out in
Hong Kong .
In
every exa m ple,
it is
c lear ly demons t ra ted
how the
specif ic langu age , cu l tu re , and pedagogy m olds wha t i s happe ning in the
classroom . At the same t im e, however, w e w ou ld l ike to cla im that it i s a lso
possible
to
gen eral ize
f rom the
c u l tu r a l ly
specif ic
examples
and
a r gumen t s
presented
in
this
book. W e argue
that whatever skil ls , whatever ways
of
th ink ing th e s tudents a re expected to develop, there a re necessary condi-
t ions for the developm ent of these sk i l ls . These con d i t ions are
specif ic
to ev-
ery s pe cific sk il l , to every
specif ic
way of th ink ing , and they m us t be met
regardless o f where the learn ing is tak ing p lace , a nd rega rdless o f wha t o ther
condi tions there m ight be .
Third , th is boo k— just l ike other books— is good fo r cer tain th in gs and
not so
good
for
other th ing s .
A s
imp lied earlier ,
if you
w a n t
to f ind ou t how
cer tain specif ic capa bi l it ies (such as using elem entary ar i thme tic in
flexible
way s , d i s t ingu ish ing be tween
different
tones in Can tonese, seeing bodies in
mot ion
in
accordance wi th
a
Newtonian f ramework , r ea l iz ing
w hy
green
plants
are
essent ial
fo r l i fe on
Ear th)
can be
best developed,
you
w i l l p roba-
bly f ind
th is
book
use fu l . However,
i f you
w a n t
to f ind out
about gen eral iza-
t ions that
are
universal ,
if
they exist
a t
al l , such
as how
people become
creat ive, wh at is the best ar range m ent for learning in gen eral , the exact nu m -
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P R E F A C E X I
ber of
intel l igences
or
learning styles
in
humans ,
to
what extent those
intel l igences
or
learning styles
are
biologically, eco nom ically, cultural ly,
or
l inguist ical ly
determined, and so on, this
book
is
probably
not a very good
source
o f
inspirat ion.
This
book,
w e
w ish
to
emp hasize,
is not
abou t univer-
sal general izat ions about learning,
nor is it
about
the
development
of
spe-
cific
c apa bil it ies per se.
This
book is abou t the
necessary condi t ions
for the
development of any specific capability.
W e
w ou ld l ike
to
sugg est that this book
is
best used
in field
practice
for
teacher educat ion and in-service training for teachers . W e feel that it w i ll be
of m ost pract ical use when read in conjunct ion wi th arrangem ents w hereby
teachers and
studen t teachers have o ppo rtunities
to
observe different teach-
ers teaching
th e
same topic,
an d to
investigate
teacher-student
discourse
in
l ight
o f the opportunit ies fo r learning that are afforded.
Th is book can, however, also
be
juxtapo sed w ith other theoretical accou nts
of classroom learning. Dealt w ith
in
this way,
it can be
used,
w e
believe,
in ad-
vanced
sem inars in teacher edu cation, and for courses at Master's level in ed-
ucat ional
studies.
A C K N O W L E D G M E N T S
T he
research carr ied
o ut in
Hong Kong
w as
m ade poss ib le throu gh
a
grant
awarded to Professor P aul M orris ( then Chair Professor of Edu cat ion, The
Universi ty o f
Hong Kong ,
now
President
of the
Hong Kong In s t i tu te
of Ed-
uca t ion) f rom the Standing Commit tee on Language Educat ion and Re-
search in Hong Kong (SC OL A R). W e w ould l ike to express our s incere
grat i tude to
Professor M orris ,
a
bri l l iant scho lar
and a
m ost generous col-
l eague .
1
Ference M arton and Ul la Run esson w ould like to acknow ledge the sup-
port
of The
Tercentennary Foundat ion
of the
Bank
of
Sweden ,
and the
Swedish Re search C ounc i l, w i thout w hich thei r work w ould not have been
poss ib le .
The authors of th is volum e wo uld also l ike to thank the form er D epart-
m e n t
of C urr icu lum S tudies (now part of the Facu l ty of E ducat ion) at The
U niversity of Hong Kong, fo r providing the Departmental Research Fund,
wh ich
a l lowed
the
authors
to pay for
expenses incurred
in
collaborating
with
Goteborg Universi ty
and in
securing l inguist ic edit ing assistance.
The research team included Dr. Tam m y Kw an, whose contr ibut ion to th is
book is indicated by expl ici t references to her work. V ikki W eston has car-
ried
out a w ond e rf u l job of
editing
th e
l anguage
o f the
m anuscr ip t. An nie
Chow, M iranda Cheu ng, and W inky M ok at The U nivers ity of Hong K ong,
as wel l as Lisbetth Soderberg and Barbro Stromberg at Goteborg Univer-
sity,
have,
in different but
essential w ays, helped
us to put the
m anuscr ip t
in
shape .
W e thank them al l .
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X ll
P R E F A C E
Tw o reviewers , C our tney C azden of Harvard Graduate Schools and
Gaalen Er ickson of the U nivers ity of Br i t ish Columbia, have provided ex-
t r emely usefu l
and
critical
comments
that have sharpened
the
f o c u s
of the
book. W e are very
gra teful
to them . Fina l ly , th i s book w ould never have ma-
ter ial ized without
the
support
o f
N aom i S i lverman, Sen ior Ed i to r ,
and
Lori
Haw ver, A ssistant E di tor ,
o f
Law rence E r lbaum A ssocia tes , bo th
o f
w h o m
have been most encouraging, accommodat ing, and efficient . To them we
owe our deepest g rat i tude.
-—
Ference
M a r l o n
— A m y
B . M .
Tsui
E N D N O T E
'Part of the
findings from this
project have
been repo rted
previously in F.
M arton
& P.
Morris. (Eds.). (2002).
What
Mat ters: Discover ing
Crit ical
C o n d i t i o n s
o f
Classroom
Learn ing . Goteborg , Sweden :
Acta
Universitat is G othoburgensis .
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O n Learn ing and Language
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1
The
Space
of Learning
Ference Marton
U l l a
Runesson
A m y B . M . T s u i
Schoo l is an inst i tut ion with w hich a l l c i t izens in the industr ia l w orld have
extensive fam il iar i ty, and one that
f requent ly
a t t racts considerable public
and po li t ica l a t tent ion. T he discussions abo ut school can be heated an d the
opinions polemic : "W e should have less who le-class teaching," " W e should
have more pro jec t work," "W e should have more peer learning," "W e
shou ld have more problem -based
learning,"
"By the yea r 2006, a t least 20%
of a l l learning in our school should be information technology ( IT) sup-
ported," "Students should have more homework ," "Students should have
less homew ork," "W e should do away w i th age group ing," "W e shou ld re in-
troduce age grouping," "W e should have streaming," and so on.
A ll
these opinions about w hat should
be
done assume,
o f
course, th at
do-
ing this or doing that is bet ter than doing som ething e lse . B ut i f w e ask the
ques t ion , "Better for w hat?" the an sw er is l ikely to be, "Better for learning,
of course." "But
for the
learning
o f
w h a t?" "For
th e
learning
of
everything?"
These are the ques t ions tha t must be addressed.
Th e point is that i t is highly u nl ikely that there is any one pa r t icular way
of arrang ing for learning that is condu cive to all kinds of learning. In order
to find
effective w a y s
o f
arranging
fo r
learning, research ers need
to
first
ad-
dress what it is that should be learned in each case, and
find
the
different
con dit ions that are conducive to different kinds of learning.
It is only when we have a
fair
understanding of what learners are ex-
pe cted to learn in particu lar situations, w hat they ac tually learn in those si tu-
at ions, and w hy they learn som ething in one si tuat ion but not in another, that
pedagogy becom es a reasonably ra t ional se t of hum an a ct ivi ties . I t is the
aim
of
this book
to
provide such
an
u nders tanding.
3
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M A R I O N ,
R L ' N E S S O N , T S U I
W h e n
people argue
fo r a
p ar t icu lar
way o f
ar ranging
for
l ea r n ing ,
or for a
par t icular teaching method, such as wor k ing in groups or the use of p e d a -
gogica l d rama, they should make i t c lear wh at the par t icu lar a r rang em ent , o r
the par t icular m ethod, is good for and why . Ped ag og ica l ac ts shou ld take as
their point
o f
departure
the
cap ab i l i t i es they
are
supposed
to
co n t r ibu te
to
develop ing . The po in t o f sch ool ing i s no t tha t s tude nts shou ld or sho uld no t
be
grouped together
in
ce r ta in ways un d er ce r ta in con d i t ions— such
as b e-
ing
divided
up
according
to
age, abil i ty level,
or
gender . N ei ther
is the
p o i n t
that teachers should do cer tain th in gs in cer ta in w ays, or tha t ce r t a in con ten t
should
be
covered.
T he
po in t
is
tha t
the
s tudents should develop cer ta in
ca-
pabi l i t ies . '
T H E
O B J E C T
O F
L E A R N I N G
Learn ing
is
a lways
th e
acq u i r ed knowled ge
o f
s o m e t h in g .
A n d w e
shou ld
a lways
keep in
mind w ha t t ha t " someth ing"
is , tha t is , w e
s h o u l d
b e
c l ea r
about
the
object
o f
learn ing .
In th is
book ,
the object of learning is a
capab il ity ,
and any capa b i l i ty has a
general and a sp ecif ic aspect. T he genera l aspect has to do w i th th e na tu r e of
the capabili ty, such as rem em ber ing , d i scern ing , in terpre t ing , g rasp ing , or
viewing, that
is, the
acts
o f
learn ing
ea rned
o u t .
T he specif ic
aspect
h as to do
with the th ing o r sub jec t o n w hich these ac t s are car r ied o ut , such a s fo rm u-
las , engineer ing problems, s im ultan eo us equ at io ns . W orld W ar I I . or Fran z
Kafk a ' s
l i terary heritage.
In
other words,
the
ge ne r a l
aspect
r efer s
to
ac t s
(the indirect object of learn ing) , w hereas the specific aspect r efer s to w ha t i s
acted upon ( the
direct
object
o f
learn ing) .
T he
learner s ' focus
is
no r ma l ly
on
what they
a re
trying
to
learn ( the d irect object
o f
l ea r n ing ) , w her eas
the
teacher 's focus should
be on
both;
no t
on ly
on
tha t w h i ch
the
learners
are
trying
to
learn,
bu t
also
on the way in
w h i c h
the
learners
are
t ry ing
to
m a s te r
what they
a re
trying
to
l eam .
W e
m ight assum e therefore , tha t teachers
are
trying to work toward an object
of l e ar n i ng .
This o b jec t may be m ore or less
conscious for the teacher and i t m ay be mo re or less elaborated. Bu t , w ha t-
ever
the
c i r cumstances , w hat teachers
are
striving
for is the in tended
ob jec t
of learning, an object o f the teacher 's awareness , tha t m igh t chang e dynam i-
cally during the course o f learn ing .
Th i s
is the ob jec t of learn ing as seen
from the teacher's
perspec tive,
and as
such
is
dep ic ted
i n
th is book
as
be ing
evidenced
by
wha t
the
teacher does
and
says .
W h a t is of imp or tance for the s tudents , how ever , is not so m u c h how the
t eache j intends
the
object
o f
learning
to
come
to the fore, but how the
teacher structures the conditions of learn ing so tha t i t is po ssible for the ob-
j e c t o f
learning
to
come
to the
fore
of the
learners ' awareness . What
the
s tu-
dents
encounter is the enacted object o f learn ing , and it d e f ines wh a t it is
possible to leam in the
actual sett ing, from
the
po in t
of
view
of the specif ic
object o f learning.
There
are obv ious ly cer ta in necessary cond i t ions fo r
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1 . T H E
S P A C E
O F L E A R N I N G
learning one
thing
or
another.
T he
enacted object
of
learning
is the re-
searc her 's descript ion of w hether, to w hat ex tent , and in w hat form s the nec -
essary condit ions of a part icular object of learning appear in a certain
set t ing.
The enacted objec t of learning is described
from
the point of view of
a certain
research
interest and a part icular theoretical perspective.
Wh a t is of decisive importance for the students, is what actually
conies
to
the fore of their at tention, that is , w hat asp ects of the si tuation they discern
and focus o n. In the best case, they focus o n the cntical aspects of the object
of learn ing, and by doing so they learn w ha t the teacher in tended . B ut they
m ay also
fail to
discern
and
focus
on
some
of the
cri t ical aspects,
or
they
m ay discern
and
focus
on
other aspects . Wha t they a ctua l ly learn
is the
l ived
object
of learning, the o bject of learning as seen
from
the learner 's p oint of
view,
that
is, the outcome or
result
of
learning.
T h e O r i g i n
of
Powerful Ways
of A c t i n g
Learn ing is the process of becoming capable of doing som ething
("doing"
in the wide sense) as a resul t of having had cer tain experiences (of do ing
some th ing
or of som ething happen ing) . D eveloping a learner ' s cap abi l i ty
of hand ling novel si tuations in pow erful way s is
considered
to be on e of the
m o s t imp ortant educa t ional a ims. In order to address how this can be done,
w e
have
to
ref lect
on the
na ture
of powerful
w a y s
o f
act ing, that
is,
w a y s
o f
engag ing in acts ins t rum ental to ach ieving one 's goals eff iciently. Ac t ing in
powe r f u l
w ays mea ns, therefore, doing
different
th ings
to
achieve different
a i m s ,
and
doing
different
th ings
in different
s i tua t ions .
T he
power fu lnes s
o f
on e's acts is relat ive to
one 's
a ims and the s i tua t ions .
L et u s
f i rst cons ide r
the
s i tua t ions .
A s
r a t i on a l be ings ,
w e
a lways
try to
act
in
a cco rdance wi th
an y
given s i tua t ion, that
is, the
s i tuat ion
as we
per-
ce ive
i t.
W h a t k n o w l e dg e
w e
m i g h t
try to
exp lo i t depends
o n h o w w e
m a k e
sense of the s i tua t ion . Our previous exper iences
affec t
t he way i n w h ich
w e perceive
the s i tuat ion, but the way in wh ich w e perceive the situation
also
affec ts
wha t exper i ences we see as relevant in tha t par t i cu lar s i tua -
t ion . W e a re
trying
to ac t in
pow er fu l w ays , tha t
is, w e a re
t ry ing
to
ach i eve
our a i m s ,
not in
relat ion
to the
s i tuat ion
in an
obje ct ive sense,
but in
r e l a -
t ion to the s i tua t ion as we see i t . P o w e r f u l w a y s o f ac t ing spring from p o w -
erfu l w a y s
o f
seeing.
Let
u s
take
an
exam ple . Someone
is
standing
in a
lake wi th
th e
water
up to
his
knees
and
aiming
at a
fish
in the
w ater with
a
harpoon.
He
m ight
a im at
the
fish
where it appears to be, that is, where he actually sees it, or at a
sl ightly adjusted angle, that
is,
w here
he
th inks
it
should actual ly
be if he
takes
the
refraction
of the
l ight into considera t ion.
These tw o
different w a y s
of act ing are based on two different w ays of understanding the si tuation and
the
latter is
m ore
pow erful than the former. Let us take ano ther exam ple. Let
us imagine that a sales tax of 10% is introduced in Hong Kong. One car
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M A R I O N , R U N E S S O N , T S U I
dealer selling expen sive cars sim ply increases the prices by 10%, while an-
other adds only 5% on to the previous prices. T he first car dealer assumes
(wrongly) that sa les tax mu st be added to the previous pr ice an d the buy er
m ust a lw ays pay for i t . However, the second one p redicts ( r igh t ly) tha t de-
m and w il l be adversely affected by the pr ice increase and real izes that even
if
10% of the net price has to be given to the tax auth or i t ies , a par t of this sum
has to be absorbed by the se ller. (A sim ilar exam ple is e laborated in chap. 8).
A gain, there are tw o different w ays of unders tanding the same s i tua t ion and
hence tw o w ays of ac t ing , one of which i s mo re po w erful than the o ther .
Let us look a t some other exam ples th at i llustra te the thesis that po w erful
w a y s
o f
actin g derive from p o w e r fu l w a y s
o f
seeing.
L et us
take
a
very s im -
ple one to
begin w ith.
A
wo rd problem
w as
given
to
some 7-year-old ch i l-
dren. T he problem is as fo l low s: "I d idn ' t have m uch m oney th i s m orn ing
w hen I w ent to schoo l . B ob gave back 4 kronor th at he had borrow ed f rom
m e last w eek, and w ith that I cou ld buy a green chocolate bar for 7 kronor.
How m u c h m o n ey did I have th i s morn ing w hen I c a m e to school?
1 1
Some of the chi ldren knew the answer a lm ost ins tant ly , w hereas o thers
struggled in vain. W as there anyth ing tha t th e form er could do tha t the latter
could not? A ctual ly none of the chi ldren had ever seen a problem l ike th is ,
nor did they remem ber any addit ion tables . Those w ho d id not do too w el l
saw the problem as one of addi t ion ; the chi ld had some kronor to begin w i th
an d
then
he got 4
more , which made
7
al together .
B u t
w ha t then caused
these children diff iculty was the ques tion: How can you add w hen you do n ' t
k n ow w h a t
to add to? Th e
chi ldren
w ho did not f ind the
problem
di ff icul t a t
all said som ething like this
to
them se lves :
"I can sa y
tha t
he had 7
kronor
a l-
together and I know that he got 4 kronor from Bob. S o I have to take aw ay 4
kronor f rom 7 kronor."
They
cont inued , "One goes aw ay: 6 . Tw o goes away :
5. Three
goes
away : 4. A nd four goes a w a y : 3. So he had 3 kronor th i s mom -
ing." O thers m igh t have said, "I have to look for the o ther part . I hav e to f ind
out how
many kronor
I
have
to add to the 4
kronor
I got from
Bob ,
to get 7
kronor a l together . So the answer is 3 ." These chi ldren s ta rted w i th wh at they
had got , w hich w as 4, then they coun ted three un i ts , 5 , 6 , 7 , and visu al ize d
the "threeness" of those three u ni ts . Or others perhaps s im ply knew tha t 7
can, among other things, be broken down into 4 and 3. Th e chi ldren w ho
cou ld come up w ith the answer easi ly did not see the problem as an addit ion /
subtraction problem but as a
part-whole
problem: the who le and one of the
parts are given, the w h o l e is 7 and the given part is 4; the m iss ing par t m us t
then be 3. So the dif ferenc e between the chi ldren who han dled the prob lem
easi ly an d the others w ho did not was not so m uc h w ha t they did, bu t ra ther
w hat they saw, that is , how they understood the prob lem . The ch i ldren w ho
could solve the problem saw i t in term s o f par ts and w ho le , and therefore
could
solve
i t easily,
whereas
the children w ho could not solve the
problem
saw it in
term s
of the
ar i thmetic operat ion, that
is,
addi t ion ,
and
therefore
had diff icult ies
solving
i t . Th e
po int here
is
tha t ,
in
ma ny cases , see ing s im-
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T H E
S P A C E
O F L E A R N I N G
pie ar i thmet ic problem s
in
term s
of part-whole
relat ions
is a more
powerfu l
w ay
of seeing them than seeing them in terms of ari thmetic operat ions
(Neuman, 1987) as al ready shown. The
part-whole
way of seeing works
very wel l
for
an y
of the
p rob lem s
in
which
tw o
par ts
are
given
and you
have
to find the whole, or when the who le and one of the par ts are given and you
have
to
look
for the
other part .
For
example ,
a + b = _
a-b =
= c
a-_ = c
Seeing the prob lem as a
part-whole
relat ion en ables the ch ild to act in a
p o wer fu l w a y ,
in the
sense
o f
hav ing
a
capab i l i ty
to
deal wi th
dif ferent
prob l ems .
An other w el l-known
a nd
more complex exam ple
of how
"the ca pa bil i ty
of seeing" is of decisive im portance, is de Groot's (1965) wo rk on expertise
in
chess p lay ing .
"What
is it that chess m asters are esp ecial ly good at?" de
Groot asked, eag er
to
find
out
w hether
it is
true,
as
ma ny people bel ieve, that
w h a t
chess masters
a re
good
a t is
being able
to
m ental ly visual ize
and try out
a n u mb e r of al ternatives act ions (and their consequences) in great depth.
However ,
this
did no t in fact
turn
o ut to be the
case.
The
chess m asters
d id
not try
m ore al ternat ive courses
o f
a ct ion than other players ,
o r
follow them
up fo r longer. B ut the courses o f act ion they considered were m ost ly more
powerfu l w a y s
of
han dl ing
th e
si tuations than other cou rses
o f
ac t ion would
have
been .
S o ,
w h a t
was i t
that enabled
the
chess masters
to
find
m ore pow-
erful
w a y s
o f
handl ing
th e
si tuations?
T he
m ost striking
fact
w as
that chess
m as ters seemed
to see the
chessboard differently
to
other people:
We know
that
inc reas ing
ex p e r i en ce
and
k n o w l e d g e
in a spe cific
f ield ( che ss ,
for in-
s tance) has the
effect tha t
th ings (prope r t ies , e tc . ) which , a t
ear l ier
s tages , had to be ab-
stracted, or even inferred are apt to be immediately perceived at later stages. To a
ra the r
large
ex ten t ,
abs t rac t ion is replaced by percep t ion , but we do not k n o w m u c h
abou t how
th i s
w o r k s , n or w h e re the bord e r l ine l ies. As an effect of th is
r e p l a c e me n t ,
a
so-cal led
"given" problem s i tua t ion
is not
rea l ly g iven s ince
it is
seen
different ly
by an
expert than it is perce ived by an inexpe r i enced pe r son , (de Groot, 1965, p p . 33-34)
Al though de
Groot also found that chess masters were m uch bet ter
at re-
m em bering posi tions o n the
board
than n ovices, this w as only true w hen the
arrangements represented m eaning ful pat terns , and was not the case w hen
the
arrangements were random configurat ions .
In the
latter case,
the
chess
masters ' memories were
no t
significan tly better than that
o f
other people.
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8 M A R I O N , R U N E S S O N , T S U I
These findings were replicated by Chase and S imon (1 973) w ho by ex-
amining the w a y s in w hich chess m asters reconstructed c on f igu rat ion s that
they
had
br ief ly seen,
and the
errors that they m ade
in
doing
so ,
arrived
at the
interpretation that chess
masters
can
remember
a
great number
o f
pat terns
of about e ight pieces, and that they interpret every co nf ig ura t ion on the
board in terms of a t m ost seven or e ight such pat terns.
These
pat terns form a
kind of giga ntic a lphabet com prising up to 10,000 le t ters , each one corre-
sponding to a cer ta in pat tern (c i ted in Berei ter & S carda m elia , 1993).
T h e
m a in d i f f e r ence be tween chess mas te r s
an d
less exper ienced p la y-
ers, acc ord ing to th is line of reason ing, h as to do w i th the d i f fe ren ces in
w ays of see ing the chessbo ard , and d i f fe re nc es in w ay s of see ing var iou s
co n f ig u ra t i o n s a s
m e a n in g f u l
pa t te rns .
I t is the
chess m as te r 's
w a y o f
see-
ing that enables
the
p l a y e r
to
engage
in
p o w e r fu l w a y s
o f
ac t i n g .
A n d
there
are o ther s im i la r find ings on the na ture of exper t i se . Glaser and Chi (1988)
showed that exper ts
an d
nov ice s
di f fe r as to the
p r o b l e m s t h e y
see as
s i m i -
lar and
those problems they
see as
dif ferent . P h y s i c i s t s
a re
ab le ,
for in-
s tance , to see tha t the problems of r iver cur rents , and the problems of
h e a d w i n d s an d t a i l w i n d s in a i rp l a n e s i n v o l v e s i m i l a r m a t h e m a t i c a l an d
p h y s i c a l a s p e c ts , s u c h a s r e l a t i v e v e l o c i t i e s ( B r a n s f o r d , B r o w n . &
Cocking, 2000) . S imi la r f ind ings or ig ina te from such d ive r se f ields as
e lec t ronic c i rcui t ry (Eg an & Sch w ar tz , 1 979) , rad io lo gy (L esg old , 1988) ,
com pute r p rogram m ing (E hr l i ch & So loway , 1 984) and t each ing (Sabe r s .
C u s h m g ,
&
Ber l iner , 1991) .
Rela t ing
these cases, Bra nsfo rd
et al.
(2000) stated tha t exp ertise
in a do-
m a i n is characterized by sensi t ivi ty to pat terns o f mean in g f u l i n f o r m a t i o n
that m i g h t no t be avai lable to o thers dea l ing w i th th e same p rob lem s w i t h in
the same dom ains. In this book, w e w ou ld l ike to assert that var ious degrees
of expertise, that is, the capabi l i ty of ac t ing in p o w e r fu l w a y s
w i th i n
a cer-
tain
d o m a i n ,
is
re f lec ted
in the
var ious way s
o f
see ing , tha t
is, in the
var ious
meanings seen in a par t icular scenar io or problem.
T h u s i t can be seen th a t people act not in r e l a t i o n to s i t u a t i o n s a s s u c h ,
but in re la t ion to s i t u a t i o n s as they pe rce ive , expe r ience , an d u n d e r s t a n d
them. O ne o f the m os t f r e que n t ly r ecur r ing f ind ings
f rom
our own r e -
search , as w el l as f rom oth ers ' r esearch , i s tha t w ha teve r s i tu a t io n peop le
enco unte r , they see i t , exp e r ience i t , and u n d e r s t a n d it in a l im i te d n u m b e r
of
qua l i t a t ive ly dif ferent
w ays (see M ar ton & Booth , 1997) . In r e l a t ion to
par t icu la r a im s,
some
w ays o f see ing a r e more po w er fu l than o the r s . Pow-
e'rful w a y s o f a c t ing der ive from p o w e r f u l w a y s o f see ing , and the way t h a t
s o m e t h i n g is seen o r exper ienced is a f u n d a m e n t a l
f ea ture
o f l e a r n i n g . If
w e w ant lea rners to deve lop cer ta in capa bi l i t ie s , w e m us t m ake i t po ss ib le
for them to deve lop a ce r ta in way of see ing or exper ienc ing . Conse-
quent ly , a r ranging for lea rn ing imp l ies a r ranging for deve lopin g
learners'
w a y s
o f
seeing
o r
exper ienc ing , tha t
i s ,
deve lop ing
th e
e y e s t h r o u g h w h i c h
the world is perceived.
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T H E S P A C E O F L E A R N I N G
WAYS OF S E E I N G
Wh a t
does it
take
to
develop
the learner's
eyes? W hat
is
meant
by "a way of
seeing something?" Whatever we at tend to is inexhaustible, in the sense
tha t
the
inform at ion that
can in
principle
be
gained
from it is
un l im i ted.
A t
the sam e t ime , as George M iller so aptly declared, a lm ost 50 years a go, our
capac i ty for process ing inform at ion i s seriously l imited (M iller, 1 956). T he
inevitable mechanism
o f
selectivity
originates
from
the
co ntradiction
be-
tween un l im i ted in form at ion
and the
highly l imi ted capaci ty
fo r
process ing
this
in format ion wi th w hich hum ans are equipped.
W henever people at tend
to
something, they discern certain aspe cts
of it,
and by doing so pay more at tention to some things, and less at tention or
none
at all to
other things.
If one
person discerns certain aspects
of
something
and
another person
discerns par t ly o r wh ol ly different aspects, we say that the two people see
the sam e thing in different w a y s . So, a way of seeing something can be de-
f ined in
t e rm s
of the
aspects that
are
discerned
at a
certain point
in
t im e.
T he
aspects
are
thus discerned (and
attended to) at the same
t im e rather than
o ne
at a t im e . A par t icular way o f seeing something can be
defined
by the as-
pects discerned, that
is, the
cri t ical features
of
w h a t
is
seen.
A n aspect of a thing co rresponds to the way in w hich that th ing m ight di f-
fer from, or be
s imi lar
to, an y
other thing, that
is, the w ay it is
perceived
to
be, or the w ay that it is experienced by someone as different from, or similar
to
som ething else. Th e problem cited previously (a bou t the child with 7 kro-
nor)
w as
unders tood,
o r
exp erienced,
by
som e chi ldren
in
te rm s
o f its part-
w h o l e
s t ructure. Some chi ldren not iced that it had the s ame who le in it
( i .e. ,
7)
as
some other problem they
had
experienced,
and in
that respect
it
d i f -
fered from
problems
in
which
th e
whole
w as
other than
7.
Furthermore,
am ong those problems
in
wh ich
the
w ho le
w as 7, i t w as
s im i lar
to
those
in
w h i c h one of the parts was 4 and different from those problems in w hich
no ne o f the parts w as 4. Seeing the problem in terms o f its
part-whole
struc-
ture mea ns, we bel ieve, seeing w hat the par ts a nd the who le
a re
and wha t
they
are
not .
However, other children understood
the
same problem
in
terms
of the
ari thm etic operation involved. They tho ugh t
i t w as
similar
to
other addit ion
prob lems , and that i t differed from problems about subtract ion. A m ong ad-
dition
prob lems ,
i t w as
similar
to
those
in
wh ich
the
second addend
w as 4,
and different
from
those
in
w hich this
w as not the
case. They probably also
t hough t
tha t i t was similar to those addit ions in w h i c h the s um is 7, and di f-
ferent f rom those in w hich this wa s not the case. Seeing the problem in terms
of the
ari thm etic operat ion involved required
a
thou gh t process l ike this ,
w e
bel ieve.
The reason that som e children c ould solve the problem and others
could not was because they saw the same problem in different ways, that is,
because they at tended
to
different aspects . At tending
to a
certain aspect
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J _0 M A R T O N , R U N E S S O N , T S U I
means compar ing something
w e
exper ience w i th o ther th ing s tha t
w e
have
experienced earl ier . Th e kin ds of thin gs broug ht into the comparison
def ine
the aspect that is attended to .
In
Lo and Ko
(2002),
the
Engl ish
lessons
of two primary
Grade
4
c lasses a re d iscussed . Eviden ce f rom the lea rn ing outcom es sug ges ts tha t
m ost chi ldren in one o f the classes un de r s tood the "s" at the end of verbs a s
s igna l ing th i rd person s ingu la r , tha t
is ,
that they "saw"
the "s" in
th is par -
t icu la r way. Th i s imp l ies ,
w e
be l ieve , tha t they m ade
an
im pl ic i t compar i-
son
o f verbs where "s" was present wi th th e same verb where " s" was
absent . In the o ther c lass , most c h i ldren d id not seem to pay a t te n t io n to the
"s." They compared, w e th ink , im pl i c i t ly , the verbs w i th o ther verbs . T he
"s" ha s to do
w i th
the
third
person
s ingu la r , t ha t
is , i t ha s to do
w i t h g r am -
m ar ; wh e reas the com par i son w i th o the r ve rbs—or o the r w ords— has to
do wi th the me aning . The m ajo r i ty of the ch i ldren in the fi r s t c lass seemed
to
attend
to
both
th e
g r a m m a t i c a l
and the
mean ing a spec t s
of the
verbs,
w hereas m ost ch i ldren in the second c lass d id not seem to a t tend to the
grammat ica l aspec t o f these verbs.
A ccording to this l ine of reason ing, a way o f seeing can be ch aracter ized
in terms of the aspects
discerned
that are attended to s imultaneously. This
defini t ion is very w ide and very narrow at the same t im e . It is very w ide be-
cause it refers to the m e a n i n g o r appearance o f a l m o s t a n y t h i n g . A nd it is
very narrow because
it
s imply a im s
a t
te l l in g apar t
d i f ferent
w a y s
o f
seeing
in respects th at a re cr i t ica l in re la t ion to the eff ic iency of the ac ts tha t spnng
from
those ways of seeing, those meanings, and those appearances.
D I S C E R N M E N T
In order
to see som ething in a cer ta in w ay, a person m us t discern ce r ta in fea-
tures of that thing. We should a lso be c lear about the
dif ference
between
discerning and be ing to ld . M edica l s tudents , for ins tance , m ig ht be advised
by
the ir professors
to try to
not ice dif ferent fea tures
o f
the i r pa t ien ts , such
as
the color of the l ips , the m oisture of the skin, the ease of breath ing , and so
on ; th is is be ing to ld . But in order to fol low th is advice , the s tuden t s m us t
experience those features, and the only w ay to
exper ience
them is to
expe ri-
ence ho w they can vary. N otic in g the color of a pa t ie nt 's l ips , for exa m ple ,
w o u l d
no t
mean ve ry m uch
if lip
color
wa s the
same
fo r
everyone.
Simi lar ly , / rawe
o f
reference
in
phys ics only mak es sense
i f we can
t h i n k
of more than on e f ram e of r eference . Even very abstract not io ns der ive the ir
m eanin g ( in the sense of the exper ience of und ersta nd ing ) throu gh var ia-
t ion. H istor ical ly, no one was aware o f na tu ra l num ber s , fo r ins t ance ,
unt i l
the re w ere o ther num bers such as nega t ive num bers . At tha t poin t , the na tu -
ra l num bers cou ld be ident i f ied as those tha t were not nega t ive num bers .
This
is wh y in a sense we of ten know very l i t t le abo ut our ow n coun try
un t i l
w e
leam about other countr ies .
A nd
th i s
i s why
teachers gene ra l ly g ive
a
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1 . THE SPACE OF L E A R N I N G 1J_
number
of different
exam ples
in
order
to
explain
a new
concept
o r
principle.
If
teach ers give one exam ple only, they do so because they them selves con -
sider the other alternatives to be obvious (which, however, they m ay not be
fo r
the students). In order to explain w hat a frame o f reference is , i t is not
suff icient
to
point
out
that when
w e
consider
a
moving body
in the sk y from
the point of view of the ground, w e con sider i t from a part icular fram e of ref-
erence . W e also have to give other exam ples, su ch as considering i t from the
poin t of view of another body m oving in the sky in paral lel with the
first
one
and at the same velocity.
B y experiencing variat ion, people discern certain aspects
of
their envi-
ronmen t ;
w e
could perhaps
say
that they become "sensitized"
to
those
as-
pects . This m eans that they
are
likely
to see
future
events
in
term s
of
those
aspects; the phy sician w il l pay at tention to the c olor of the pa tient 's l ips, the
phys ic i s t w il l pay at tention to the fram e of reference
from
w hich a body in
mo ve me n t
is
co nsidered. This
is
w h a t
w e
me a n
by
learning
to see
certain
th ings in
cer tain w ays.
O ne
m ain
way of
dealing w ith novel si tuations
is to
m ake u se of previou s expe rience. It is im portant to develop the ca pa bil i ty
for profess ional se e ing , that
is,
seeing si tuations
in
term s
of
features that
are
general ly cri t ical w ithin
one 's
professiona l f ield. But i t is equa lly imp ortant
to be able to discern o ther featu res that are not cri t ical in a gen eral sense, but
that
m ay be
cri t ical
in a
specific case.
N ot
only
do you
need
to
discern fea -
tures that have proved to be e ssential in the past , but you m ust be a ble to dis-
cern new fea tures when they are cri t ical . This is in fact very central in
research
an d it is
very m uch
how new
discoveries
a re
m a de.
Bu t we
should
rem em ber tha t even the discernm ent of enti rely new features depends on the
varia tion yo u h ave enc oun tered earl ier .
The w ord "fea ture" has been used to stand for at tribute, or aspect , such as
color of l ips, f rame of
reference,
tal lness, and so on, and we ha ve pointed to
the
fact
that human beings cannot discern
a
feature wi tho ut experiencing
variation
in a
corresponding dim ension. How ever,
we no t
only discern fea -
tures,
bu t a lso discern different qu ali t ies ( i .e. , values ) in the relevant dim en-
sions such a s "blue," "ray of light," "very short," and so on.
D i s c e r n m e n t a n d Context: Parts an d W h o l e s
So far we ha ve talked about the di scernment o f features and values
wi th in
features.
Bu t i t i s a lso poss ib le to th ink abo ut discernm ent as a del im i tat ion
of wholes
from
thei r context and as a del imi tat ion of par ts w i thin wholes
(cf . Svensson, 1976).
Mar ton
and B ooth (1 997) gave an example:
W h a t
does i t take to see a mo t ion l e s s de e r a mong the dark t rees a n d b ushe s of the
n i gh t
w oods?
To see i t at all we
have
to
d isce rn
it f rom the
su r r oun d ing t re e s
a nd
b ushe s ,
w e
have to see i ts
c o n t o u r s ,
it s ou t l i ne , the l imi t s tha t d i s t i ngu i sh it from
w h a t s u r r o u n d s
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\2 M A R T O N , R U N E S S O N , T S U I
it.
W e have t o see, a t least par t ia l ly , w h e r e i t s tar ts and w h e r e i t e nds . .. [ b u t ] no t o n l y
do we have to d isce rn i t from i ts
c on t e x t ,
a s a de e r in the woods , bu t we a l so have to d i s -
cern i ts par ts , the way t h ey
re la te
to each o ther , and the way t hey r e l a t e to the
w h o l e .
There fore , on s e e ing the de e r in the w oods , in s e e i n g its co n t o u r s , w e a l so s ee pa r t s o f
i ts body, i ts he a d , i ts a n t l e r s , i t s forequ ar ters , an d so on, and t h e i r r e l a t i o n s h i p i n t e r ms
of s tance , (pp. 86-87)
Discern ing the re la t ion of par ts w i th in wh oles and d iscern ing the wh ole
from the con tex t is an im por tan t aspect o f d i sce r nm en t . Eq ua l ly impo r tan t is
discern ing the w ay w holes r e la te to the con tex t . Th is i s because the way the
w hole relates to the con text shapes the d iscern m ent of the par ts
w i t h in
the
wh ole . W hat does th i s m ean? Le t us take some classroom data as exam ples.
Let us star t with th e role that context p lays in d e t e r min ing t he m e a n i n g
assigned
to a
p h e n o m e n o n .
In a
pr imary Chinese lesson
on
s e m a n t ic s ,
wh ich is d iscussed in chap te r 2, we see how one w ord took on a very
differ-
en t
mean ing when
i t w as put in di f fe rent
con tex t s .
In
th is lesson,
the
teacher
told a story about how one w ord in Chinese y ao (P u to ng hu a) [ -f|- ] (w hich
can be
translated l i terally
a s
"wan t")
w as
explo i ted
by a
barber, Afa n t i ,
to
carry the d iametr ical ly
opposed
m e a n i n g s , "give"
(gei)
( P u t o n g h u a )
[$&]
and
"keep"
(liu) ( P u t o n g h u a ) [^] in order to take his r ev enge on a cus tomer .
A h u n g , w ho kept
r e fus ing
to pay for the service. In the story, the barber
asked Ahu ng wh ether he
"w an ted" (yao buyao
(P u to ng hu a) [ - f c^ -l c - ]) h i s
eyebrows , w hereupon A hu ng rep l ied tha t
h e
"w an ted"
h is
eyebrows (yao),
m eaning he wanted to keep h is eyebrows .
A f a n t i
shaved of f A hu ng ' s eye-
b ro ws
and said, "You 'w an t '
(yao)
your eyebrows , so I ' l l g ive them to yo u "
Ahung was speech less because he had indeed sa id yao . Af te r th i s , A f a n t i
asked
Ahung i f he
"wan ted"
h i s beard , and Ahung, who had a b e a u t i f u l
beard , immediately said ,
buyao
( P u t o n g h u a ) [^ - fc ] , tha t
is ,
"don ' t want ,"
mean ing he did not w a n t
Afa n t i
to shave off his beard . However ,
Afan t i
shaved off his beard all the s ame . Aga in , A hu ng was speech less because he
h ad indeed said buyao
("don't
want") .
In
th is story,
we see
tha t
the
wordjao
w as
ass igned di f fe rent m e a n i n g s
in
relation to d i f ferent contexts . In the first in s t ance , A hun g r e l a ted it to the
context o f a
barbershop
where people had the ir hair and beard tr im m ed o r
cut , but wou ld n o t typica l ly have their eyebrows shaved off . Let us r efer to
this context as Contex t A . Therefore, when he said yao, he m ean t tha t he
wanted to
keep
his eyebrows. However,
Afa n t i
del ibera tely relate d i t to a
different
context where "wan t"
(yao)
can mean "give " Let us r efer to th i s
contex t as Contex t B . For exam ple , in the con tex t o f m ak ing an offer, such as
offer ing a dr ink, "Do you wa nt a
dr ink?"
a pos i t ive rep ly from the addressee,
yao,
wo uld entai l the person m ak ing the
offer
ac tua l ly
g iv ing
a drink to the
addressee . Then, in the second ins tance , when Ah ung used buyao to m e a n
that h e "did no t w a n t" h is beard, h e w a s relat ing y ao to the con tex t in w h i c h
Afan t i
w as operating in the previous exchange w here ya o m e a n t
"give,"
tha t
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1. T H E S P A C E O F
L E A R N I N G
1 J3
is C ontext B. However, A fanti
deliberately
related buyao ("don't
want")
to
the context in which A hung w as op era ting previous ly , w here y a o m e a n t
"want" or "keep,"
that
is
C ontext
A .
T he
story
in
this lesson sugg ests that
the
context
to
which som ething
is
related
cannot necessari ly
be
taken
for
granted.
In
c lassroom learning s i tua-
tions,
it is
very important that there
is a
m utua l unders tanding (be tween
teacher and students) of the context to w h i ch the teacher re la tes the
object
o f
learning in
order
to
help learners discern
its
cri t ical
features .
Let
u s
look
at tw o
lessons
on
w riting
a book
report,
for
example, also
re-
ported by Ch ik (2002). In one lesson, the teacher (T eacher A ) used genres o f
w ri ting as the
context
for
discussing
the
com ponen ts that s tudents should
include in a
book report.
She
sp ecifically used na rrative
as a
genre
of w ri ting
and
asked the s tudents to th ink abo ut th e features that dis t ing uish a book r e-
port
from a
narrative.
In the
other lesson ,
the
teacher (Teacher
B )
used
a
dif-
ferent
context
for
discussing
a
book report , that
is,
different w a y s
o f
present ing a book report .
Specifically,
she cited the use of pic tures to pres-
ent a
book report,
a
format with which students were also familiar.
Wh i c h
is a more
power fu l
context , in the sense of be ing more
effective
in
bringing about learning? W hich w il l help learners discern
the
cr i t ical f ea -
tures of a book
report?
T he
answer
to
this question depends
o n the
aspects
of the
book report
o n
w hich the teacher wants to focus. In these tw o lessons, the ob jec t of learning
is the
essentia l comp onents
of a
book report.
O ne
could argue that pic toria l
representat ion
is one kind of
form at
and that i t can be con trasted w ith a w rit -
ten format .
B u t
there
i s
noth ing m uch tha t
can be
said apart
from
this ,
and it
does
no t
help
the
s tudents
to
discern
the
com ponen t s t ha t
are
cri t ica l
to a
book report .
O n the
o ther hand, other genres
o f
w ri ting , such
a s
narra t ives,
contain various components such as time, p lace, people, and sequence of
events
tha t
are not
found
in
book reports . What dis t inguishes
one
genre
o f
wri t ing
from
another
is the
com ponents tha t they conta in .
In
o ther w ords ,
the g e n re s
o f
wri t ing, o f wh ich book reports are one instantiation and narra-
tives
another, provides
the
context
to
w h i ch
the
cri t ica l
features o f
book
re-
ports re la te .
Let us look a t how Teacher A dealt with th e com ponents cr i t ica l to a book
report . Sh e put e ight com ponents that w ere re la ted to books on the board.
They were: price
of the book,
date
of
reading, genre, call number, author,
n a m e
of the
book, summ ary,
and
com m entary ( impression
af ter
reading) .
Am o n g th e m ,
the first
four, a l though having
to do
w i th books , were
no t
rele-
vant
to book reports. The
teacher asked
the
students
to
take away those com -
pon ents that they felt should not be included in a book report. B y asking th e
students to do that , the teacher w as doing two things. Firs t , she was a t tend-
ing to the
internal relationsh ip,
a part-whole
relationship, betw een
the
c o m -
pon ents and the book report . T he com ponen ts that rem ained on the board
were author , name
of the
book, commentary,
and
summary. These
four
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J _4 M A R T O N , R U N E S S O N , T S U I
com ponents w ere related
to
each other
in the
sense th at they were co nsti tu-
tive
of a book report in such a way that if any part w as m iss ing, i t w ould no
longer be a book report . F or exam ple, if the comm entary w as m issing , the
book
report
w ould becom e a piece of text in an annotated bibl iography . Sec-
ond, she was at tending to the wa y in w hich the inclus ion of par ts that w ere
not
critical
to a
book report wou ld affect
the
who le .
F or
example ,
the
inc lu-
s ion of the pr ice of the book and the pub l isher wou ld const itu te a wh ole that
is
no
longer
a
book report,
bu t
another genre,
for
example ,
an
advert isem ent .
T he
discernmen t
of the
cr i tical com pone nts
o f a
book report
w as
b rough t
about
b y
discerning
the
book report
as an
ins tant iat ion
o f
genres
of
w ri ting.
In other words,
ge nr e s o f wri t ing
w as the con text to wh ich the book report
w as related. It is in relat io n to the book report a s a genre, as opposed to other
genres such
as the
n arra t ive , tha t discernmen t
of the
parts
w as
made poss i-
ble . In other w ords, i t i s the discernm ent of how the wh ole relates to the con-
text that enabled the discernm ent of the par ts (of the w ho le) .
VARIATION
W e i l lus t ra te the s i gn i f i cance of var ia t ion for the poss ib i l i t ies to learn by
referr ing to some s i tua t ions tha t w i l l
hope f u l l y
be eas i ly recognizab le to
the reader .
Con sider h ow w e leam w hat coldness, ta l lness , or heaviness i s . Sa ying
that
som ething is heavy does not mean an ything to us unless we experience
this agains t the background o f a difference in w e igh t , t ha t is, w e igh t t ha t can
vary.
In the
same w ay,
for
i n st ance , know ing wha t
red is
presupposes
the ex-
perience of other colors , that is , a var iat ion in colors . Even k now ing w hat
color i s presupposes an experienced variation of colors . Im ag ine for a mo-
m ent that there w as no variation of colors , tha t everything a round u s had the
same color. I t w ou ld be impo ssible for us to know w ha t red, green, or yel low
w ere, ju s t as i t wo uld be imp ossible for us to discern co lor as a feature. I f ev-
ery
object
w e
encountered
had the
same color, this
feature of the
object
w o u l d
not be discerned.
T he
s ign i f i cance
of
variat ion
for
seeing so m ething
in a new way
app l ies
to abstract objects as w el l . Research on the w ay that young chi ldren solve
simple ar i thmet ic problems has reported that chi ldren who always solve
simple addit ions ( l ike
2 + 3 =, 5 + 1 =, 1 + 4 =,
etc.)
by
start ing w ith
the first
addend, can suddenly chang e s trategy and s tar t w i th the b iggest num ber. In-
stead of 2 + 3, 1 +4 and so on, the order of the addends is chan ged , and the
child adds 3 + 2 =, 4 + 1 = (cf. Carpe nter & M oser, 1984). In this si tuation, a
variat ion of order of the addends is open ed. Y ou co uld say that an aspect that
was taken for granted or was undiscerned became a discerned aspect . By
this opening
of variat ion, a fea ture of addit ion (that is , that the sum is inde-
pendent of order of the addends) is discerned.
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1 .
THE
S P A C E
OF L E A R N I N G 1 _5
O ne o f the m ain these s in th is book is that the pa t tern of var iat ion inher-
ent
in the
learning situation
is
fundamenta l
to the
developm ent
of
certain
capab i l i ti es ( see fo l low ing tex t ) . A n exper im enta l s tudy on mo tor l earn ing
(Moxley, 1979) demonstrated
the
importance
of
variation
on
l earn ing .
The exper im ent inc luded ch i ldren prac t i c ing to h i t a t a rge t w i th a ba l l .
C hi ldren in the control group alw ays threw the bal l a t the target from the
same di rec t ion , whereas ch i ldren in the exper imenta l g roup prac t i ced
throwing
the
bal l
a t the
t a rge t f rom di f ferent d i r ec t i ons . When
the two
groups were compared t rying to hi t the target
from
a di rect ion that was
new to
both groups ,
the
group tha t
had
prac t iced h i t ting
th e
target from d i f -
ferent di rect ions w as then
found
to be superior to the group tha t h ad p rac -
t iced hi t t ing the target
from
the same direct ion al l the t ime. I t can be
con cluded that var iation
in
direction seemed
to be a
cri t ical feature
of the
pract ice and thus also cr i t ical for learning. However , we are not arguing
for variation in general , and we are not saying that the more variation there
is , the bet ter the poss ib i l i t ies to learn. W hat w e bel ieve is tha t var iat ion en-
ables learners
to
experience
the
features that
a re
critical
for a
part icular
learning as wel l as for the development of cer tain capabi l i t ies . In other
w ords, these fea tures m us t be experienced as dimensions o f variat ion.
Lea rn ing ,
fo r
i n s t ance ,
to
solve
a
prob lem
in
d i f ferent w ays requi res expe-
r ience
o f
variat ion
in
solving s t rategies . U nde rs tanding
the
"manyness"
of
a
num ber requi res the exper ience of
d i f ferent
num bers , ju s t as the ab i li ty
to
throw
a
bal l from
dif ferent
di rec t ions
and
still
hit a
target requires
the
exper ience o f th row ing an ob jec t from
different
ang l es , and rea l iz ing h ow
a
genera l p r inc ip le can encom pass
d i f ferent
exam ples requ i res the exper i-
ence of at leas t tw o
d i f ferent
examples , and so on .
In m a them at ic s , different strategies for solving problem s, different n u m -
bers,
and so on all
m a ke
up
dim ensions
of
variation.
O ne
particular solving
strategy is one
va lue
in a
dimension
of
variat ion, w hereas
a
different
strat-
egy is another value in this dim ension. And thus the strategy as used in a spe-
cif ic example i s an ins tance of tha t s t ra tegy . When we exper ience
something, we discern aspects, or features, of the object and we experience
values in the corresponding dimensions of var iat ion. The experienced as-
pects
are
discerned
as
values
in dimensions of
variation.
I
experience
the ob-
ject on my table , for example, as a b lue, cyl indrical , ceramic mug with a
handle (an instance).
"Blue"
a nd "cylindrical" are values in dimens ions of
variat ion (e.g. , these are perceived in relat ion to the experience that they can
vary).
Features of the m ug , such as the color, shap e, ma terial , and so on, are
sim ultaneo usly discern ed as a pattern of dim ensions of variat ion (or to put i t
s imply, as a pattern of variat ion), and these featu res consti tute the pa rt icular
object .
In
order
to
experience
the
object
as a
blue, cylindrical , ceramic m ug ,
all of these aspects m us t be discerned and related to potential dim ensions of
variation.
A nd because these aspects are necessary for defining th e object in
quest ion, they
are
also cal led
its
cr it ica l fea tures .
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M A R T O N , R U N E S S O N , T S U I
Patterns of Variation
A ccording to the preceding l ine of reasoning, i t i s necessary to pay close at -
tent ion
to
w h a t
varies
a nd
w h a t
is
invariant
in a
learning s i tuat ion,
in
order
to
understand wh at
it is
possible
to
leam
in
that si tuation
and
w ha t no t .
In
the different studies reported in th is book, w e are able to
ident i fy
certain
patterns
of
vanat ion :
1
. Con tras t. A s al ready m ent ioned, in order to experience som ething, a
person must experience something else
to
com pare
it
w i t h .
In
order
to un-
derstand wha t "three" is , for ins tance, a person m us t experience som ething
t ha t
is not
three: "two"
or
"four,"
for
exam ple . This i l lus t ra tes
h o w a
value
(three,
fo r
ins tance )
is
experienced wi thin
a
cer ta in dim ens ion
of
vanat ion ,
w h i c h
corresponds
to an
aspect (nu m erios i ty
or
"manyness") .
2.
General iza t ion. In order to fu l ly under s tand wh a t
"three"
is, w e m u s t
also experience varying appearances
of "three," for
exam ple th ree apples ,
three monkeys, three
toy
cars, three books,
and so on.
This vanat ion
is
nec-
essary in order for us to be able to grasp the ide a of "threeness" and separate
it
from i r relevant features (suc h
as the
color
o f
apples
or the
very
fact tha t
they
are apples) .
3.
Separat ion .
In
order
to
expenence
a
certain aspect
of
s o m e t h in g ,
and
in
order
to
separate th is aspect
from
other aspects ,
it
m us t vary w hi le o ther
aspects rem ain invariant . This
i s how the "angle"
aspect
o f
h i t t ing
a
target
wi th a bal l w as developed in one group o f ch i ldren in M ox ley ' s (1979) ex-
periment , m ent ioned previously .
The
expenm ent co uld a l so
be
expanded
by
sys temat ica l ly
varying
the
di s tance
to the
t a rge t ,
fo r
ins tance , w hi le o ther
aspects were kept invariant; then sy stem at ica l ly vary ing the w e i g h t of the
bal l ,
w hi le keeping other aspects invariant ,
and so on . In
th is
way the
ch i l -
dren could
be
prepared
fo r
various other s i tuat ions , such
as
hi t t ing
targets
from dis tances they have never thrown f rom, w i t h ba l l s
o f
vary ing (and
novel ) weigh ts ,
and so on.
4.
Fusion.
If
there
a re
severa l c r i t i ca l a spec t s t ha t
th e
learner
has to
take in to con s idera t ion
a t the
s a me t i me , t h e y m u s t
a l l be
exper i enced
s i-
m u l t a n e o u s l y . I n
eve ryday
l i f e , i t is
s e ldom tha t on ly
o n e
a spec t
o f
some-
th ing va r ie s a t a t ime , and so t he way i n w h ic h we re spond to a s i t ua t i o n ,
such
a s
h i t t i n g
a
t a rge t w i th
a
ba l l
o r a
p rob l em
o f
h u m a n re l a t i o n s , sp r in g
f rom
a
more
genera l ho l i s t i c perce p t ion
of the
s i t u a t i o n .
W e c a n
c o m p a re
t h i s
w i th a m ar r i age cou nse lo r ' s p ro fes s iona l w ay o f s ee ing hu m an re l a -
t i onsh ip p rob l ems . The counse lo r i s p robab ly s ee ing d i f f e r en t cases in
terms
o f a l i m i t e d n u m b e r o f a n a l y t i c a l l y s e p a ra t ed , b u t s t i l l s i m u l t a -
neous ly exper ienced, aspec t s .
O u r
c o n j e c t u r e
is
tha t see ing
a
cer ta in
c l a ss o f phen om ena i n t e rm s o f a s e t o f a spec t s tha t a re an a ly t i ca l l y s epa-
ra ted b u t s i m u l t a n e o u s l y e x p e r ie n c e d p r o v i de s a mo r e ef fec t ive bas i s fo r
p o w e r f u l
ac t i on t han
a
g l o b a l , und i f f e r e n t i a t e d
w a y o f
s ee ing
th e
s a m e
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1 .
THE SPAC E O F L E A R N I N G T 7
c lass
o f
p h e n o m e n a .
W e
bel ieve th at sep arat ing
th e
aspec t s
f i rs t and
then
fus ing them
together is
more ef f i c ien t ( f rom
th e
view
o f
being able
to
adap t to chan ging condi t ions ) than never t ak ing th e cr i t ica l aspec t s apa r t .
W e also bel ieve that th is
fus ion
wi l l unavoidab ly t ake p lace th rough th e
s i m u l t a n e o u s
var ia t ion in the d imens ions o f var ia tion cor responding to
th e
cr i ti ca l aspec t s .
A nother exa m ple of th is type of
fusion
is presen ted in the com parison of
tw o
primary classes
in
Chinese languag e
in
chapter
4,
whereby different
as-
pects of the same word ( form, meaning , p ronuncia t ion) are successful ly
fused in one of the
classes,
but not in the
other.
In
chapter
8,
there
is a further
example of this type, in the comparison of two groups of secondary eco-
nomics classes .
In
this exam ple,
the
elasticity
o f
demand
and the
elasticity
of
sup ply are f irst separated and then
fused
in the classes in one group ("the
learning study" group),
but not in the
other group ("the lesson study"
group), in w hich they are only deal t w i th one at a t ime .
S I M U L T A N E I T Y AN D AWARENESS
W e
have thus m ade
the
point that
in
order
to
discern
a
feature,
a
person m us t
experience variation
in
tha t
feature .
For
example ,
in
order
to
experience
a
teenage girl as strikingly tall , w e must have encountered teenage girls as
typ ica l ly
being sho rter
or
considerably shorter than this pa rt icula r girl .
The
experience of tal lness derives
from
jux tapos ing w hat we see and w hat we
remem ber ; wha t we exper ience now and w hat we have experienced befo re .
W e
have
to be
aware
of
both
at the
same t ime.
In
general ,
to
experience variation am oun ts
to
experiencing different
in -
stances at the sam e t im e. A part icular co lor is experienced aga inst the bac k-
groun d of other colors tha t w ere experienced in the past; an act of kindn ess
is
experienced against
the
background
o f
acts
o f
kindness
o r
cruelty that
w ere experienced in the past . V ariat ion is experienced very m uc h as we ex-
perience
a
m elody. Each tune
is
experienced
in the
context
of
other tun es.
O f
course ,
we w ou ld never experience a m elody i f w e experienced each tone
separately, one at a t im e. In the sam e w ay, w e can never exp erience variat ion
in
any respect i f w e expe rience every instance one at a t im e. In order to exp e-
rience variat ion
in a
certain respe ct ,
w e
have
to
experience
the
different
in-
stances that vary
in
that respect s imul taneously , that
is , we
have
to
experience instances that
w e
have encountered
a t different
points
in
t im e,
at
the s a m e
time. W e call th is
diachronic
s imul tanei ty . This i s the s im ul taneou s
experience of different ins tances at the same t ime, which is necessary for
experiencing variat ion in a certain dim ension and for discerning the aspect
of an
instance
corresponding to the
dimension. How ever,
you
wi l l remem -
ber
that
w e
have previously defined
a way o f
seeing som ething
as the
dis-
cernment of var ious cr i t ical features of an ins tance s imul taneously . This
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j_8
M A R T O N , R U N E S S O N , T S U I
type of s im ul tanei ty , is cal led
synchronic s imul tane i ty ,
and is the experience
of different co-exist ing aspects of the same thing at the same t ime.
Let us br ief ly return to M oxley 's s tudy of chi ldren p ract icing to hit a tar-
get with a ball . In the ci ted exam ple, variat ion in the direction or an gle of the
throwing w as com pared to the absence of var iation, in relat ion to a group 's
abili ty
to
per form
the
task
o f
hi t t ing
the
target
f rom a
direct ion that
was new
to both groups . A s we m ent ioned, i f the chi ldren were to leam to hit a target
wi th a ny bal l , f rom any di rect ion, unde r any c ondi t ions , they w ould need to
pract ice throw ing the bal l f rom different di rect ions , w i th
different
ba l ls (e .g .
each one a different w eigh t ) , under different con di t ions (e .g ., different w i n d
force) . M as ter ing th is capab i li ty w ould am ount to be ing ab le to discern a ll
o f
those features
and
being able
to
take them
a ll
in to considerat ion
at the
same t im e ( i .e . , seeing bal l -throw ing s i tua t ions
in
t e rm s
o f
features cr i t ical
for hi t t ing a target ) . Doing so amoun t s to exper iencing th e different aspects
present at the same t ime s im ul taneous ly . In a m etaphor ica l sense , w e could
ta lk abo ut spat ial in tegrat ion o r synchronic s imul tane i ty a t one par t i cu lar
point in t ime.
W hat does
it
take
to
experience
different
aspects
o f the
s ame p h e n o me -
non? C lear ly , the aspects m ust be discerned and the person m ust be focal ly
aware o f t h em . So s imu l tanei ty in the synch ronic sense is obvious ly a func-
t ion
of
di scernm ent .
Ex per i enc ing va r i a t i on i s , however , a s w e have show n , con t i ng en t on
th e
s i mu l ta n e o u s a w a r e n e s s
o f
i n s t ances t ha t appea r
a t d i f fe ren t
p o i n t s
in
t im e . W e w ou ld no t be ab l e to s ee a s t ory a s a s to ry w i tho u t t he s im u l t a -
neous awareness o f o ther s to r ies tha t we have come across in the pas t .
T h i s is a k i n d o f t e mp o r a l i n t e g r a t i o n , a s i m u l t a n e o u s a w a r e n e s s o f w h a t
w e a re exper i enc ing and wh a t w e have exper i enced be fo re . C l ea r ly , a s
w e l l ,
i n w h a t w e a r e e x p e r i e n c i n g , w h a t w e h a ve e x p e r i e n c e d b e f o r e
m u s t be or m u s t h a ve
been
d i s ce rned in order for us to e x p e r i e n c e it . In
th i s r e spec t , no t on ly synch ron i c bu t a l so d i ach ron i c s i m u l t a n e i t y is a
fu n c t i o n
o f d i s ce rnmen t . Fu r the rmore , t he re can be no exper i ence o f
s y n c h ro n i c s i m u l t a n e i t y w i t h o u t
th e
e x p e r ie n c e
o f
d i a c h r o n i c s i m u l t a -
ne i ty ,
b e c a u s e
in order to
exper i ence
tw o
aspec t s
of the
s a me t h i n g
to -
ge the r we mus t d i s ce rn bo th s epa ra t e ly , and t h a t c a n o n l y h a p p e n b y
h a v i n g exper ienced va r i a t i on i n t he d im ens ions o f va r i a t i o n co r respond-
in g
to
e a c h
one of the
a spec t s .
There
is another
form
o f the s im ul taneo us expenenc e in the synchronic
sense, tha t is, one t ha t is different from exper iencing different aspects o f the
same th ing at the s ame t im e . W ha t w e have in m in d is the s im u l taneous ex-
perience of the w hole and i ts par ts ; the wh ole be ing, for exa m ple, a deer in
the
fores t (m ent ioned previously) ,
a
text
w e
read
in
school,
o r
bas ica l ly any-
th ing that can be m ea ning ful ly divided into com ponen t par ts .
In an example tha t appears in chapter 4, tw o teac hers ' w ays of teach ing
Chinese a re com pared. B oth teach ers w ere try ing to develop t h e s t uden t s '
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1.
THE
S P A C E
OF
L E A R N I N G
1 _9
vocabula ry in the context o f the same story. O ne of the teachers deal t w i th
the story as a whole first, then wi th
different
paragraphs, sentences, and fi-
nal ly with individual words, taking each feature of the words (such as
m eaning , sp el l ing, i .e . ,
stroke
pat tern, and pronun c ia tion) o ne at a t im e . In
other words,
the
teacher dealt with
the
vocabulary i tems (words) sequen-
t ial ly and in isolation, instead of in context . T he other teacher seemed to
act in
accordance w ith
the
view tha t
the
m ean ing
of a
character
is mo di f ied
by
the
word
or phrase in
w hich
it
occurs; that
the
m ean ing
of the
wo rd
or
phrase is m odif ied by the sentence in w hich i t appears; and that the m ean -
ing of the
sentence
is
m odi f ied
by the
text
in
wh ich
it
forms
a par t . S he
tried to make sure that al l of the different levels of the text (story, para-
graph, sentence, w ord, character)
were
present in the s tudents ' awareness
at the
same t ime ,
by
deal ing with each level
in the
context
of the
nex t
superordina te
level. Furtherm ore , she deal t w i th di f ferent features of the
cha racters in the con text of each w ord, instead of deal ing w ith each char-
ac ter
as an ind ividua l un i t as the other teacher had done.
Awareness
B u t ,
where
are instances, aspec ts, parts, and wh oles w hen they are exp eri-
enced sim ultan eo usly ? In a vivid sense they are present to us. They are not
s imply s tored away somewhere deep down
in our
m e m o ry;
we can
hear
them or see them , feel them, sense them or imag ine them . They are in our
awareness .
Awareness (w e use the
word
as a
synonym
to
consc iousness)
is the to-
tality of a pe rson 's experiences of the wo rld, a t each p oint in t im e. I t i s a l l
that
is
p re sen t
on
every occas ion . A wareness changes dyna m ica l ly
all the
t ime and every s i tuat ion is experienced against the bac kg rou nd o f previ-
ous experiences. T his occurs to varying degrees of course , bu t poten t ia lly ,
aw areness is present aga inst the backg round of a very, very g reat nu m ber
of previous experiences. And to
affect
our experiences a t this very mo-
m ent , here and now, these previous experiences a l l have to be present a t
any one
t im e .
In a
wa y ,
i f we
exaggera te th ings
a
l i t t le ,
we
m i gh t
say
tha t
we are aware of everything a l l the t ime, s imply not in the same way.
Actua l ly there
are
very
few
th ings tha t
we can be focal ly ,
tha t
i s ,
sharply,
aware of at the same t ime , but a lot can affect the way in w h i ch we are
aware o f these th ings . In accordance w i th Gu rw ich ' s (1964) account , w e
mi g h t say tha t the charac te r is t ic of hum an aw areness i s tha t a l im i ted num -
ber of ob jects , aspects of objects , or s i tuat ions com e to a t t rac t our a t tent ion
( i .e. , become focused), whereas a very great number of other things are
there as bac kg rou nd. I t i s against this back grou nd that w e experience the
things that w e are foca l ly
aw are
o f, that is, the things that are the focus o f
our a t tent ion .
A
gen eral ized
and
ever chang ing f igure-grou nd st ructure
is
t hus characteris t ic
for our
awareness .
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20
M A R T O N , R U N E S S O N , T S U I
Discernment,
Awareness and Si mul ta ne i ty
Al though learning can be viewed as the developm ent of both cap abi l i t ies
and
values,
the
focus
o f
this
book,
as we
stated earlier,
is on
learning
as the
developm ent o f capab i l i ties . The kinds of
capabil i t ies
we
focus
on are those
that empow er learners to deal w ith s ituat ions in
power fu l
w ays , t ha t is, to si-
m ultaneously ( in the diachronic sense) focu s on features cri t ical for achiev-
ing a
certa in a im. However,
we can
o nly exper ience s im ul tane ou s ly tha t
w h i c h w e can discern; we can only discern wh at we experience to vary; and
we can only experience variation i f w e have experienced different instances
previously
and are
ho ld ing them
in our
awareness s imul taneous ly
( in the
diachronic sense). So the three (or rather
four)
key concep ts of the theory
are intimately l inked, each of them being a func t ion o f another.
T H E SPACE O F L E A R N I N G
A s w e have a lready pointed ou t , nobo dy can discern a certa in feature w i t h -
out exp eriencing varia t ion in a d im ens ion corresponding to that fea ture . L et
us assume that tw o
persons,
A and B, are engaged in a conversat ion w ith a
stranger, C , in a sm al l cot tage in a N epa le se m oun ta in v i ll age . A f t e rward , it
turns o u t tha t A had not iced that C spoke w i th a typica l southweste rn N epa-
lese dialect (a ctually all
three
o f them did so), w hile B did not notice this at
all. W hy was it
tha t
B did not
discern
C 's
d ia lec t w hereas
A
d id? W hat
w as
varying, as far as dia lects are concerned? A s it was , no th ing var ied in the ac-
tual
situation,
but A had
heard
a lot of different
Nepalese dialects previ-
ously
and he re la ted C's w ay of speaking to w ha t he had experienced and
not iced the s im ilarity w ith a pa r t icula r N epa lese d ia lec t , and the difference
w hen compared
to
other
Nepalese
dialects.
B , on the
other han d,
had
never
been ou ts ide
h is
v i l lage ,
had
never w atched
T V o r
l i s tened
to the
radio,
and
had actua l ly never heard any other dialect . He cou ld no t discern the d ia lec t
because he did not
know
of any
other.
T he
variation exp erienced
by A was a
resul t of the m em ories of past events that A brou gh t into the s i tuat io n, and
t hus a lso into his encoun ter w ith C .
Now let us
assume that
C
speaks
a
different dialect.
If this were
the
case ,
A
w ould probably not ice
th e fact, bu t
also
B
wo u l d
not ice that
C
speaks
in a w ay
that
is
different
from all the
other people
he has
ever
heard (he may even find it very
difficult
to understand C). A t the same
time,
h e
w ould probably becom e co nscious
of the fact
tha t
he
h imse l f
has a
certain
way of
speaking.
In the first
example,
the only variation w ith
respect
to dialects w as the
fac t
th at A had had previous exp erience of hearin g other dia lects , and that
C's way of
speaking
w as
juxtapo sed w i th th i s exper ience .
In the
second
example , there
is
variation
to be experienced in the
actual s i tuat ion.
T he
ins igh t th at there are
di f ferent
w a y s o f speaking can be derived from s i m -
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1 . T H E S P A C E O F L E A R N I N G 21
p ly
being exposed to them in this s i tuat ion.
There
is a space created for
gaining
this
insight in the second case.
This
space is created by chal leng-
ing
th e taken-for-granted nature of the
experience
o f people's w a y s o f
speaking
in the
person
wh o h as
previously only been exposed
to one way
of speak ing . Creat ing a space m eans opening u p a dime nsion of variat ion
(as
compared
to the
taken-for-granted nature
of the
absence
o f
var ia t ion) .
As o u r exam ple i llus t rates , however , som eone w hose past experiences a re
suf f ic ien t
fo r
pe rce iving
th e
necessary pat tern
o f
variat ion
can
exper ience
variat ion w i thou t that space ( i .e .,
t h e
necessary pat tern
o f
variat ion ) being
cons t i t u t ed in the
imm edia te s i tua t ion .
T he
space o f learning re fers
to the
pat tern o f var iat ion inherent in a s i tuat ion as observed by the researche r .
This
space
is a
necessary condition
for the
learner's experience
of
that pat-
tern of var iat ion unless the learner can experience that pat tern du e to w ha t
she has encou ntered in the pas t .
N ow let us consider another type of var iat ion. W hen w e con sider a mov-
ing
body for example , w e usu al ly look at i t f rom the po in t of view of the
ground.
W e can say
that
the
ground
is
taken
as
a f rame
of
reference.
But we
could
also look
a t the
m oving body
from the
po in t
o f
view
of
another
f r ame
of
r eference;
from our own mo ving body ins tead o f the ground, for ins tance .
A nd if we do that , w e introd uce variat ion in
f rames
of re ference . T he very
idea
o f f rames of refere nce presuppo ses variat ion, as does the insight tha t
looking at a body in movement f rom th e point of view of rest (the ground)
amo unts to
adopt ing
a
par t icular f ram e
o f
re ference .
In
addit ion
to
looking
at
m oving bodies
from the
point
of
view
o f
rest ,
w e
also ha bitually look
at
them when they
a re
under
the
influence
of the
gravita-
t ional
force of the
earth.
So
wi thout being aware
of
this ,
we
take
the
gravita-
tional force for granted. In order to break this taken -for-granted natu re of our
awareness of the world, variation in the gravitational force mus t be intro-
duced.
This can be done by traveling in a space shuttle, or more
easily,
by
looking
a t
pictures
f rom a
space shuttle,
by
engaging
in a
simu lation
of the ef-
fects of varying gravitat ional force or sim ply carrying out a thoug ht experi-
ment .
These tw o
dimensions—gravity
and frame of
reference—form
a space
of learn ing . A space of learning
com prises
any
number
of
dim ensions
o f vari-
ation and denotes the aspects of a situation, or the phenomena embedded in
that
situa tion, that
can be
discerned
due to the
variation presen t
in the
situa-
t ion.
V ariation that
is not
present
in the
situation
can
still
be
discerned, how -
ever,
if variat ion is brought in by m eans o f the learner 's m em ory of previous
experience.
W e
should notice, here, that
a
space does
n ot refer to the
absence
of
constraints,
but to
something actively constituted.
It
del im i ts w hat
can be
possibly learned (in sense of discerning) in that pa rticular situation.
B ut w e are not interested in al l types o f variation. W e m ust look at the sit-
uation
from the
point
o f
view
of a
particular object
of
learning.
And by do-
ing so we can find out
whether
or not it is
possible
for the
learner
to
appropriate that part icular object o f learning in that par t icular s i tuat ion.
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22
M A R T O N , R U N E S S O N , T S U I
Th e Object of L e a r n i n g
The object
of
learning can be d efin ed by i ts cri tical fea tures, that is, the fea-
tures that m ust
be
discerned
in
order
to
const i tu te
the
m eaning a imed for .
The
quest ion
w e
mu s t
ask
therefore,
is to
wh at ex ten t
we f ind
variation
in
the relevant respects. A s learners can only discern that which vanes, w e
m ust look for the pattern of variat ion necessary for deve loping the required
capa bil i ty. U nless the re is variat ion in al l the respects corresp ondin g to the
cri t ical fea tures, that
is, the
necessary pattern
of
variat ion
is
presen t , this
ca-
pabil i ty cannot
be
developed.
W e a re
thus ta lking about
the
necessary p at-
tern
of
variat ion.
In
order
to
develop
a
cer tain capabi l i ty ,
the
l earner mu s t
enco unter a cer tain p at tern of var iat ion, regardless of the arrange m ents for
teach ing
tha t
are
m a de,
a nd
regardless
of the w ay in
wh ich learn ing
is
orga-
nized (e .g . , wh ether the learner par t ic ipates in an au the nt ic pract ice, or s it s
in a lecture h all with 300 students). The space o f learn ing tel ls us wh at i t is
possible
to
learn
in a
cer tain s i tuat ion.
In
th e
light
of a
specific object
of
learning ,
the
space
of
learning
is a
rather
specific
character izat ion of the in teract ion in the classroom. As al ready
pointed out ,
the
object
of
learning
is
there,
to
beg in w i th ,
as an in tended o b-
ject
o f learning as seen
from
the teacher 's perspective, then i t is somehow
realized in the
classroom
in the form of a pa rt icular space of learning. This is
the enacted object o f learning as
seen
from th e
researcher ' s po in t
of
view,
const raining w ha t i s poss ib le to leam .
W e
can see
tha t
the
space
of
learning con st i tu ted
in the
classroom
is the
enacted object
of
learning.
This is how the
object
of
l earn ing
is
con st i tu ted
in the m ost con crete sense. A nd i t is this that m atters rega rding op portuni-
t ies to learn in school . F actors such as c urr icu lum , teach er ' s in te nt ion , and
so on, are
m edia ted th rough
the
enacted object
of
l earn ing .
The way
that students see, understand,
and
make sense
of the
object
of
learning when
th e
lesson ends
and
beyond,
is the l ived object
o f
learning.
T he
pedagogical s i tuat ion
and
w h a t
the
students
actual ly
learn
can
thus
be
described
in the
same terms.
So now we can describe
learning
and
teaching
in
relat ion to one another, from the point of view of learn ing, not as a rela-
t ionship
between cause
and
effect ,
but as a
re la t ionsh ip be tween w hat
is
m ade poss ib le and w hat poss ib i l i t ies are actu al ly m ade use of .
The focu s should thus be on learning in the first instanc e and on teaching
in the second; the
focus
should be on wh at shou ld be learned and w hat i s ac-
tual ly learned.
A nd
w h a t
is
actua l ly learned should
be
understood
in
term s
of the con dit ions of learning . If learning is ac tua lly tak ing place in the class-
room, w e should try to unders tand w hat the students leam in term s of wha t
is
taking place
in the
classroom. Whatever takes place
in the
classroom
makes
differing
sense to different students. This is one of the most solid
conclusions that can be drawn f rom our own research (Marton & Booth ,
1997)
o r
tha t
of
others.
N o
co ndi t ions
of
learn ing ever
cause
lea rning. They
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1 . T H E S P A C E O F L E A R N I N G 23
only m ake i t possible for learners to learn c ertain things. A nd this , in our
view,
is exact ly wha t pedagogy is about , especial ly the type of pedago gy of
learning that we are putt ing forward in this book, that is,
making
learning
poss ible. Le t us consider tw o si tuations ( tw o classroom scenarios)
from
the
point of view of learning or developing a certain c apabil ity. W e m ight de-
scribe what i t is possible to learn with view of that capabil i ty in the two
classrooms; we might descr ibe what i s taking place in each classroom in
terms o f the possibilities for learning that are brought about, an d in terms of
w h a t kind o f space of learning i s con st i tu ted. The space
of
learn ing thus de -
pic ts the possibil it ies of learning in relat ion to the ca pab il ity in qu estio n.
Th rough out th is book, w hen w e talk abo ut wha t i t i s poss ib le to learn, w e
restrict ourselves to the kind o f learn ing we h ave discussed in this chap ter,
namely learning to see certain things in certain w ays. But even bearing this
res t ric tion in m ind, there w i l l und oub tedly be a great num ber of th ings that
vary, and hence that w i ll or could be discerned. The space of learning does
not d enote al l that is possible to leam , even in the restricted sense of learn ing
(i.e., learning to see). The space of learning ca ptures o nly what i t is pos sible
to learn in a situation
from
the point of view of wha t is m eant to be learned.
W hat i s m eant to be learned is the o bject of learning, wh ich in our case is
a c apab i l ity of seeing som ething in a cer tain w ay. A s we p ointed out ear lier,
a
cer tain way o f seeing som ething can be character ized in term s of the as-
pec ts of a s i tuation or phenom enon that are discerned and focused on s imul -
taneously, or more precisely, the crit ical aspects of the situation or the
phenomenon that are discerned and focused on s imul taneously . Now the
quest ion is : How do we know w hat dimensions o f var iat ion w e should look
for?
How do we know w hat cr i t ical features there are for a certain class of
s i tuat ions
to be seen in a cer tain w ay? How can w e character ize the nature of
a certain capability?
C arlsson (1 999) investigated "the a natom y
o f
ecological u nders tanding,"
com pris ing, am ong other th ings ,
th e
unders tanding
o f
pho tosynthesis , recy -
cl ing,
an d the con servation of energy. One of the cr it ical feature s— actua l ly
the most cr i t ical feature of al l of these component capabil i t ies—was the
idea
of
transformation, that
is ,
that
one
thing turns into something qualita-
tively different: Sunl igh t and water are t ransform ed into carbohydrates a nd
oxygen in photosynthesis; material microscopic part icles from hum an be-
ings
and
an im als,
and so on, are for
instanc e rearrang ed into soil,
and
soil
re -
arranged into plants; and on e
form
of energy, such a s hea t , can be turned into
and stored in solid or l iquid form through th e conservation of energy.
In what sense
is
t ransformat ion
a
critical feature
of
ecological under-
standing
and how can i t be found or discovered? Is it by m eans of co ntem-
plat ing the concept o f ecologica l unders tanding W ell, this w as definitely
not
the way in
wh ich C arlsson found
it. In
C arlsso n's study, this critical fea -
ture (transformation) appeared empirically, as a contrast to another
frequent
w ay
o f thinking that im plied that certain things were perceived a s consum ed
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24 M A R T O N , R U N E S S O N , T S U I
(e.g., sunlight, water, dead bodies, energy)
and
that other things were per-
ceived
as
independen tly produ ced (e.g., coal, oil ,
or the
chlorophyl l
in f low-
ers and
trees).
The law
o f
variation applies thus
to the
research er 's
work
as
w el l.
It is not
possible to discern a certain way o f th inking about something wi thout the
contrast
o f other
ways
of
th inking about
the
same thing.
T he crit ical feature
is
critical
in
dis t inguishing
one way of
th inking
from
another,
an d is
relative
to the group participating in the study, o r to the p opu lat ion represented by
the
sample.
F or
instance ,
if all the
p art ic ipants
in
Carlsson's study
had em-
braced the idea of transform ation, t ransform ation m ay never have shown i t-
self as a cri t ical feature. The cntical features have, at least in part , to be
found
empir ical ly—for ins tance, through interviews wi th learners and
through the analysis of w hat i s happening in the classroom — and they also
have to be fou nd for every object o f learning
specifical ly,
becau se the cnt i -
cal features are cri t ical features of spe cific obje cts of learn ing.
Th e Space of Le a r n in g Is the E n a c t e d Object of L e a r n i n g
The enacted object of learn ing is the research er 's descr ipt ion of w hethe r , to
w hat extent
an d in
what fo rms ,
the
necessary condi t ions
of a
par t i cu lar
ob-
jec t of learning appear in a certain set t ing. Th e ena cted obje ct of lear nin g is
t hus what w e have also called the space of learning, thereby de pict in g w ha t
is
po ss ib le
to
l earn . W hat fo l low s from th is l ine
o f
reasoning
is tha t
w h e n
w e talk about learning, teaching , and other related mat ters, w e shou ld try to
be exp l ici t about w hat we h ave in our m inds as far as the quest ion of "W hat
is
learned?"
( i .e. , "What should be
learned?"
"What can be poss ib ly
learned?" "What
is
actu al ly learned?")
is
concerned.
In th i s way , the space o f l earn ing , w hich com pr ises different d imens ions
of variation, is con sti tuted by l ing uist ic m ean s in the inte rac tion between
teacher and students.
T H E
L I NGUI S T I C
CONSTITUTION
OF THE
SPACE
O F
L EARNI NG
In
the
previous discuss ion,
w e
descnbed
learn ing as the
process
o f
coming
to experience the world in a certain way. W e put forw ard the thes is tha t the
space o f learn ing is the space of variat ion, and that the dim ens ions of varia-
t ion that can
be
opened
up and
those tha t
are
actually opened
up
contribute
to qua l i ta t ive di f ferenc es between the wa y in w hich so m ething
c a n be
expe-
r ienced an d the
ac tua l
way in
w h i c h
it
is experienced.
T he
space
o f
l earn ing ,
therefore,
is
also
an
experiential space.
In talking abo ut the space of learning as an experiential space, w e are re-
ferring
to experience not as an in stan tiat ion , but rather as a po tentia l for ex-
periencing, seeing, and un der stan din g (see also Hal l iday & Mat th iessen ,
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1 .
T H E
S P A C E
O F
L E A R N I N G
25
1999). It is in relation to this potential that learners can m ake sense of a par-
t icular object of learning. A s such , this space is elastic; i t can be w idened if
the teacher affords learners opp ortunit ies to explore the ob ject of learnin g in
a variety of ways.
A nother thesis
we put
forward
in
this volum e
is
that language plays
a
cen-
tral
role in the construal of experience,
that
it does not
simply
represent
expe-
rience, as is widely perceived, but mo re imp ortantly, it constitutes experience.
Seen in
this l ight, languag e plays
a
central role
in
learning,
and
understanding
how the learning experience is being con stituted by langu age is crucial to un-
derstanding
how
different ways
o f
experiencing
the
object
of
learning
are be-
in g
brought about
in the
classroom.
L a n g u a g e a n d t h e C o n s t r u a l o f
E x p e r i e n c e
L et
us clarify w hat w e mean by langu age and the construal of experience.
The p osi t ion that w e are adopt ing is that the same phenom enon can be expe-
rienced in qualitatively different ways, and that the different construal of
the experience w il l be ref lec ted in the lang uage used. For exam ple , le t us
imagine that the jan i tor of a school locked the door o f a com puter laboratory
and
tha t tw o teachers were t rying to open the door bu t co uld no t . Teacher A
said, "The
jani tor
locked
the
door," whereas Teacher
B
said, "The door
is
locked." The same phenomenon was construed in different w ays by these
tw o
teach ers . For Teacher A , the jani to r w as the point of departure o f the
message, whereas for Teacher B, the door was the point of departure .
Hence , for Teacher A, the m essage w as about w ha t the jan i tor did: that is ,
that he had
locked
the
door.
B y
contrast ,
for
Teacher
B, the
m essage
w as
about the state of the door, that is , that i t w as locked and therefore could no t
be opened.
The re la t ionsh ip between langu age and experience can be best seen by
examining data on chi ld language development . Hal l iday's (1973, 1975)
seminal work on Nigel ' s language development shows that for ch i ldren ,
learning language
is also learning
about
the
world through language.
Hall iday ( 1 993) observed that
Whe n c h i l d r e n lea rn langu age , they
a re no t
s imp ly engag ing
in one
type
o f
l ea rn ing
am ong m any; ra ther , they a re learning the foun dat ions o f learning itself . T he dist inc-
t ive
cha rac te r i s t i c o f
human l e a rn ing
is
tha t
it is a
process
o f
m a k i n g m e a n i n g — a
semio t i c process ;
and the
p ro to typ ica l f o rm
o f
h u m a n semio t ic
is
l a n g u a g e ,
(p. 93)
A s
the child
experiences
th e
world
and as he learns how to mean
(Hall iday, 1973), his m eaning p otent ia l is being recon st i tuted. The reconst i-
tut ion of his m eaning potent ia l finds its rea lization in the w ay the chi ld re-
constructs his
"grammar"
so that i t eventually shares the conventions of
adult gramm ar.
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26 M A R T O N , R U N E S S O N ,
T S U I
Let us take for exam ple chi ld lang uag e developm ent . A t an early s tage
of language deve lopment , the ch i ld ut ters words as "annotat ions of experi-
ence"
(H alliday 1993,
p .
99).
For
example ,
on
seeing
a
round objec t ,
a
Cantonese speaking chi ld w il l say "bo bo"
[ > .
$.] (b a l l ), no m a t te r whe the r
it is a round doorknob, a balloon, or a basketball . A s adul t s comm ent on
the
chi ld 's ann ota t ions
b y
say ing , "Yes, it 's
a
bal l"
o r
"No, th a t ' s
not a
ba l l ;
it 's a
doorknob,"
they a re c lass i fy in g th ings for the ch i ld . ( In Can tonese ,
"bo" [ j& ] (bal l) is a generic term for a ll kinds of ba l ls . ) W hen the ch i ld ap-
propriates the
adul t c lass i f ica t ion
of a
round o bjec t
as "a
ball ,"
he is
also
implic i t ly c lassi fying what is not a bal l . In Hal l iday's
terms,
he is
"outclassing" (1 993,
p.
99).
2
In other words, the chi ld experiences varia tion am ong the round objects
that he sees: Objec ts tha t a re round and he can p lay w i th h i s m om m y are
called
"balls,"
and
objects that
are
round
and are
stuck
on
doors
are
"not
balls." This
experienced
variation
is
realized
in the
language that
th e
child
uses
to
m a k e
a
dis t inct ion between different k inds
o f
rou nd ob jects . Later ,
the child experiences variation within the class of "balls." He experiences
balls that can be blown up into big on es, are
l ight,
and can nse into the air,
and those that cannot. This kin d of "ball" is called a "balloon." A t this stage,
the
child
is
experiencing variation
in the
dimension
of
"ball,"
and
there
are
three values in this dim ension : "ball," "balloon," and "not ball." W ith this
further
dist inction, the ch i ld 's seman t ic sy stem of "ball" changes . It is no
longer a system w ith two term s, but w ith three term s. The m eaning of "ball"
changes
as
we l l.
"Ball" no
long er ju st means "not doorknob";
it
m eans "not
balloon"
a s w ell.
The re la t ionship between langu age and experience is dia lect ic . The ex-
perienced variation enables
the
chi ld
to
discern
th e
d is t inc t ion s tha t
are
real-
ized in languag e , and the l inguis t ic d is t inc t ion enables the ch i ld to discern
the variation. A s Ha llida y (1 978) observed, in this process:
th e
construal of reali ty is inseparable
from
th e construal of the semantic
sys tem
in
wh ich the reali ty is
encoded.
In
this sense, l anguage
is a shared
m ean ing
poten tial , at
once both a part of exper ience and an inter-subjective
interpretation
of
experience,
(pp. 1-2)
This m eaning potent ia l
is
being reco nsti tuted every t im e
the
ch ild experi-
ences language
in
use,
and
experiences what
he can do
w i th l anguage .
L a n g u a g e an d Di s t i nc t i o ns
In order to m ake sense of w hat w e have experienced, w e need to be able to
reduce the in defin i te ly varied phenom ena of the world into a mana geable
number o f phenomena of sim ilar types. A s Britton (1970) pointed out, o b-
jec ts in the wo rld do not present them selves as readi ly
classified.
T he c lassi-
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1 .
T HE S P A C E O F L E A R N I N G 27
f icat ions are given by hum ans in order to handle the world, and language is
a
principal
m e a n s
o f doing this . W e say "a principal means" because there
are certain class ificat ion s that
can be
done w i thout languag e .
F o r
example ,
if
someone
is asked to class i fy all the clothes in the w ardrobe, he could pu t
all
the w inter clothes in one pile, all the
w ork
clothes in ano ther pi le, and all
the
form al evening clothes in a third pile. However, in the m ajori ty o f cases,
it is not possible to m a k e
class i f icat ions wi thout language.
F or
example ,
how
does one
dis t inguish betw een
a
m ale hum an being
who i s
related
by
blood
to
one's father
and one who i s
not ,
by
nonl inguis ti c m eans?
A s
Sapir (1961) pointed out ,
.. . language
is
pr im ari ly
a
vocal actualization
of the tendency to see
realities symbo l i-
cal ly ... an
actualization
i n
terms
of vocal express ion of the tende ncy to
master
reality
not b y direct and ad hoc hand l ing of
this
elem ent but by the reduc tion of experien ce to
famil iar
forms, (pp. 14-15)
Adopting a similar stance to Sapir, Hall iday (1978) proposed that
Language
has to in te rpre t t he
w h o l e
of our
exper ience ,
r ed uc ing the indef in i t e ly var-
ied p henom ena o f the wor ld
a round
us , and
also
of the
wor ld
inside us, the processes
of
our own co nsc iousness , to a
manageab le
num ber o f
c lasses
o f
phenom ena : types
of
proces ses, events
and ac t ions , classes o f
objects ,
peop le and ins t i tu t ions , and the
l ike. (p . 21)
W e
po in ted o ut earl ier in this chapter tha t the contradiction between the
unl imi ted and
inexhaus tib le am ount
of
inform at ion avai lable
to us an d the
l imi ted capaci ty
of the
hum an mind requi res tha t
we be
select ive
in
wha t
w e
attend to. Th e th ings that w e at tend to are th ings tha t w e discern as cr i t i ca l ,
not in a
general sense,
but
cr i t ical
in
relat ion
to a
cer tain co ntext .
F or
th is
reason ,
the
dist inctions
or
c lassi f ica t ions
that
w e
ma k e
in the
process
o f re-
ducing the indefini tely varied phenom ena of the world into a m a n a g e a b le
n u m b e r
o f
classes
o f
phenomena
a re
n ecessar i ly select ive.
Let us
take
fo r
example
the way
th ings
are
class i f ied
in
different cu l tu res .
The fam ou s B ri ti sh anthropologis t Mal inow ski (1946) observed that societ-
ies
classify thei r surroundings according
to
thei r needs
and
interests ,
and
that
th is is done through language. F or example , in M al inowski ' s s tudy of
pr imit ive
l anguages ,
i t was
found that
the
indigen ous people
o f a
p r imi t ive
communi ty t ended
to
identify
and
different iate
the few
objects that were
use fu l
to them an d the rest were treated as an undifferen tiated heap . A p l an t
or a tree in a fo res t that was not connected to them t radi t ional ly or ri tually, o r
that
w as not usefu l to
t hem w ou ld
be
s im ply dismissed
as "a
bush."
A
bird
tha t p l ayed
no
part
in
the ir tradition
o r was not
part
o f
their diet w ou ld
be re-
ferred
to as "just a flying animal" (1946, p . 331). How ever, if an object w as
useful ,
it
w o u ld
be
n a me d
an d its
uses
and
propert ies described
in
detai l , that
is, it
w o u l d
be
dis t inct ly individua l ized.
T he fact
that trees
and
b i rds were
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28
M A R T O N ,
R U N E S S O N , T S U I
not nam ed separately for their individual appearance s does not m ean that
the people o f th is com m uni ty could not see that th e trees o r b i rds were phys-
ical ly different . I t s im ply m eans that to them the di fferenc es were not so cr i t-
ical in
relat ion
to the
specif ic
contex t
o f
their everyday l ives
as to
warran t
m aking di s t inc t ions
b y
l inguis t i c m eans .
On e of the
m ost widely quoted examples
is
that Esk im os have seven wo rds
fo r
"snow,"
each of which m akes very fine distinctions between th e size of the
flakes of snow to indicate ho w heavy the snow is. Th e Sam i l anguage has al-
mos t 200 w ords for "snow," a nd each word indicates the con di tion of snow,
that is,
whether
one can
w a l k
on it, or ski on it,
w hat tem perature
it is,
whether
it
w i l l change quic kly
and how
(see V uolab, 2000). L angu age, therefore,
en-
codes
the
dist inctions m ade
and the
c ri tical features
of the
dist inctions;
th e
distinctions
are
app ropriated
and
m ain ta ined
so as to
ma k e
th e
di scernmen t
of
the cri t ical features possible.
Another example
is the
central i ty
of the fami ly and the
impor tance
o f
rank according to gen erat ion in the Chinese cu l tu re . This is ref lec ted in the
complex kinship terms that make very fine d i s t i nc t i ons be tween w he the r
one is
related
to the
fa the r ' s s ide
or the
m othe r ' s s ide,
and w ho is
related
to
w h o m
in the f ami ly
tree.
These
dis t inct ions
a re
cr i t ical
in
Ch inese cu l t u re
because they indicate the place that one occupies in the fami ly tree, and
hence
the
status
in the f ami ly ( in the
sense
of the
ex tended
fami ly) .
Because
of these dis t inct ions , it is possible to have a s i tua t ion w h e re a ve ry youn g
person has a h igher rank than somebody who i s con s iderab ly o lder, and
therefore the younger
person
i s addressed w i th a kinsh ip term that indicates
he or she is
zhang b e i ( P u t o n g h u a )
[ -^ j£ ],
t ha t
is, of a
m ore senior genera-
t ion
in the
extended family .
Dist inct ions that have been m ade
to
su it socia l purposes
a re not
only
e n-
coded
in the
l anguage
bu t
a lso ma in ta ined
b y
m e a ns
o f
l anguage .
I n
other
words,
th e
categories
se t up, and
hence
th e
di s t inc t ions m ade
by
language ,
no t
only express
the
social s tructure
but
also create
the
need
fo r
people
to
conform to the behavior a ssociated w i th these categories . The com plex kin-
ship term s
in
Chinese
a re a
real izat ion
a s
w e l l
as a
me a n s
o f
m a in t a in in g
the
hierarchical human relat ions
in
Chinese societ ies.
A s
Hal l iday (1978)
pointed out , "By thei r everyday a cts of m ean ing, people act out the social
structure, aff i rming thei r ow n statuses and roles, and es tabl ishing and trans-
mit t ing th e
shared system
of
value
a nd
know ledge"
(p. 8).
N ot
only
are
distinctions m ade
to
suit social
purposes,
they
a re
also m ade
to serve spe cific nee ds at par t icu lar m om ents in t im e . Let us use, for e x a m-
ple, color dist inc tions . Th e dist inction betwe en brigh t red and dark red is
commonp lace
and
mos t people w ould
be
able
to
di s t ingu ish
a
bright
red car
from a dark red car. Suppose you w i tnessed an acciden t between a dark blue
car and a br ight red car and you were asked by the pol ice to provide an eye-
witness account
of
w hat happened.
Y ou
probably w ould
say
som ething l ike
this:
"A red car was
going
a t full
speed when
a
b lue
car
c o mi n g
from the op-
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1 . T H E
S P A C E
O F
L E A R N I N G
29
posite direct ion suddenly swerved into the opposite lane and coll ided
head-on wi th
the red
car."
Y ou
w o u ld
not
take
the
trouble
to say
"the bright
red car" and the "dark blue car" because the distinction between and bright
and
dark colors is not c ri t ical . How ever, if it w as a bright red car co l liding
wi th a dark red car, then the dist inction between dark red and bright red
w o u l d be cr i tical . Of cou rse, if there w as o nly one car , there w ou ld be no
nee d to
describe
the
color
at
al l .
For
exam ple,
i f you saw a car
crashing into
a
supermarket , your eyewitness account to the police would be something
l ike
th is : "I saw a car crashing into th e supermarket at 10:00 a.m . this m orn-
ing,"
but not "I saw a
bright
red car
crashing into
the
supermarket
at
10:00
a.m." be ca us e the co lor of the car is not c ri tical in relat ion to the e vent or the
contex t .
C ri t ical to the event or the con text is w ha t happe ned.
In
the contex t of a learning si tuation, such as the
classroom,
the lan-
g u a g e
th a t is use d by the t eache r and the s tude nts to m ake di s t inc t ions in
re la t ion
to the
ob j ec t
o f
learn ing
is
often
o f
cr i t ica l imp or tance .
L et us use
an e x a mp l e
f rom
a lesson tha t w i l l be repor ted in greater detai l in chap t e r
5.
A sc ienc e t eacher , in the contex t o f teach ing how a reed re lay
3
ope ra te s ,
asked the s tudents what happened to the electrical resistance va lue w hen
l i g h t w as shone o n a l ight-diode res is tor
4
( L D R ) . O n e s tudent rep l ied ,
"Sm al l. " W hen the s tudent used the adjec t ive
"small,"
she was m ak ing a
dis t inc t ion b e t w e e n th e size of the res i s tance in the LD R be fo re and af ter
the
l igh t
w as
shone
on the
L D R .
In
o ther w ords ,
she was
descr ib ing res is -
tance as a state. T he teacher, however, w as no t happy w i th the descript ion
b e c a u s e he r ques t i on was "What happened to the res i s tance?" In o ther
w o r d s , she w anted the s tuden ts to descr ibe the chang e of s t a te cause d by
l i gh t sh in ing on the LDR , and "small" was therefore no t an ap propr ia te an-
swer .
S he
ins i s ted tha t
the
s tudent
use the
verb
"decreases"
i n s t ead
of the
adjec t ive "small." This t eacher w as no t n i tp i ck ing , bu t was m a k in g an im-
por tan t
di s t inc t ion be tween a state
and
a c h a nge
o f
state.
In
o ther words ,
the two s ta tes were
c lass i f ied
as two dif ferent p h e n o m e n a . In o ther con -
t ex t s , such
a
di s t inc t ion
m a y n o t
have been imp or tan t
a t
a l l ,
but in the
c o n -
text
o f un der s tand ing a p h e n o me n o n in phys ics , spe c i f i ca l ly the ope ra t ion
of a ree d relay, th is w as an im portant dis tinct ion (see chap. 5 for a m ore de-
ta i led
exp l ica t ion of the reed re lay) .
Let us take another example from a classroom learning s i tuat ion. T w o
H o n g Kon g primary teachers were teaching lessons about festivals.
O ne o f
the
objects
o f
l earn ing
in
both lessons
w as to
he lp
the
s tudents
to
indicate
their p references for the festivals, usin g th e phrase
"like best."
Both teachers
gave thei r s tude nts the sam e l ist o f
festivals.
Teacher A asked the s tudents to
first indicate
the
festivals
that they l iked and then indica te w hich one they
l iked bes t .
B y
doing this ,
th e
teacher opened
up a
dim ension
o f
variat ion
in
indicat ing preferen ces that included "like"
an d
"like best,"
an d
p resupposed
th e
choice of "do not like." In other w ords, in the sem antic system of
"like,"
there we re three choices : "do not like,"
"like,"
and "like best." B y j ux t apos -
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30 M A R T O N , R U N E S S O N , T S U I
ing
"like" a nd
"like
best," the teacher w as able to help the students experi-
ence variation in their fee ling s towa rd these festivals an d thereby discern the
meaning
of
"like
best" as the
superlative form
of
"like."
B y
contrast ,
Teacher
B
made
no
such dist inction.
S he
sim ply asked
her
students
to
indi-
cate what they "liked best." Consequent ly , some of the s tudents in this class
took "like
best" a s
having
a
s imi lar m eaning
to "like."
La n gu a ge
an d
Structure
of
Awareness
In our discuss ion of s im ul tanei ty and aw areness, w e pointed out that aware-
ness is the total i ty of our experience of the w orld an d that w e experien ce ev-
ery
s i tuat ion against
th e
b a c k g r o u n d
o f a
vas t number
o f
p rev ious
experiences . W e fur ther pointed ou t that the c harac ter is t ic of hu m an aware-
ness is that only a limited num ber of thing s com e to the
fore
and becom e fo-
cused, whereas
the
rest recedes
to the
background.
W e
observed that
the
f igure-ground s tructure of awareness i s dyn am ic and ever ch an gin g.
In the discuss ion o f language and the const rual of experience, we pointed
out that the enc oding o f previous ex perience by l inguis t ic m eans enab les us
to m ake sense of w hat we are experiencing. W e w ish to further argue tha t
language also plays
an
im portant role
in not
only represe nt ing
the
structure
of
aw areness
but
also
in
changing
it . Let us
take
the
previou s ly c i t ed exam -
ple of the janitor locking the door of the computer laboratory. If we say.
"The janitor locked
the
door,"
the
jan i to r becom es
the
t hem e
or
sub jec t
o f
the clause and is the grounding for the rest of the clause . That is.
what
the
janitor d id w as the figu re. How ever, if w e say, "The door w as locke d by the
janitor," the
fact
that the door w as locked becom es the ground, and the ja n i-
to r becomes the f igure .
In classroom situations, it is very imp ortant
that
the teacher is able to bnng
critical fe ature s of the object of learning into s tuden ts'
focal
aw areness. That
is to
say,
it is
crucial that
th e
teacher
is
able
to
bring
out the figure and
ground
relationsh ip. This is often achieved through linguistic means, and m ost obvi-
ously through
the use of
questions because
th e
structure
of all
quest ions
in-
volves
a f igure-ground
relationship.
For
exam ple,
the
often ci ted question,
"Have you stopped beating your w ife?" presupposes that yo u have been beat-
in g
your wife
and
queries whe ther
y ou
have stopped
th e
action
or
no t .
In
other
words, "beating yo ur w ife"
is
ground,
a nd
"have
you stopped" is figure.
W h at
th e
teacher presents
as
ground
is
wha t
he
assumes
to be
shared knowledge,
and wh at he presents as f igure is w hat he w ants to be the focus o f the students '
attention. For exam ple, let us see how
different
questions asked by different
teachers can result in different learn ing experiences for students ( this exam ple
is presented in m ore detail in chap. 5). Tw o primary E ng lish teachers in Hong
Kong were teaching
the
determ iner "some"
to
indicate inexac t quanti ty. Both
teachers used O ld
M acDonald
's
Farm as the
context
for
teaching,
and
both
showed th e students a series of pictures with different kinds of animals and
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T H E
S P A C E
O F L E A R N I N G
different
numbers of animals on the computer screen. Both teachers also
started by showing one anim al and asking the students w hat they c ould see so
as
to
elicit
th e
n a me
of the
anim al shown. After this,
the first
teacher repea t-
edly
asked
th e
students, "How many (name
of
animal)
can you
see?"
This
elicited exact num bers, such as
"three,"
"four," "five," and so on. The second
teacher, how ever, repeatedly asked the students, "What can you
see?"
and did
not ask
"How many?"
The
question "How m any cats
can you see?"
presup-
poses that the an ima ls that the students can see are cats and queries the exact
num ber of cats . Hence, the cats are the ground and the num ber of cats the fig-
ure.
This question focuses the students' attention on the exact number. The
question
"What can you see?" presupposes that the students can see some-
th ing
(on the
computer screen)
and
queries
"what"
it is
that they
can
see.
In
other
words,
the
exact number
of
animals they
can see is not the f igure.
Their
focus of
attention
is on
whether there
is
only
one or
more than
one
animal .
The students ' performance in a test administered at the end of the lesson
showed that
the
students taugh t
by the first
teache r
did
less we ll w hen u sing
the
determiner
"some"
to indicate inexact qu an tity than the students taug ht by
the
second teacher.
T H E
SEMANTIC DIME N SIO N
OF THE SPACE O F L EARNI NG
S o
far ,
w e
have focuse d
on the
necessary co ndi t ions
f o r
learning,
the
nec-
essary con di t ions being the discernm ent of cr it ical features of the objec t
o f
l earn ing th roug h expe r iencing dimens ions of var ia t ion re la t ing to th i s
speci f ic ob j ec t
o f
l earn ing bo th diachronica l ly
an d
synchronica l ly ,
and
h o l d i n g
these c r i t ica l fea tures
in
focal awareness s imul taneous ly . How-
ever , these necessary con di t ions
m ay no t be
suf f ic ien t
fo r
pow erfu l l earn-
ing to
t ake p l ace .
Let u s
take
fo r
exam ple some science lessons that
wi l l be
explained
in de-
tai l in chapter 6. Two science teachers e xplained the process o f
neutraliza-
tion to their students. Both explained that neutralization is a reaction
between acid
a nd
alkali that results
in a pH
value
of 7.
Both
o f the
teachers
used
laboratory demonstrat ions
to
show w hat
happens
when neutral izat ion
occurs , by us ing a chang e of the color of the solution as the m eans of m aking
the
process visible. Both varied
the
prop ort ion
of
acid
and
alkali ,
and the
chang e of pH
value
to
indicate
the
levels
of
acidity
and
alkalinity,
to
help
students understand the concept of neutral izat ion. However, one teacher
used many everyday examples that were familiar to the students to help
them make sense
of
neutral izat ion (e.g. ,
the use of
alkaline ointment
to
sooth the i tchiness caused by a cids injected into the skin by m osquitoes, a nd
the use o f alkaline toothpaste to neu tral ize the acidic sal iva w h e n cleaning
our
teeth) .
The
other teacher, however, dealt w ith neu tral ization very m uch
as
a proc ess of m ixing ac ids and alkalis in a laboratory experim ent. B y using
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32 M A R I O N , R U N E S S O N , T S U I
examples that the students were able to relate to easily, the first teacher
m ade available possibili ties for students to assign a m u c h richer mean ing to
the object o f learning. F o r these students, neu tralization w as no longer ju s t a
process
that
took place
in the
laboratory,
b ut a
also
a
process
tha t
had a
p lace
in their daily lives.
T he
space
o f
learning
is
const i tuted therefore
no t
only
by the
possibi l i t ies
for discernmen t of cr it ica l features of the object of learnin g, of ten b rough t
about
by
l inguist ic means,
bu t
also
by the
examples
and
ana log ies tha t
the
teacher uses,
the
stories tha t
the
teacher tells,
the
contexts that
the
teacher
brings
in, and so o n. I t is
constituted
by the
me anin gs th at learners assign
to
these examples, analogies, stories,
and
contexts ,
as
w e ll
as by the
previous
experience that they bring
in as
they
try to
m ake sense
of the
object
of
learn-
ing. A ll of this const i tutes the sema ntic dimen sion o f the space of l ea rn ing in
w hich the cr i tica l features of the object of learning are interpreted and un-
derstood.
A
space
o f
learning that
is
semant ica l ly
rich
a l lows s tudents
to
come
to
grips wi th
th e
crit ical features
of the
object
o f
l ea rn ing m uch m ore
effectively
than one that is semantical ly impover ished.
T H E SHARED SPACE
O F
L E A R N I N G
In order for us to discern cr i t ica l features of the ob jec t in q u e s t i o n , w e need
to be able to make sense o f w h a t w e are exper ienc ing in re la t ion to w h a t we
have
experienced
before; this is the d iachronic d im ension o f our aw areness .
A s we poin ted out before , w e cannot ta lk about ta l lness un less w e have a lso
exper ienced shor tness; w e canno t say wh at br igh t red is un less w e have ex-
per ienced other shades of red. In other wo rds, w ha t learners have expe r i-
enced before
is
crucia l
to how
they m ake sense
o f
the i r cur rent expenen ce .
In
order
to
m a k e
i t
possible
fo r
learners
to
discern
cri t ical feature s
of the ob-
j e c t o f learning, teachers mu st be aware o f w hethe r lea rners c an make sense
of
these cr i t ica l features through their previous exper ience.
T he
teacher
m ust a lso be aware of how m u c h is shared be tween h im se l f and the learners.
In other words, w hat the teacher presents a s ground should b e shared com -
m on
ground between h im se l f
and the
s tudents ,
so
tha t w ha t
he
presents
as
f igure can be made sense of by the s tuden ts in re la t ion to the ground. In this
sense, the space o f learning is a shared space o f l e a rn ing .
Lan guag e is the key m eans by w hich th is shared space is con st i tuted. W e
have
i l lustra ted this poin t in the previous discussion on teach ers ' quest ion s.
The fo l lowing is a further exam ple . In a s tudy of some m athem at ics lessons
of Brazi l ian kindergar ten chi ldren, in wh ich the teacher was tea ch ing addi-
tion and the concepts
o f
m o r e and
less,
Cestan (2001)
found
that the use of
unclear deic tic reference and the lack of an explic i t indica t ion as to wh ich
rea lm the teacher was m oving in confused the s tudents and made them un-
able
to
answer
her
quest ions.
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1 .
T HE S P A C E O F L E A R N I N G 33
The lesson was a mathematics lesson at kindergarten level and the stu-
dents w ere around 5 or 6 years old. T he teacher w as teaching addit ion and
v/as helping the s tudents to unders tand not only addi tion but also the m athe-
mat i ca l
concepts
o f
more
and
less.
T he
teacher
put
three boxes
on one
side
and tw o
boxes
on
another.
S he
then asked the s tudents whether there were the same number of boxes on
both s ides , w hich s ide had m ore, and wh ich s ide had less . The teacher had
no prob lem s get t ing the s tudents to indicate that the s ide wi th three box es
had m ore. However , w hen she asked the s tudents about the s ide w i th two
boxes , confus ion
set in. The fol lowing is an
excerpt
f rom the
lesson:
1.1
[Cestan,
2001]
5
T :
W hich s ide
has
m ore?
6 S: 3
7
T :
(The side)
of how
m a n y?
8 Ss :
O f 3
9
T :
Which
has 3. A nd
this side, w hich
has 2?
10 S: 2.
11
T:
H m m ?
12 S: 2.
13 T: This side has m ore or less? (po inting to the side with 2 boxes)
14 S: M o r e
15 T:
H m m ?
16 Ss:
M o r e
Ss:
Less
17
T : W hy
less?
It is
becau se there
are
only
.. .
18 Ss: M o r e
19
T: 2, and here there are m ore beca use there are . ..
20 Ss: Less
21 T: Here there are m ore becau se how m any are there?
22 So me
Ss: 3
23
T: 3, then 3 is bigge r than . . . ?
24 S: 2
In
line
9 ,
w h e n
the
teache r asked
the
que stion, "And this side, w hich
h as
2?" one s tudent s imply reported the num ber of boxes on the other s ide ( line
10), and the same answer w as given when the teacher asked for the answ er
again w ith an
interrogative
interjection
(line
11). The teacher then repeated
her
quest ion
in a
sl ightly fuller form that included
the
q uant i ta tive com para-
tive no t ion
"more
or
less."
She
also g ave
a
more expl icit indicat ion
of
w h ic h
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34 M A R IO N , R U N E S S O N , T S U I
side she was referring to by point ing to the s ide w ith tw o boxes ( l ine 13).
This,
how ever, did not meet with m uch success. T he c lass w as sp l i t between
"more" an d "less" (see lin e 16). In line 1 7, even thou gh the teacher provided
the l inguist ic sc affoldin g to help the s tudents to
jus t i fy
why one s ide was
less than the other side, and tr ied to get them to fill in the b lank w i th
"two."
she still faile d to elicit the correct answ er. I t was not un t i l sh e made the j u s t i -
fication very explic i t by s ta t ing the qu anti ta t ive com parat ive no t ion "more"
and the number "how many are there" ( line 19 and line 21) tha t she
f inal ly
succeeded in get t ing th e correct answer.
Cestari (2001) ident i f ied the source of confus ion as em ana t ing from the
absence o f a
defini te
reference in the incom ple te in te rroga t ive in l ine 9, and
observed
that even tho ug h the teacher t r ied to repair the com m un icat io n gap
by
point ing
to the
s ide w ith
tw o
boxes
and
exp l i c i tly a sk ing wh e the r
i t had
more or less , the con fus ion rem ained. Th e confus ion has very m uc h to do
with the fact that the teacher was t rying to establ ish a correspondenc e be-
tween the n u m b e r o f boxes and the m a t h e m a t i c a l n o t io n o f "more" and
"less," and the fact there w as a lack of com m on ground, or m utu a l i ty , be-
tween her and the s tudents with regard to whether she was moving in the
realm of quant i ty of boxes, or in the rea lm of the m ath em at ica l no t ion of
"more" and "less." In line 9, w hen the teache r asked the cryp tic qu est io n
"And th is side , which h as 2?" she was m oving in the rea lm of the m athe m at-
ical notion
o f
"more"
and
"less,"
and
t rying
to ge t the
s tudents
to
ex t rapola te
f rom the ques tion w hat she wan ted them to te ll he r, w hich was w hether the
side with tw o boxes had more or less boxes than the s ide w ith three boxes.
The students , how ever, were m oving in the realm of the qua nti t y of box es.
W hen the teacher then tr ied to get the studen ts to ju s t i fy wh y one s ide had
less , she was m oving in the realm of the qua nti ty of boxes and w as t rying to
get the s tudents to com ple te the ju s t i f ica t ion by s u p p l y i n g the n u m b e r o f
boxes ( l ine
17 and
lin e 19). Yet,
the
s tudents were m oving
in the
r ea lm
of the
m athemat ica l not ion o f "more" or "less." I t was on ly when she m a d e the re-
la t ionship e xplic i t between the m a thema t ica l no t ion o f m o r e and the quan-
tity
of boxes ( l ine 21) and said,
"Here
there are m o r e because
ho w
m a n y are
there?" that
the
students w ere able
to
answer
the
ques t ion . This exam ple
il -
lustra tes nicely that unless the teacher and the learners share a common
ground in relation to the ob jec t o f lea rn ing , it is no t po ss ib le for the learners
to make sense of the object o f learning.
There
is a fur the r sense in wh ich the space of lea rnin g is a shared space.
W e have a lready pointed ou t th at previous exper ience is the f r ame o f refer-
ence against which current experience is interpreted or made sense of , but
that the current experience a lso mo dif ies the way in w hic h the previous ex-
perience
is construed. This is an ever-changing and interact ive process in
which
the
features that
w e
discern
in a
situation
and
w h a t
w e
discern
as
criti-
cal keep being revised.
O ne
crucia l mean s
in
wh ich th i s
is
done
is by
t a l k i n g
over events w ith people an d by ref lect ing on the events after they have oc-
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T H E
S P A C E
O F L E A R N I N G
curred (B ritton, 1 970) . L angu age n o t only plays a crucial
role
in the m odif i-
cation
o f
each other 's un derstanding
and
perception
of the
world
bu t
also
becom es part of the exper ience itself. T he m odif ica t ion of the learners ' and
teacher 's un derstanding
of the
w orld
is
w hat c lassroom teaching
and
learn-
ing is all
about . This
process is
brough t about joint ly
by the
teacher
and the
learners through interaction in which meaning is neg otia ted and co-con-
structed. In this sense, th e space of learning is a shared sp ace of learning. In
chapter 6 , we see how the s tudents m odify each
other's
understanding of the
wor ld by engaging in collaborative talk. In chapter 7, we see how the teacher
and the students togeth er co-construct an understan ding of the funct ion of a
"clan"
(a
comm uni ty
in
w h i ch
a ll
m embers have
the
same surname)
in a
his-
tory lesson .
TOWARD A
P E D A G O G Y
O F
L E A RN I N G
The expression pedagogy o f learning may strike the reader as vaguely odd.
Pedagogy is about teaching and upbringing after all; and teaching and upbring-
ing is m uch about learning, so is the pedagogy of learning not a tautology?
Well ,
it could have been, but it is not . W e set out at the beginning of this
chapte r
by
poin t ing
to the
fact that discussions abo ut pedagogy are,
a s a
ru le ,
not
phrased in terms of learning but in term s o f the co ndit ions of learning ,
and that they of ten lack precise s ta tements about the ways in which those
condi t ions facili tate learning and what kind of learning they would
facil i-
ta te . It is of ten s imply assumed that t he condit ions argued for w o u l d facil i-
tate all kinds of learning.
W hen w e use the expression
pedagogy
of
learning,
we do not refer to the
process whereby the condit ions o f learning are taken as the poin t o f depar-
ture
an d it is
s imp ly assum ed that these condit ions embo dy " the
a rt of
teach-
ing
a l l thin gs to a l l men." T he pedagogy of learning m eans ta kin g learning
as
the po int of depar ture an d exploring the con dit ion s that m ight be condu -
cive to br ingin g that learning ab out .
As lea rn ing
is
a lw ays
th e
learning
of
som ething, there
are
severe lim its
to
discussing learning in gen eral , w ithou t reference to w hat is learned. W hat is
learned is the ob ject of learning and we argue that a pedagog y of learning
m u s t take as i ts poin t of departure the very o bject of learning .
Most
of the stu dies reported in this book
follow
the simple design of com-
paring how the same o bject of learning was dealt w ith in two or more
different
classrooms.
W e
have used this model because
w e
believe that
the way in
which
the obje ct of learning is dealt w ith in the classroom is of decisive im -
portance , and that w e can o nly f ind out how the object of learning is dealt w ith
in
the
classroom
by
com paring
it
with another
way of
deal ing w ith
the
same
object of learning (this follows from the theory of variation discuss ed in this
chapter) .
In this book, w e describe m uch of w hat we found about differences
in the w a y s in w hich the same objects of learning were dealt w ith.
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36 M A R T O N , R U N E S S O N , T S U I
In
all
studies reported
in
this book,
w e
t ranscr ibed verbat im everything
that w as said in the
classroom
and carried out our analyses on the t ran-
scripts.
W e
have also used som e
of the
transcripts
or
par ts the reof (w i tho ut
ident i fying
the school, class, or the teacher) in seminars and workshops .
Frequently we let the
workshop
par t ic ipants—educational researchers,
school administra tors , teacher educators , and teachers—read through the
transcripts
and
then address
our
in i t ia l ques t ion:
"W e
have here
tw o
classes
deal ing w ith the same top ic (content or obje ct of l ea rn ing) . W h a t w o u l d y o u
say you f ind the most s t r iking dif feren ce between the two?"
Very rarely
did we
hear comm ents
on the way in
w h i c h
th e
object
of
learning
w as handled in the two classes, that is, w h a t it was possible for the student to
leam
in one
case
and
wha t
it was
possible
for the
student
to
learn
in the
other.
M ost comm ents concerned w hether there was a case o f
wh ole-class
teaching o r
group work, w hether the teaching w as teacher-centered or student-centered,
whether
or not
audiovisual tools,
IT ,
m am pulatives were used,
and so on.
W e do no t
deny that
the way in
w h i ch
the
lea rn ing s i tua t io n
w as
a r ranged
in each c lass w as of impo rtance for the pos sibi l i ty to learn. For ins tan ce, w e
agree wi th the a rgument tha t the opportuni ty fo r c o m m u n i c a t i o n in the
classroom
is of
impor tance
fo r
s tudents ' lea rn ing ,
and w i t h the
a rg u m e n t
that
the wa y in
w h i ch
the
learners
are
able
to
par t ic ipa te
in the
cons t i tu t ion
of the ob jec t o f learning i s a lso imp ortant . How ever , w e c l a im that w h a t s t u -
dents a re com m unica t ing and w hat they a re in te rac t ing abou t i s ju s t as s ig-
n i f ican t
as how
they in te rac t
and
c o m m u n i c at e .
Le t us use an example
from
a s tudy of a m ath em atics lesson repor ted by
Voigt (1 995,
pp .
173-174)
to show that there can be features of the learning
si tuat ion other than interac t ion tha t are a lso impo r tant fo r s tuden t s ' l e a rn ing .
Voig t described
how two
students , Jack
and
Jamie , went about so lv ing
a
group o f ar i thmetic tasks:
1 .
5 0 - 9 = 41
2 . 60-9 = 51
3. 6 0 - 1 9 = 41
4. 41 + 19 = 60
5.
31+29
= 6 0
6. 31 + 19 = 50
7. 32 + 18 = _
L et us take a look at how problem 7 was ta lked about by the boys.
Jack: U h-huh, that 's
18, not 1 9.
Jamie: Yeah , but th at 's 32 no t 31.
Jack: Oh
yeah
Jamie:
They're the
same th ing .
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1 .
T HE S P A C E O F
L E A R N I N G
Researcher: What's the
same thing?
Jam ie : These two. [He points to the 3 1 + 1 9 = 50 and 32 + 1 8 = _ ]
Researcher: Hang
on , I w as
asking Jack. Which
ones?
W e've
got 3 1
and 19.
Jack: Makes 50.
Researcher : Yeah.
Jack:
A nd
look,
32 and 18.
See,
its
jus t
one more
than that
[points to the task], and that 's one higher than that .
It can be
seen
f rom the
excerpt that
the
last task
w as
solved
by a
compen-
sation
s tra tegy, a s tra tegy that the boys actual ly had not u sed in the previou s
tasks.
S o,
this tas k
w as
handled differently from
the
previous ones.
In
other
w ords, the boys learned to handle the problem in a new w ay. V oigt (1 995)
used
the not ions "negotia t ion o f mathemat ica l meaning" and "meaning
taken as shared" (p. 174) for understanding and explaining students ' learn-
ing .
H e a rgu ed tha t wi thout the interact ion between the boys, this new
strat-
egy never would have emerged. Undoubtedly, th e interaction was o f
im po rtance for the s tud en ts ' learning . in this case . How ever, can this new
w ay of han dling the task, and hence the s tudents ' learning, be ex plained by
the interact ion and the negotia t ion of meaning
on ly?
W e be lieve we m ust
also
unde r s t and w ha t
it is
po ssible
to
learn
in the
s i tua t ion
in
order
to ac-
count
for
w h a t
the
participan ts actua lly learn.
If
w e
take
a
closer look
a t the
problem s,
it is
possible
to
look
at
this other
side of learning ; that i s , what i t w as possible to learn. To us as authors , it is
obv ious tha t
the way in
which this group
of
problems
w as
composed
af-
fected w h a t
i t was
possible
to
learn.
In
this group
of
problem s, there
was a
pa rticula r variation present. S om ething varied,
whereas other
things were
invar iant
be tween the problem s. Firs t o f all , there was a varia t ion between
addi t ion
and
subtract ion (problem
1
through
3 and 4
through
7,
respec-
t ively).
Further, if w e f irst an alyz e problem s 4 and 5 in detail , w e w ill find
another var ia tion , nam ely tha t
the
tenths chang ed both
in the f irst and the
second addend (from 41 to 3 1, and from 19 to 29, respectively). B oth these
addit ions have the same tota l sum ( i.e. , 60), bu t they have a different par t
par t -whole re la t ion .
Let us now
look
at
problem s
6 and 7.
Problem
6 in-
volves and
combines numbers
from
problems
4 and 5. Th e f irst
addend
is
the
sam e as the f irst adden d in prob lem 5 and the second a ddend is the sam e
as the second addend in problem 4. In problem 7,
there
is a change of the
one s in both the adden ds ( i .e ., increas ing from 3 1 to 32 and dec reasin g from
1
9 to 1 8, respect ively) . Obviously, there was a very system atic var ia tion in
the com posi tion
of the
problems.
W e
would
say
that
a
particular p attern
o f
var iat ion
w as
afforded
to the s tudents to exper ience. An d
from
the excerpt
ju st cited w e interpret that the students did discern a pattern of variation. For
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38
M A R T O N ,
R U N E S S O N , T S U I
instance, one of the boys said: "See, it 's ju st o ne more than that [points to the
problem], and that 's one high er than that." So , we w a n t to co nc lude tha t th e
afforded varia tion w as a feature of the learning si tuat ion that w as a lso s ig-
n i f ican t
fo r
s tudents ' learning.
In
these exam ples, w e have tr ied to poin t out a varia t ion tha t w as presen t
in the learning environm ent , a var ia tion tha t i t was possible for the learners
to exper ience. What w e a rgue for in the
fo l lowing
chapters is that this a f-
forded
variation is a cr i t ica l feature in re la t ion to the way in w h i ch the in-
tended learning is brought about , as w e l l as be ing a cr i t ica l feature fo r
students ' learning. The thesis o f th is book is tha t the dif ferences in w h a t the
students leam is to a large extent a funct ion of w hat they can poss ib ly leam .
W h a t
they
can possibly
leam
is a space of
learning co nstituted
by
tha t which
it
is
possible
to
discern.
In
the aforementioned example , there is cer ta inly an interact ion taking
place tha t contr ibutes to const i tut in g the space of learn ing. But the ser ies of
problems a lso cont r ibutes to c on s t i tu t ing the space of lea rn ing . W itho ut the
pa rticula r pattern
o f
var ia t ion tha t
is
embo died
in the
p rob lem s ,
the
s tudents
w ould not have been ab le to com e u p w i th the idea of comp ensa t ion , not in
that par t icular s i tuat ion, at least. In several places in th is book, w e give ex-
amples
of how the
space
o f
learning
is
cons t i tu ted
in the
in te r ac t ion .
In
chapter 5, chapter 6, and ch apter 7, for instanc e, we see how the teacher and
the s tudents join t ly co nst i tute the space of learning as the teache r takes on
the s tudents ' responses and opens them up for inq uiry and further develop-
m ent . W e a lso see how s tudents in te rac t ing in groups , jo in t l y cons t i tu ted the
space of learning by b r inging in their own cu l tura l and
da i ly
exper iences to
m ake sense o f the object of learning . For exam ple , in chap ter 6, w he n stu-
dents discuss h ow the appearance of the s loth sh ou ld be descr ibed, several
of them th ink tha t a ll eyes are b lack and tha t the re fore there is no need to in-
clude the color of the s loth 's eyes. In other w ords, they are not able to dis-
cern the color o f i ts eyes as a crit ic al feature . H ow ever , one s tudent draw s the
group's
attention to the
fact
tha t a rabbit ' s eyes a re r ed, thu s show ing tha t no t
all eyes are black. A nother s tuden t agrees w ith his observat ion. The group
f inally agrees on inc lud ing the color of the s loth 's eyes in the descn ptio n.
W hat is happ ening here is that through col labo rat ive inte ract io n, the s tu-
dents are able to br ing in dime nsio ns of var ia t ion tha t m igh t otherw ise be
neglected if students are not afforded the oppor tuni ty to in te rac t am on g
themselves.
W e are not
denying tha t
the
space
of
learning
may in
part,
or
ent ire ly,
be
const i tuted in the interact ion between students . However , the point we
w ould l ike to m ake is that reference is f requent ly m ade to interact ion (s tu-
dent centeredness, activity approach, task-based learning, etc.)
as
some-
thing that is inherently conducive to learning, without relating the inter-
act ion to what is learned. And that the l ived object of learning is—as a
ru le—not expla ined in any precise way. Interact io n, s tude nt centeredness.
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1 . T H E S P A C E O F L E A R N I N G 39
and so on, are assumed to be good for learning in
some
very general , but
rather vague sense,
and for
their
ow n
sake.
In this
book , we try to
establish
the precise
l ink between learning
and
condi t ions of learning.
This
link is established by m ean s of the relat ionsh ip
between the object of learning and the space o f learning, where the enac ted
object
of
learning
is
identical
to the
space
o f
learning, both
of
w hich refer
to
the ob jec t of learning as it real ized in the classroom . It is the ob jec t of learn-
ing that the studen ts encounter, and the ob ject of learning th at they ca n pos-
sibly
learn,
o r
learn about , making
it
into
a
part
of
themselves .
If we are
interested in how
students learn
to see
certain things
in
cer tain ways,
w e
m ust ask o urselves w hat c r i tical features of the ob jec t o f learning s tudents
can
possibly discern in a part icular classroom si tua tion . N obo dy can learn to
see
cer tain th ing s
in
cer tain w ays w i thout experiencing cer tain pat terns
o f
var iat ion. This s tatement is true in general as far as this kind of learning
( learning to see
som eth ing
in a
cer ta in wa y)
is
concerned,
and it
im pl ies that
very
specific
pat terns of variat ion are necessary condi t ions for the learning
o f—o r learning abou t— specif ic objects of learning.
Having
said that,
we do not
w ish
to
im ply that
i t
does
n ot
m at ter whether
th e
teaching
is
wh ole class,
or
whether students work
in
groups; w hether stu-
dents are engaged in task-based or problem-based learning, or in project
work;
whether teaching
is
student centered; w hether
IT is
used;
or
whether
there is a joy fu l atmosphere in the classroom or not . Differences in the way in
w hich the co nditions of learning are organized m ay u ndo ubtedly constrain or
facilitate the
constitution
of the
space
of
learning necessary
fo r the
develop-
m ent of a certain capab ility. But in order to understand how these differences
inhibit or facilitate the developm ent of a certain cap ability, w e have to under-
stand h ow
they con strain
or
facilitate
th e
constitution
of the
specific space
o f
learning necessary
for
developing that specific capability.
A nd
this under-
standing
can
never
be
derived
from
a
general
way of
organizing
the
condi-
t ions of
learning.
F or
this reason,
we can
never
truthfully
argue that
one way
of
organizing
th e
con ditions
of
learning
is, in
gen eral , bet ter than another w ay.
In
this book we try to develop a theore tical perspective and a conceptua l
f ramework
for
unders tanding learning
in
schools
in
t e rm s
of
w h a t
it is
poss i-
ble to
learn
in
schools.
I f we
know w ha t
the
studen ts shou ld learn,
and if we
know w hat condi tions a re necessary fo r them to learn , then w e co uld rea-
sonab ly
work toward creating those necessary condit ions. I t must be re-
m em bered, however , that
for
each
specific
capabil i ty
(of
seeing something
in a certain w ay ), there are necessary, specific con dit ions. Even i f w e know
in general that there m ust
be a
certain space
of
learning that
com prises di-
mens ions
o f
variation th at correspond
to the
cri t ical features defining th is
specific way of seeing a specific p h e n o m e n o n , we do not know w hat these
crit ical
features
are in
every specific case.
This "blessed
ignoranc e" is a
w eakness that
can be
turned into
a
strength
by en gag ing the teachers themselves in finding the missing insights that are
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40
M A R T O N ,
R U N E S S O N , T S U I
needed fo r achieving
different
par t icu lar educat ional a im s , and for develop-
ing speci f ic capabi l i ties an d par t i cu lar ly pow erfu l w ays of seeing part icu lar
phenom ena. Teachers focu s ing
on the
same ob jec t
o f
learning
can do so to-
gether by f inding the cr i t ical features in each case, creat ing what are be-
l ieved to be the necessary condi t ions fo r develop ing tha t capab i l i ty ,
check ing wha t
th e
stude nts leam
an d
w h e t h er
th e
co n jec tures were ju s t i f ied ,
revising th e fr amew ork if neces sa ry, check ing aga in , docu m en t ing th e pro-
cess as we l l as the ou t com es , and sharing it
w i th
o ther t eachers .
Teachers could
in
th is
w ay
par t i c ipa te
in the
co l lec t ive cons t ruc t ion
o f
professional knowledge , not on ly a s a par t of t he i r ow n profe ss ional devel -
opmen t but also as scientif ic research that m ay y ie ld new ins igh t s . Severa l
examples
o f
such
an
enterprise
are
ou t l i ned
in
c h a p t e r
8 of
th is
book .
E N D N O T E S
'T o be
fu l l y a ccu r a t e ,
o f
cour se ,
w e
shou ld say , "deve lop ce r t a in capab i l i t i e s
and values However , a l though
not
w i s h i n g
to
p l ace m o r e i m p o r t an ce
on one
r a ther than
th e
other,
th e
f o c u s
o f
th i s book
i s on the
d e v e lo p m e n t
o f
c ap ab i l i ti e s
r a ther than va lues ,
a s
th is
h a s
been
th e
f o c u s
o f o u r
s t u d i e s .
2
The pron oun "he" is used in a sex n e u t r a l s en se to a v o id a w k w a r d use o f "he o r
she."
3
A
reed re lay
is a device th a t w i l l cha nge a weak e lec t r i ca l cu r r en t in to a very
st rong cur rent when it is connec ted to e l e c t ri c c i r cu i t s . R eed r e l ay s a re u sed in
m any e lec tr ica l a pp l i ances tha t r equ i r e l a rge cur r en t s fo r o p e r a t io n , su ch a s e l eva -
tors, motors, and so on.
4
A light
d iode
resistor ( L D R ) ca n p r even t a n e l ec t r i c cu r r en t f rom pass ing
th rough a n e l ec tr i c c i r cu i t becau se of i t s g rea t res i s t a nc e . L ig h t d iode r es i s to r s a re
sensi t ive to ligh t . W hen exposed to b r i g h t l i g h t , th e r e s i s t an c e r edu ces , t h u s a l l o w -
in g the e lect r ic cur rent to pass th rough .
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O n
Learning
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2
Variation
and the Secret
of the
Virtuoso
Po
Yuk Ko
Ference Marton
MAKING
SYSTEMATIC USE OF
VARIATION
In chapter
1 , we
argued that whatever object
of
learning learners,
try to ap-
prop r iate , cer tain cr i t ical features
o f
that objec t have
to be
d iscerned, that
is ,
learners must learn to see cer tain s i tuat ions in cer tain ways. B u t learners
can
never discern anyth ing w ithout expe r iencing var iat ion. T he exper ience
of
pat terns
o f
var iat ion
specif ic
fo r different
objects
of
learning
is a
neces-
sary condi t ion for appropr iat ing those objects o f learning. If this is true,
then
success fu l
teachers mus t
b e
good
a t
con st i tu t ing such necessary con di-
t ions
in the
classroom, that
is, the
specif ic
pat terns
o f
var iat ion.
One of the
m am
po in ts o f th is book is tha t w e have m anaged to identify a cr i t ical factor
in
teach ing , a
factor
tha t d is t inguishes
be tween
teach ing tha t
m a k es
a cer-
ta in
learning possib le and teach ing that
fails
to achieve this . Th e em pir ical
compar i sons in chap ter 3 and chapter 4 demonstrate th is in greater detai l .
In
any
ins tance
o f
teach ing ,
there are
th ings that
are
repeated
and
there
are
thing s that vary.
On e of the
fea tures
of
good pract ice
and
pow er fu l peda-
gogy is the
eff ic ient
use of var iat ion and repet i t ion, whether i t be con-
sciously
or
less consciou sly .
Let us
look
a t an
example .
K w a n ,
Ng, and
C hik (2002)
offered a
por trayal
of an
innovat ive teache r 's
w ay of t r ansform ing the intended object of learning into an enacted ob jec t
of learning in the course of a double lesson in Chinese ( the class was a pri-
mary Grade
2
class
in
Hong Kong) .
T he intended object o f learning could be split into tw o in ter twined as-
pec ts that were n ot to be dealt with sepa rately, but at the same t im e. T he s tu-
43
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4 4 K O A N D
M A R T O N
dents were expected to become better at the fo l low ing sk i ll s : (a ) describing
animals , and (b) using the four language ski l l s in an in tegra t ive manner .
T he doub le
lesson
b u i l t on the previous lesson in w h i c h th e s tudents h ad
learned to discern
di f fe rent
aspects o f a pan da, such as i t s app earanc e (body,
head, four l im bs, color) and its movement . A s the po in t o f departure fo r the
double lesson, a 3-m inute film sequence w as shown to the c lass . In th e f i lm
sequence , th e s tudents s aw a young s lo th , w h o according to the na r ra to r h ad
lost
its
m other.
T he
s tudents
saw the
s loth c l im b down
f rom a
tree
in
search
of a new home, swim
across
a nearby river, and c l im b u p ano ther tree w here
it encountered
another sloth—which w as luck i ly f r iend ly—and t hus the
young s lo th found a new home.
The s tudents f i rs t watched the v ideo wi th the narra t ion, then watched i t
a ga i n wi t hou t
th e
na r ra t ive ( see ing , l i s t en ing ) . N ext they foc used
on the
sloth ' s appearance by discu ssin g it s var ious fea ture s (body, he ad, four
l imbs,
color) and its movement
(speaking, l i s tening) .
Then the
s tudents
w rote down th e i r descr ipt ions
on
overhead t ranspa rencies
and
showed them
to the re st o f the c l a ss (w r i t ing , r ead ing) . F ina l ly they appo in ted a m em ber
of the
group
w ho
c a me
to the f ront of the
c lass
a n d
ac ted
a s
na r ra to r
a n d
read
a loud the i r desc rip tion w hi l e the m uted f ilm seque nce w as rep layed on the
video (speaking, l istening ).
Dur ing
th e
lesson,
a
h igh ly co m plex pa t te rn
o f
va r i a t ion
w as
j o i n t l y c o n-
st itu ted by the teache r and the s tu den ts . Let us look a t some inte res t ing pa t-
terns o f var ia t ion and invar i ance .
To begin w i th , the s tudents were expected to
sh i f t
the i r a t t en t ion be tween
tw o
aspects
of the
an imal :
its appearance and its
m ovement.
W e
cannot
say
t h a t these
tw o
aspects var ied ,
but the
s tudents them se lves were a sked
t o
vary
the foc us of the i r a t ten t ion between the two
di f fe rent
aspects and the four
di f ferent par ts of the animal . This show s tha t va r ia t ion can th us be exper i -
enced by exp er i enc ing va r i a tion genera ted by the env i ron m ent ( e .g . ,
focus-
ing on
d i f ferent animals)
or by
varying
one's
at tent ion
o r
imaginat ion (e .g . ,
f oc us ing
o n d i f ferent a spec t s of the same a n im al ) . Fur the rm ore , va r i a t ion is
a lway s exper ienced aga ins t the backgro und of wh a t i s invar i an t . So the re -
fore w e
speak
o f "patterns o f
va r i a t ion
and
invar iance ."
In our
spec i f ic case
w e have th e fo l lowing :
Variation Invariance
di f ferent
a spec ts same an im al
and
Variation
Invariance
di f ferent par ts same aspect (app earance )
B y genera t ing two k inds of varia tion in re la t ion to the same an im al ,
differ-
en t
aspects
and
different parts
can be
discerne d.
B ut is
th is specif ic
to
th is ani-
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2.
V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O 45
m al? In order to generalize the acts of discernm ent, they have to be applied to
m ore than
o ne
an imal .
As the
same exercise
w as
also carried
out in
relation
to
a
pa nda dur ing the previous lesson, th is condi t ion w as ac tual ly m et .
Variation Invar iance
dif fe rent
an im als same ac ts o f d iscernm ent
(panda and s lo th) (be tween aspects , and between par t s )
So fa r w e
have been dea l ing w i th
t he first of the two
in tende d ob je c ts
of
l ea rn ing :
be ing ca pab le o f describ ing an an im al . W hat about the second in-
tended object
of
learning, using
the four language
skills
in an
mtegrative
m a n n e r ? A s a m a t te r o f
fact ,
the two in tended ob jec ts o f learn ing can be
b r o u g h t
toge the r
b y
app ly ing them
to the
same task : tha t
is ,
desc r ib ing an i -
m als in
speech
a nd in
w ritten
fo rm, and
tak ing par t
in the
desc r ip tion
by
l i s -
t e n i n g a n d r e a d i n g . T h e s t u d e n t s t a l k e d a b o u t t h e a p p e a r a n c e a n d
m ovem ent o f the s lo th , they wro te down the ir observat ions , they read eac h
other s ' observat ions , they com m ented on the fi lm sequence wh en the sou nd
w as
o f f ,
and they
l i s tened
to
each others' c o m m e n ts .
Variation
Invar iance
different same thing
described
com m unica t ive ac ts ( the s lo th)
W e can see here the double funct ions o f var iat ion, that is, tha t d i f ferences
between the
different
ac t s can be d iscerned when the i r
objec t
i s the same .
This
is
w h a t
w e
refer red
to as separa t ion in the
previous chap ter .
It is the di-
m e n s i o n o f co m m unica t iv e ac ts t ha t is be ing separa ted from other aspects o f
the relat ionship between the descr iber and the descr ibed, that is , between
the
s tudents and the s tory about the s loth . But because the object of these
ac ts is the sam e, com m onal i t ies a re b rought ou t as wel l : w ords , express ions ,
and sen tences .
Dif ferent
acts are d iscerned and broug ht together at the sam e
t ime. A
th ird pat tern
o f
var iation presen t
in the
lesson m akes
it
possib le
fo r
the
s tuden ts to ar r ive at the ins igh t that the sam e task can be c ar r ied out in
dif fe rent bu t
e qual ly correc t w ays . However,
th e
different w a y s
o f
d o ing
som eth ing on ly becom e v is ib le
if
they
a re
perceived
as
being
different
w a y s
of doing
t he
same
thing
(otherwise
different
acts and
different
tasks co-vary
and can not be separa ted from each o ther).
This
is exa ct ly the c ase in the les-
son
d iscussed here ;
the
sloth
i s
described
in
different w ays , t ha t
is, by
m e a n s
o f d i f ferent communica t ive ac ts .
The teacher in th is example is a Chinese teacher from Hong Kong . I n
fact,
a lmos t
all of the
examp les
in
this
book are
abou t Ch inese teachers ,
and
m ost o f them are
from
Hong Kong. St igler and Hieber t (1999) emphasized
that
teach ing is a cu l tural act iv ity a nd argued tha t teachers in different cu l -
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46 KO AND M A R T O N
tures follow different scripts. If so , is it the case that there is a spe cific Chi-
nese pedagogy, a Chinese script that is characterized, among other things,
by
an elaborate use of patterns of variation and invariance?
Is it reasonable at all to expect a speci f ic Ch inese pedagogy? Trying to
find
out
whe ther there
is one or not
wou ld
be an
im possibly large undertak-
ing because
of the
sheer vastness
and
va riabil i ty
of the
Chinese cu l ture.
A n
easier question to address—and one tha t for our purposes is ac tua l ly more
interes t ing— is this : W hat
are the
pedagog ical pract ices considered
to be ex-
emplary
in
C hina? This
was the
question addressed
by one
me mb e r
of our
team (Ko, 2002),
and the
fo l low ing sect ion bu i lds
on her
work .
A
L E S S O N
O N
S E M A N T I C S
In th is sect ion, we present a lesson tau gh t by an expert teach er in the Peo-
ple ' s Re publ ic of Ch ina (PR C; the lesson w as referred to br ief ly in cha p. 1) .
The t eacher is a "Special Rank Teacher," and the w inner of a pres t ig ious
s tate-granted tea chin g aw ard.
T he
do uble lesson
is a
dem onstrat ion lesson
that
w as
audiotaped, t ranscr ibed,
and
pu bl i shed (Qian , 1985) ,
in
order
to
dissem inate the teac hing expert ise of the teac her as a m odel lesson for his
counterpar t s
to follow. It
a l low s
us to see
w h a t
is
considered
to be
good ped-
agogy
in the
P R C .
The sample lesson is a reading lesson based on a prescribed text ca l led
"Semantics ," wh ich is a piece of exposi tory w ri t ing abou t the lexical m ean -
ings of w ords. In the lesson, the teacher a im ed to introd uc e several
l inguis t ic
concepts on semant ics , including th e
scope
of m e a n in g o f words; the level
of
generali ty
of
words ; homonym s, synonyms,
and
an tonym s,
and
thei r
us-
age. In the fol lo w ing , w e first describe the lesson and then a na lyze the varia-
t ional pattern.
S u m m a r y of the L e s s o n
Instead
of
in t roducing
th e
l inguis t ic know ledge direct ly ,
the
teacher started
w ith a s tory aim ing to i l lus t ra te that the m ean ing of words can vary a ccord-
ing to the co ntex t , and that i t is im portan t to be aware o f the co m plexity of
the me a n i n g o f words .
Afan t i
was a
hairdresser. There
was one
cus tomer ,
A h u n g ,
w ho
a l w a y s w e n t
to
A f a n t i ' s
p lace
to
have
his ha ir cut but
never paid
for the
service.
It
made
Afan t i
very
angry.
He
wan ted
to
p lay
a
t r ick
o n A h u n g . One day A h u n g
c a m e
t o Afan t i ' s aga in .
Afan t i f i r s t cu t
A h u n g ' s
hair .
T h e n
he
began
to
s h a v e A h u n g ' s
face, and
asked,
"Do
you w a n t
you r
eyebrows?"
A h u n g
rep l i ed ,
"O f
course
W hy
ask " Then,
qu ick
as a
flash, Afan t i
shaved
off
A hu ng 's eyebrows and said, "You wan ted your eyebrows, so I
w i l l
g ive them
to
you "
A h u n g was too m ad to say
any th ing ;
because
he had
indeed
said
he
"wanted"
his
eyebrows.
M e a n w h i le Afan t i
asked,
"Do you
w an t your
beard?"
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2.
V A R I A T I O N
AND
THE
S E C R E T
OF THE V I R T U O
A h u n g
had a
beau t i fu l
beard , and he imm ed ia te ly sa id , "M y beard? No, no I d o n ' t
w a n t my beard " B u t aga in
Afan t i
proceeded to shave off his beard .
A h u n g
s tood up
and saw an egg- l ike head in the m ir ror . [Both the teacher and
s tuden ts
l augh . ] Fur i -
ously, A h u n g reproved Afan t i , " W h y did you shave of f my e y e b r o w s and beard?" "I
w as on l y
fo l lowing
y o u r
orders, s ir "
Afan t i
a n s w e r e d calmly. There w as
no t h i ng
A h u n g cou ld
say to
tha t
After tel l ing the story, the teacher asked questions to help the studen ts to
unravel
the
ambivalence
of the
mean ing
o f
"want"
( in
Chinese,
y a o
(Pu tonghua)
2.1
T :
Af ter
l is tening to this story, do you know what kind of tr ick
Afant i
played on
Ahung?
Ss: Afan t i played a trick using the word "want."
T :
W hat did A fanti m ean by asking "Do you
'want'
your eyebrows?"
Ss: It
meant
"to give."
T :
Exact ly
It
mean t
"to
give."
You
w ant them, then
I
shave them
off
and
give them to you. Then what i s the meaning of the word
"want"
in "Do you
w ant your
beard?"
Ss:
"T o
keep."
T :
Yes,
it
me a n s
"to keep." But how did
A hung interpret
th e
w ord?
H e
st il l though t
i t was to
"give"
h im h i s
beard.
That's w hy he im -
media te ly answe red, "I don ' t wa nt it." A nd he fell in to the t rap.
S o you
see,
the
word
"want" has tw o
meanings .
It can
mean this ,
or it can
mean tha t. Afant i exploited
the
am bigui ty
of the
m e a n-
ing of "want" to trap A hun g. This story tel ls us i t is im portant to
master the m ean ing of a word a nd its scope of m eaning [Teacher
writes o n the blackboard: meaning, scope of m ean ing ] .
In the
story,
the
word
"want" (yao
(Putonghua) [-lc])
had two
mean-
ings
— ei ther "to keep" (liu (Pu tonghua) [ ̂ ]) or "to give" (gei (P u tonghua)
[ £«•]) acc ording to different contexts. Afant i exploited the am bigui ty of the
mean ing
o f "want"
(homonyms)
to
t rap Ahung. When Ahung interpreted
"want" as meaning "to keep," A fan ti deliberately interpreted the
"want"
as
m ean ing "to give," and vice versa. A s a result , Ah ung lost his eyebrow s and
his beard. In the teache r-led discussion that im m ediately fo l low ed the read -
ing, the teacher did not u se m etalan gu ag e (i .e., the term
hom on y m s )
to illus-
trate the semantics concept, but simply highlighted the complexity of the
mean ing
of
words .
Nex t ,
the
teacher showed
the
class some books
and
asked students
to
name them.
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4 8 K O A N D M A R T O N
2 2
T : . . . I first
w a n t
you to
look
at
some th ings
a nd
nam e them
[holding
up a
book] . W hat
is
this?
Ss: A Chinese book.
T :
[hold ing
u p
another book] W hat
is
th is?
Ss : An E ng l i sh book .
T :
[holding
up two
books tog ether]
I f w e put
them toge ther, wh a t
do
w e cal l them?
Ss: Books .
T: Narrow down th e scope.
Ss:
Textbooks.
T: [holding up a dic t ion ary] W hat is this?
Ss: A dic t ionary.
T: Is i t a book ?
Ss: Yes, it is.
T: W hat k ind
o f
book?
S s:
Re fe rence
book?
T: W hat are these three a l l togeth er?
Ss: Books.
T :
That's
right. Chinese book, textbook, book, the scope of the
meanings becomes b igger an d b igge r .. .
In this excerpt, we see that the teacher started with specif ic k inds of
books and
then asked
the
students
to
provide
a
general w ord that could cover
both kinds o f books. B u t w e also see tha t the teacher tried to he lp the s tu-
dents
to see the
differenc e
in
scope
o f
m e a n in g
b y
showing
how one
k ind
o f
book subsum es an other kind of book, such that lan gu ag e books are a kind of
textbook and textbooks are in turn a kind of book, jus t as a reference book is
also a kind o f book.
On one
hand,
th e
teacher cleverly juxtap osed books
at the
same level
of
specificity—a
Chinese languag e book
and an
English language book—and
showed that it is only necessary to go one level up in order to su bsum e both
books,
name ly
by
us ing
th e
word
"textbook."
Hen ce, there
is no
need
to
sub-
sume them both under th e very general term
books .
T he teacher then jux ta-
posed textbook and reference book, which are also at the same level of
specificity, and showed that the next level up to subsume both would be
"books." T he
class were therefore presented w ith three levels
o f
generality,
and the relationship between the examples w as a hierarch ical structure, that
is, with one subsum ing the other.
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2 . V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O 49
In order to help the students see the relat ionship b etwe en w ords of differ-
en t levels of generality, which is denoted by the word relat ion known as
h y p ony m s , the teach er varied the com bination of the spe cifics and the levels
of ge nerali ty. A s pointed out , th e com bination of the Chinese l anguage book
and the
Engl ish language book
can be
subsumed precisely under " text-
books," w hich is at a m ore gene ral level , but less precisely under
"books,"
w hich is a t a yet
more general level . However, when
the
co m bination
is of
var ious
types
of
books (i .e. , text books
and
reference books) ,
the use of the
word
"books"
is the m ost app ropriate.
The teacher helped the s tudents unders tand the semant ic features of a
book by con sidering w hat i s not a book ( i .e ., by us ing
con tras ts,
m en t ioned
in
chap .
1 ):
2 3
T :
...
[holding
up
pieces
o f
new spaper]
Is
this
a
book?
S s: N o ,
that ' s newspaper .
T: W hy is i t not a
book?
S s:
B ecause there 's
no t
enough [pages] .
S :
Eve n a pi le of new spaper ca n ' t be cal led a book. A book has a
cover,
a
new spaper do esn ' t .
S: N ot exactly. If I have a book, and I tear off the cover, the book is
still
a
bo ok. Pictorials also have covers,
b ut
they aren't c alled books.
S: A
book
is a
com pos i tion boun d
by a
cover.
T :
[ho lding
up an
exercise book] This also
has a
cover , hasn ' t
it?
B ut
w e
do n ' t c al l that
a
book .
A
book
is a
l iterary com posi t ion
bound by a
cover.
You can see
that w i th dict ionaries , r ight? [s tu-
dents nodded thei r heads]
T o be a
book,
it has to be
bound
by a
cover, and a t the
same t ime
it ha s to
fulfi l another requi rem ent :
that
o f be ing a compos i t ion . Books are bound compos i t ions .
This
is the
definit ion
of the
word.
Now can you
give
me the
defi-
ni t ion of a
textbook ?
S : A
textboo k
is a
composi t ion used
for
t each ing , bound
in a
cover .
T :
R ight Then please give
me the
definit ion
o f
th is C hinese book .
S:
A
com pos i tion used
for
teaching Chinese, bound
by a
cover.
T :
V ery good
W e put in
m ore l im i ts here. From
the
exam ple above
w e
can see that , from "book" to "textbook" to "Chinese book,"
w h a t
happe ns to the scope of m eaning?
Ss: I t
becomes narrower.
T :
Then
how
abou t
the
m eaning? Does
it
become m ore
specif ic , or
m ore genera l?
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50 KO AND M A R T O N
Ss: Specif ic
T: A gain , you have discovered a rule: the sm aller the scope of the
mean ing ,
the . . .
w h a t
. . . the
mean ing becomes?
Ss : The
m ore specif ic
the
m ean ing becomes .
T :
Then
how
about ,
th e
b igger
th e
scope?
Ss: The more general the meaning becomes .
The teacher varied the examples of "not a
book"
and looked at the fea-
tures they had in comm on and those that
differed.
Having a cover, for exam-
ple,
is
c er tainly
not a
cr i t ical feature becau se a l thou gh
a
m agaz ine
and an
exercise book both ha ve covers
an d a
new spaper does no t ,
a ll
three
o f
them
are not books. The defini t ion of the sem ant ic features of a book paved the
way for def ining
more
specif ic
k inds
o f
books,
fo r
example ,
the
l anguage
textbook. B y getting students to def ine what a language textbook is, the
teacher demonstrated tha t
as the
scope
o f
m ean ing ge ts narrower ,
t he
m e a n-
ings
of the
words
get
m ore specif ic .
The teacher also t ried to relate scope of m ean ing to levels of gen eral i ty .
From book to textbook to langua ge book, the scope becom es sm al ler and
smaller. From
book to
textbook
to
langua ge book,
the
level
o f
gene rality
be-
comes m ore
and
m o re speci f ic .
T he
teach er used several
d i f ferent
contex t s
to
i l lus t rate
how
words
a t
d i f -
ferent levels
of
generali ty should
be
used
in
relat ion
to d i f ferent
contex t s :
2.4
T : S o, I 'd
l ike
to
ask, should
we be
more speci f ic
or
more genera l
w h e n w e
make choices
o f
words
in
w ri ting
an
essay?
S :
Somet imes
it is
better
to be
specif ic ,
bu t
somet imes
it is
better
to
be general .
T : A ny
examples?
S: I f
somebody asks , "How m any books
do you
have?"
A nd you an-
swer, "I have one m a th , one Chinese, one Engl ish , one phys ics
and on e chem istry book, so five book s in total ." That w ou ld be
very clumsy.
W e
w ould just say,
"I
have
five
books."
T :
Any o ther com m ents?
S : Sometimes w e should be more sp ecific. For exam ple, if that is a
rabbi t ,
w e
should
no t
ju s t g ive
a
general answer
and
only
say
tha t
it is an a n i ma l .
T:
V ery good.
In
w riting
and
speaking,
how
should
w e
choose
our
words? More specific ones
or
more general ones?
It
depends
on
th e need of individual expressions. B e specific when necessary.
T he same applies to being general. Your b iggest problem w hen
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2.
V A R I A T I O N A N D T H E SECRET O F T H E V I R T U O S O 5_[
choosing words
is
that
you
tend
to be too
general
and
vague when
you
need
to be specific. You saw a
rabbit,
but you say you saw an
animal .
S o
people don't know what
y ou
actually saw. Could
you
give m e
some examples
of us ing
words with vague meanings?
...
Afte r
dealing with levels o f generality, th e teacher dealt with another
type
of
word
relation:
synonyms.
To bring out
this kind
of
word relation,
the
teacher contrasted
it
with homonyms, which
had
already been covered
in the story of
A fan t i.
Although
homonyms
are
words
with two meanings,
synonyms
are the opposite; that is , the same meaning denoted b y
d i f f e ren t
words.
In
other
words,
synonyms
are
understood
in the
context
of the
rela-
t ion
between meaning
an d
word; synonyms being
o n e
kind
o f
meaning
word relationship
and
homonyms being another kind
of
meaning word
re-
l a t i onsh ip .
2.5
T :
. .. So , now w e come to another question. In the story w e men-
tioned, the word "want" used by Afanti has two meanings. But
there
are
other situations where
one
meaning
can be
expressed
by
a
number
of
words.
Can you
give
me
some examples?
S : For example "see," we sometimes use d i f ferent words like look
up
at, glance at,
"look
down, etc. All these basically mean
th e same as
"see."
T:
Very good. These
are the d i f ferent
interpretations
of the
word
"see." Now, I'd like you to find some
more
examples of different
words representing the same meaning.
S :
Father, daddy, papa.
T:
Y ou
learned
a
noun
in the
Poem
of
Mulan recently. What
was i t?
S:
Pater.
T: Father, daddy, papa,
and
pater
are a ll in the
same semantic scope.
L et
u s illustrate the scope o f meaning by circles. F o r example,
book, textbook,
a nd
Chinese book [teacher draws
a
circle
on the
bo ard] . If this circle indicates
"book,"
then where should w e p u t
the word textbook?
Ss:
Inside
the
circle.
T :
[drawing another circle] Then,
h ow
about
the
circles
o f
pater,
f a-
ther , daddy, and papa?
Ss:
They
are of the
same size.
T: Al l
these four circles
are
overlapping.
W e
call these four words
synonyms.
W e
also consider them equivalent
as
they share
the
same meaning....
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52 KO AND M A R T O N
Because
the
teacher contrasted these different examples,
the
students
be-
came aware of the two different re la t ionsh ips be tween w ords and m eanings ,
that
is, the
dif ference be tween hom onym s
and
synonyms.
Follow ing th is , the teac her drew the stude nts ' at tention to the use of syn-
onyms . Different examples were used
to
i l lustrate t ha t
d i f ferent
synony-
mo u s
words
should
be
used
in
differen t contexts
for
exam ple: form al versus
informal ("father" vs. "daddy" or
"papa");
t echnica l versus nontechnica l
("sodium
chloride"
vs. "salt"); and different degrees of politeness ("wrinkly
old fel low" vs. "Grandpa").
The teacher then revisi ted the
different
levels of gen eral i ty.
2 6
T: S , please read out the first and second paragraph. [The student
reads
it
ou t ] W hich sen tences have
you
m a r k e d?
S :
I
have m arked
the
las t sentence
in
bo th paragraphs .
The two
tha t
talk abou t the concepts of "ship" and "paper."*
[*The last sentenc es
in the two
paragrap hs are : "The conce pt
tha t
'ship'
as a kind o f marine transportat ion vehicle is generalized
from the comm on propert ies tha t all sh ips share," and "The c on-
cept of
'paper'
is a lso ge nera l ized
from
the com m on proper t ies
shared by all paper."]
T: Now I ask you, how does the general concept of "book" come about?
S: I t c o me s f rom the com m on proper ti es tha t are shared by d i f ferent
kinds of books .
T :
Then w ha t a re the com m on proper t ies o f books?
Ss:
They
are
b o u n d
by a
cover.
T :
A n d . . . ?
Ss: They are com posi t ions bou nd by a cover.
T: These
are the
com m on properties that every book has . W ith these,
w e can generate the concept of book. The con cepts of
"ship"
and
"paper" a re also g enerated l ike this . Thu s, we can unders tand the
creation
of a
concept.
S ,
could
you
please read
th e
following para-
graph? [co nt inues to read, from "Comrade M ao Zedong" to
"these tw o books"] W hat sentences have y ou m arked?
Ss: [most s tuden ts] This one: "In select ion of w ords , one m us t be
clear about the meaning and the scope of meaning in order to
choose
an
accu ra t e
and
sui tab le word."
T :
Have
you
no t iced wha t Com rade
M ao
said? This rem ark
is
in ter-
est ing. A ccording to our theory, have you
seen
th e word "men?"
S s:
[some] Yes,
w e
have, [some]
N o , we
h a ve n ' t,
no t
acco rd ing
to
the
book .
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2.
V A R I A T I O N
A N D T H E S E C R E T O F T H E V I R T U O S O 53
T : N o n e of you have seen the word
"men."
"Men" is an abs t rac t
concept . W hat we see are Cheung , Lee , W ong, Ch iu , and so on .
They are concrete , real people. W hat i s the relation between the
concept "men"
and all
real people?
S: A ll
real people have general propert ies .
T :
— The com m on proper ti es genera te a concept . Have you seen
the word "building?"
Ss:
N o.
T: W e see the
words "teaching block,"
"classroom," and
"our
ow n
flats," w hich are our
"homes."
A ll these are the solid "bu ildings"
that
w e can rea lly touch .
In
t h i s exce rp t , t he t eache r r e f e r r ed back t o t he d i s cus s ion abou t
"books"
a n d
a sked s tuden t s
to
n a m e
th e
c o mm o n p r o p e r t ie s
o f
d i f fe ren t
kin ds of book s . Then the teac her gave a
fu r ther
i l lu s t r a t ion o f the con cep t
of the
d i f fe ren t
l evel o f ge nera l i ty o f w ords . For exam ple , "bu i ld ing" i s a t
a h ighe r l evel o f ge ne ra l i ty o r abs t rac t ion than "teaching block," w h i ch
r e fe r s to a s p e c i f ic b u i l d i n g .
Af te r c la r i fy ing
th e c o n c e p t , th e t e a c h e r
g u i d e d
the s tudents to apply the knowledge to an exerc i se in the t ex t -
b o o k .
In
the
las t par t
o f the
lesson,
the
teacher in t roduced another w ord re la-
t ion
in
semant ics , tha t
is ,
antonyms.
H e
first asked s tudents
to
s u g g e s t
w ords w i th cont ras tive m ean ings (em inent -m ediocre , c lever-stup id , a r -
rogant-modest). B y
search ing
fo r
examples
to
e xem pl i fy an tony m s , s t u -
dents foc used on the cr i t i ca l fea ture s o f these types o f wo rds— con t ras t in
m e a n i n g .
2.7
T: Now we w i ll d i scuss another phenom enon in semant ics— con-
trast
in
m eaning . Could
you
please tel l
m e,
w h a t
is the
term
for
words wi th contras t ive meaning?
Ss: [all ] A ntonym s.
T : Can you g ive m e some examples o f an tonym s?
S: Em inent and m ediocre .
S:
Clever and s tupid.
S: Arrogant and m odest .
T: I t seems qui te easy for you to give examples for an tonym s . W ha t
I real ly want you to focus on i s how m uch un ders tanding an t-
onyms
can
help
in presenting our ideas? For
example,
when we
grasp the pair "arrogant" and "modest," h o w c a n we present our
unders tanding o f these antonyms? Comrade M a o h a s stated ...
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5 4 K O A N D M A R T O N
S :
"Modesty helps
you
improve, arrogance makes
you
decline."
T: Y ou see, w e express our ideas from both the posit ive and neg a-
tive p oint of view. W hat is the advantage of doing this?
S: W e can present our ideas com prehensively.
S:
Thoroughly.
T: Co m prehensive, thorough, are both correct . A n addi t ional point
I
w a n t to m ake : L anguage presented in a thorough w ay requires
our own
thorough th inking.
It is
better
to
consider
a
problem
from both the posit ive and negative sides. Thu s, ma stering rich
antonym s can a lso help us to consider a problem thoroug hly. I
wil l
w ri te som e w ords below
and I
w a n t
you to
tell
m e
their ant-
onym s. Then, please use these antonym s to com pose a sentence
in
order to show th e meaning of these words.
[Teacher writes praise, arrogant , good . Students state the ant-
onyms:
condem n, modes ty , bad ,
and the teacher w rites them down
on
th e
board.]
T : Now , please use these words to make sentences. Remember,
present them
in a
thorough way.
S:
It is
good
to be
praised. How ever,
it
wo u l d
be bad if we
became
arrogant .
T: Good Then w hat should w e do after being pra ised?
S:
The
m ore praise
w e
receive,
th e
more mo dest
w e
should
be . W e
not
only learn
from
criticism,
w e also
appreciate praise.
T: You see,
after
learning these anton ym s, we can tackle a problem
thoroughly, and present our ideas met icu lous ly . OK, we wi l l stop
here . I hope w e have a good com m and of
an tonyms— help ing
u s
toward a deta i led presenta t ion; the more antonyms we master ,
the more complete will be our meaning. After school, please
read the rest of this intellectual short essay, "S em antics 1 ," and
m ark the im portant sentences.
T h e Sys tema t i c
Us e o f
V a r i a t i o n
in the
Lesson
A t the beginning of this chapter, w e proposed that a systematic use of varia-
t ion m ight
be a
specific
feature
of
Ch inese pedagogy,
o r at
least
o f
wh a t
is re-
garded as good teach ing in Ch ina. The lesson "Sem antics," w hich was taught
by a state-selected expert teacher, exem plified that the teac her use d variation
system atically to create an optimal space of learning for the students.
There
are several
different patterns
of
variation-invariance
in the
lesson.
For example, the story of Afanti highlighted a variation between w ord and
m eaning: tha t is , the concept tha t one word ("want") s ignif ies t wo m e a n -
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2.
V A R I A T I O N A N D T H E S EC R ET OF T H E V I R T U O S O 55
ings
("keep" and "give") was
illustrated
by
making
the
word
("want")
invari-
ant while varying the meanings ("keep" and
"give").
This allowed students to
discern
a split between word and meaning (cf.
"separation,"
mentioned in
chap.
1).
When introducing
the
concept
of
synonyms,
the
variation
of
word
and meaning
w as
used again.
T he
concept
of synonyms w as
highlighted
b y
keeping
the
meaning (e.g., "see") invariant
and
varying
the
words used
to re-
fer to this meaning (e.g., "see," "look up, glance at, "look down ), which
al lowed students to see that th e same meaning could be represented by differ-
ent
words. B y varying the relationship between word and meaning, students
were guided
to
discern
the
complex relationship
a nd
also
to
discern
th e differ-
ence between homonyms and synonyms.
Homonyms:
Variation Invariance
meaning word
Synonyms:
Variation Invariance
word meaning
T h e
awareness
of the
level
o f
generality
o f
words
w as
highlighted
b y
another
set of
variation, namely "books"
as a
category,
and
d i f ferent types
o f books (e.g., Chinese book, reference book, and textbook). When the
teacher guided students to compare the lexical meaning of "book" with
categories that were within
the
scope
of
meaning
of "book,"
students dis-
cerned that there were d i f ferent levels o f generality within th e same cate-
gor y o f words.
Variation
Invariance
level of generality category ("books")
Another pattern
of
variation
was
used
to
illustrate
the
relationship
be-
tween words an d contexts. T h e teacher drew students' attention to d i f fer-
en t synonyms
and
their level
of
generality. This
was
done
by
keeping
the
words (the
d i f fe ren t
synonyms) invariant a n d varying th e contexts. Stu-
dents' attention
was
drawn
to
focus
on the
match
or
mismatch between
words
and the
d i f ferent contexts,
an d
they were also made aware
o f the im -
portance
of the
usage
of
words
in
relation
to the
contexts. What
is
interest-
in g i s the w ay in which th e teacher tried to simultaneously bring into th e
students' awareness what
was
covered
in the
previous episode, that
is, a
k ind
of
word relation that pertained
to
levels
of
generality,
and the
critical
semantic features of a word or a phrase.
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5 6 K O A N D
M A R T O N
Variation
Invar iance
con text synonym s ( i .e ., one synonym at a t im e)
When
the
dist inct ion between
the
synonyms
w as
clar if ied
by
m e a n s
o f
showing their appropriateness to one context but not to another, the teacher
also dem onstra ted that the appropria te synon ym s var ied w ith con text . This
is an example o f "fusion" as described in chapte r 1
(i .e., fusion
between syn-
onym and context ) .
T he
teacher constructed
the
lesson coherent ly
by
m e a n s
o f
correlated
var ia t ion. The l inguist ic concepts in this lesson were not introduced dis-
cretely; but were closely linked together by the teacher's use of the same
word
as
example
or
coun te r example .
F or
ins t ance ,
the
word
"books"
w as
used
to
i l lustra te concep ts th at have d i f ferent
bu t
re la ted m e a n i n g s .
I t w as
also used to il lustrate the difference be tween nar row and wide scope of
meaning (Chinese book, reference book, and books, respect ively) . And in
the la t ter par t of the lesson co ncerning synonym s, the exam ples book,
text-
book, and Chinese book were referred to again, a s a contrast to a new set of
exam ples, pater , father, daddy, and papa , in order to
i l lustrate
tha t the latter
shared the same scope of m ean ing. Likew ise the w ord "want" w as used in
the
story
o f
Afan t i
to
i l lu stra te that
th e
w ord mean ing r e l a tion
can be
a m b i g -
uous , and was la te r used aga in as a coun te rexam ple of synonym s.
This
analysis shows that
the
teacher used var ia t ion constant ly
and
sys-
tematically to raise students' awareness of the
richness
of the meaning of
words,
as
w e l l
as the
higher order structure
o f
words, such
as
h o m o n y m s ,
narrow-wide scope o f m eaning, spec if ic -genera l m ean ing, synonyms, ge-
neric and
specific
re fe rence , and antonym s.
A N O T H E R
TH E O RY
OF VARIATION
In chapte r
1 , we
presented
a
theory
o f
learning tha t revolves aroun d
the
con-
cept of
var iat ion.
In this chapter, we described two d i f ferent examples of
teaching carried
out by
Chinese teachers
w ho
bo th made pedagog ica l ly
so -
phist icated use of varia t ion. B asing our assessment on the a fo rement ioned
theory, both teach ers are doing a good job and can be expected to m a k e u se
of var ia t ion in pedag ogical ly po w erful way s. I t shou ld be noted that another
theory
o f
learning based
on
variation
w as
presented long before
our
own,
b y
a mathemat ics educa tor
from
Shan ghai , Gu Lin gy uan (Gu, 1 991) . Interest-
ingly, unl ike our theory, which was der ived from our character izat ion of
learning in the edu cat iona l context , Gu developed his theory indu ctively by
observing cases o f good practice, that is, cases o f teach ing tha t resul ted in
good learning. So , in a way, Gu 's theory o f variation is itself a depict ion of
features o f good
Chinese
pedagogy.
Gu's theory
is
more psychological ly or iented than ours (which
is an ex-
per ient ia l theory) , insofar as Gu is character izing learning—notably the
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2 . V A R I A T I O N
A N D T H E S E C R E T O F T H E V I R T U O S O 5 7
learning o f m athem at ics in term s of
three
consecutive, h ierarchically orga-
nized levels of functioning, or educational goals. The following brief ac-
count
of som e parts of his theory is adm ittedly colored by the
fact
that one
theory (Gu's) is here seen through the lenses of another theory (our own).
W hat fo l low s is our understanding of Gu 's theory on the way in w hich the
m astery of the levels of m athem atical insights can be achieved by m eans of
consti tuting different patterns
of
variation.
1 .
U n d e r s t a n d i n g
th e P r o c e d u r e s o r
Pri nc i p l es
This section
is
about
th e
ways
in
w hich
it can be
m ade possible
for
students
to
discern
th e
critical features
of a
certain concept
or
principle.
Due to the
fact
that Gu developed his theory within the field of geometry and only subse-
quently
gen eralized it to other fields of m athem atics and to other school sub-
jects ,
w e use the geom etrical i llustrations from G u's original pu blication.
a. Widening of the concept , b y blocking o ut eatures erroneously assumed
by s tudents to be cri t ical features of the concept . For
instance, s tudents
most ly think in terms of s tandard f igures , tac i tly (and erron eously) assum -
ing that th e difference s between s tandard a nd nonstandard figures represent
critical
feature s (see F ig. 2.1) .
In th is case, the variation builds on the teacher ' s understan ding of the s tu-
den ts ' understanding of the concept prior to the inst ruct ional sequen ce.
b. M a k in g
it
possible
for the
s tudents
to
discern what
is
taci t ly under-
s tood, by
me a n s
o f
contrast ing noninstances.
F igure 2.2 is an example .
c. M aking i t possible or the s tudents to m ake d is t inct ions be tween cases
that they t reat
as
m e m b e rs
of the
same se t .
Here , contrast ing cases
are
intro-
FIG. 2 . 1 . Dist inguishing b etween essential an d nonessen t ial features by contrasting
standard
and nonstandard
figures. From
L . Gu (1991) , Xuehui Jiaoxue
[Learning
to
teach],
p. 68.
Beij ing, PRC : Peop le 's Educat ion Press .
Copy right ©
1991
by Gu
L ing
Yuan.
Reprinted with perm iss ion.
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58 K O A N D M A R T O N
duced
in
order
to
make
the
dist inctions
possible. T w o
examp les
are
shown
in Fig. 2.3.
A ll three of these different ways of contributing to make i t possible for
the students to discern the cri t ical features of the concept or principle in
quest ion,
presuppose
that
the
teacher
has a
good unders tanding
of the
stu-
dents 'preconce ived ideas and of their hab itual w ays of deal ing w i th the con-
cept. T he first pattern of variation corresponds to gen eralizat ion and the two
other patterns to
contrast
as defined in chapter 1 .
2.
U n d e r s t a n d i n g
the
Process
of
Fo rmi ng
the
Procedures
or
Pri nc i p l es
This
sect ion h as to do w ith Gu 's observation tha t s tudents
f requent ly
have
difficulties discerning the figure-ground structure o f geom etric form s, that
is, w ith the qu est ion of discernm ent of wh oles and parts of pa rt icular in-
stances ra ther than the discernment of features across instances. This is
very m uch l ike the discernm ent (or del im ita t io n) of the deer and i ts parts
discussed
in
chapte r
1 .
The dis tinct ion between the discernm ent of
features
and the discernm ent
(o r
de l imi ta t ion)
o f
parts
and
wholes reminds
us
that
the
lat ter
w as
intro-
duced
b y
Svensson (1976)
to
characterize
differences
in the
unders tanding
of the
sam e text. (Svensso n arg ued tha t readers differ
as to how
they de l imi t
the
w holes
a nd
parts
a nd
therefore ma k e different senses
of the
same text.)
FIG. 2.2. D i s t i ngu i sh i ng be tween
the
presence
and
absence
o f
essent ia l f ea tures
by
contras t ing conceptua l and n o n c o n c e p t u a l
f igures .
From L . Gu ( 1 9 9 1 ) ,
Xuehui
Jiaoxue [Learning to teach] , p . 69. Be i j in g , PR C: People ' s Edu ca t ion Press . Copy-
r igh t © 1991 by Gu L i n g Y u a n . R e p r i n t e d w i t h pe rmiss ion .
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2 . V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O
59
F IG. 2 .3 . Foc us ing
on
e s se n t i a l f e a t u r e s
by
om i t t ing t he m . F r om
L. Gu
( 1 9 9 1 ) ,
Xuehui
Jiaoxue [Lea rn ing to teach] , p. 70. B e i j i ng , PR C : P e op l e 's E du c a t i on P r e s s .
C o p y r i g h t
©
1991
by Gu
L i ng Y ua n . R e p r i n te d w i t h pe r m i s s i on .
This dis t inct ion between the tw o form s of discernm ent i s discussed in m ore
detail in chapter 3.
T he
k ind
of
variat ion th at
Gu
proposes
to
make
i t
po ssible
for the
s tudents
to
discern the
part-whole
(and figure-ground) structure, is the trans form a-
t ion o f the
same
figure
through rotat ion
and
otherwise (see F ig. 2.4).
The s tudents can in th is w ay discern how com plex f igures are com prised
of s imple f igures. Another example can be seen in F ig. 2.5.
FIG. 2.4. Se para t ing geom etr ica l ta rgets f rom c om p l e x b a c kg r ounds b y va r i a t i on .
F r o m L .
G u
( 1 9 9
\) ,
Xuehui
Jiaoxue
[Lea rn ing
t o
t each] ,
p . 73.
B e i j i ng , PR C : P e op l e ' s
E duc a t i on P r e s s . Copy r i gh t © 1991 by Gu L i ng Yua n . R e p r i n t e d w i t h p e r m i s s io n .
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60
K O A N D
M A R T O N
F I G . 2.5. Sep ara t ing com po nen t par ts o f geom et r i ca l f igures b y
s tr u c tu r a l \ a n a t i o n .
F r o m L . G u (199 ) ,X u e h u i J i a o x u e [ L e a r n i n g to teach] , p. 74.
B e i j in g ,
P R C : P e o p l e ' s
Educa t ion
Press . Copyr igh t
©
1991
by Gu
L i ng Y ua n .
Rep r i n t ed
w i t h p e r m i s s i o n .
3. D i s c o v e r i n g New
Procedures
and
P r in c ip l e s
by t h e S t u d e n t s Themselves
This is the third form of variation in the sense that here th e students produce
variation,
or
open their m inds
to
variation (rather than enc oun tering va riation),
within constrains
posed by
questions. This type
of
variation
is
illustrated
in
chapter
3,
when
w e
look
at the
open-ended problem
of
"the p ostm an's route."
VARIATION
W I T H
REPET I TI ON — TH E
F E A T U R E
O F G O O D TE AC HIN G IN CH I N A
Unti l
recently,
teaching
in
m ainland China
w as
m ostly described
as
conser-
vative,
textbook -oriented,
and
charac ter ized
by
teache r-centered rote learn -
ing
(e.g. , Cleve rley, 1985; Se ybolt , 1973). Som e resea rch ers, su ch
as
L e u n g
(1991), claimed that the conservat ive features mainly s temmed from tw o
tradit ions: the C onfu cian pedagogica l t radi tion , and the Sovie t m ode of in-
struction. This resulted in a hybrid pattern of
t each ing
and l e a r n i n g
tha t
w as
more
or less textbook-based, teacher-centered, and
con ten t -over loaded .
T he
predominance
of
drilling
and
repet i t ion
in
Chinese c lass rooms sug-
gested
that Chinese teachers believed that repeti tion skil l dev elo pm en t
should precede interpretat ion (Gardner 1989).
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2.
V A R I A T I O N
A N D T H E
S E C R E T
O F T H E
V I R T U O S O
6 ^
Som e studies, as represented by Pa ine's (1 990) work, described the dis-
t inctive
teaching pract ice
in
modern China
as
being
a "virtuoso model"—
hen ce the t i t le of this chapter. In Ch ina, direct w hole-group instruction an d
teacher ta lk were found to be prevalent in classrooms. Paine (1990) ob-
served that
"It is
this f lair—a special t iming,
an
elegance
of
language ,
a
power
of
expression— that dis tinguishes
the
great teach er
from the
ordinary
one '
1
(p. 69).
S he
recognized
the
shortcomings
of
this model
in the
sense that
the
teacher plays an active role whereas the students have a passive role; the
teacher i s the actor, the s tudents the audienc e. She com m ents that
A l t h o u g h t e ache r s in C h i n a f r equen t ly v o iced conce rn abou t r e ach ing th e s tud en t s ac -
ademica l ly , t h e
l i te ra ture
and in te rv iews w i t h t e ache r s sugges t tha t th e m a i n i n t e l l ec-
t u a l
th rus t
o f t each ing c e n t e r s on the t e a c h e r s ' p e r f o r m a n c e an d m i n i m i z e s o r
i nadver t en t ly neg lec t s
th e
in t e rac tiona l p o t e n t i a l
o f
c l a s s room expe r i ence . A da p t i ng
t e ach in g to par t i cu la r aud iences , t hou gh c l ea r ly th e m a r k of a good teach er , is no t a
necessa ry r e qu i r e m e n t of the f ine c l a ss room pe r fo rm er , given the d o m i n a n t co n c e p -
t ion
o f the
t e ache r ' s
role .
( Pa in e , 1990,
p. 6 8)
However, Paine admits that despite
the
negat ive impl icat ion
o f
th is
mo de l , the emphasis on teaching as a vir tuoso performance incorporated
both a
recognition
o f the importance of
know ledge
and an
acknowledgment
of the role of personal , humanis t ic qual i t ies o f aesthetics, af fect ion , and
com m itm ent in t each ing .
Cheng (1 992)
had
similar view s
on the
pract ice
o f
t each ing
in
China ,
and
used the metaphor of "drama" to describe it:
So m e t im es , I t h i n k , to t e ach a lesson in C h i n a is to be l ike an a c t o r p e r f o r m i n g a
dr a ma . E v e r y t h i n g s h o u l d be p l a n n e d in deta i l ; ev e ry ac t ion shou ld fol low the scr ipt .
T h e r e
is no
room
for any
m i s ta k e s .
T he
lesson plan
is
j u s t
l ike
the scrip t of a
d r a m a ,
(p .
107,
in
C h in es e ,
ou r
t rans la t ion )
Cheng (1992) believed that the emphasis on strict lesson planning may
have
an
undesirable
effect , as it
reduces
the
opportunit ies
for
students
to
contribute to the plan ning o f the lesson. H ow ever, Cheng points out that the
emphas i s
on
serious lesson planning reflects
the
conscientious at t i tude
of
teache rs in China that contributes to m aintainin g the quali ty of the teac hing
profess ion
in the
country .
It
sho uld be noted th at there is also other— m ostly more recent— litera-
ture that portrays
the
Chinese classroom
as
interactive
and effective.
These
works argue that
the
whole-class ins t ruct ion method commonly
found in
Chinese classrooms al low s each chi ld to have the m axim um opportunity to
benef i t
from the
teacher,
an d to
enhance conceptual unders tanding;
and
tha t
it is this that contributes to the excellent perform ance of Chinese students in
international academic campaigns (Stevenson & Lee, 1997). These re-
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62 KO AND M A R I O N
searchers have also found that Chinese classrooms are active, and that stu-
dents participate in though t-provoking tasks o r ques t ion ing (Co rtazzi 1998;
Cortazzi
&
Jin, 2001). Some researchers
are
also interested
in
t racing
the
historical origin
o f
some
of the
dist inct ive perceptions
o f
t e ach ing
and
learning in Chinese c lassrooms. They ident i fy the impact of Conf uc i a n
views of teaching and learning on educat ion in C hin a and some o ther East
A sian coun tr ies , as the C onfuc ian-her i t age-cu l tu re (CH C) l ea rne r phenom -
enon (e.g., Biggs, 1996;
Ho,
1991).
These
researchers
try to
associa te som e
of the dom inan t learning approaches adopted by studen ts in the East A sian
countr ies w ith the C onf uc i an cul ture . They p oin t out tha t a l th ou gh Ch inese
classrooms
are
apparently
full o f
rote learning,
the
repetit ion
is
used
by the
learners
as a
means
to
enhance unders tan ding. These researchers a rgue tha t
the emphas is on repe t i t ion and memor iza t ion should not s imply be d is-
m issed as conservative , as Ch inese teachers a lso em ph asize reci ta t ion w ith
ref lect ion,
and
m em orizat ion w ith un derstan ding (B iggs, 1 996; Lee , 1996) .
B y
us ing
a
combina t ion
of the
variation theory
o f
lea rn ing presented
in
chapte r 1 , and Gu 's theory o f variation as a con cep tua l f ram ew ork , Hu ang
(2002) recently character ized mathematics teaching in China (more pre-
c ise ly in S hangha i ) as be ing both h ig hly teacher -cente red and h igh ly s tu-
dent-centered ( if we use "teacher-centered" in the sense of the enacted
object
of
learning
being close to the
intended object
of
learning,
and
"stu-
dent-centered" in the sense of the s tudents owning the space of learning,
that is , tha t they par t ic ipate in br inging it abou t) . Those lessons
tha t
a re con-
sidered
to be
good
in
China
are
p lanned, cho reographed,
and
w e l l t h o u g h t -
out lessons. B ut their e laborate design never theless stil l offers p lenty o f
space for the s tuden t s ' ow n independen t and spon taneou s ideas . T he s tu-
dents
a re
h ighly ac t ive
and
they
pay
a t tent ion
to the
teacher .
In a
s imi la r way .
the teacher, having thoroughly orchestrated the lesson, can fully focus on
the var ious ideas the s tudents com e up w ith. B y usin g her previou s exper i-
ences
and her
know ledge
o f the
w ays tha t
the
s tudents often th ink a b o u t
the
specific objects o f learning, the teacher is able to ant ic ipa te wh at the stu-
dents
are
going
to
come
up
wi th spontaneously .
T he
m a them a t ic s le sson
from
a Shanghai c lassroom descr ibed in chapte r 3. is ano the r example o f
this
way o f
teaching.
A s w e
a l ready m ent ioned , Pa ine (1 990) a rgued tha t
in
the Chinese c lassroom , the teacher is the perform ing actor w hereas the s tu-
dents m ake up the pass ive audience . A more accu ra te m etaphor w ou ld be ,
w e believe, to see the teacher as the director, and the s tudents as the actors
playing
in accordance
w i th
a
script that they ha ve never seen.
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3
D i s c e r n m e n t
an d th e Question,
W h a t
Can Be
L e a r n e d ?
U l l a Runesson
I d a A. C. Mok
In
chapter 2, the pr imary focus was on variat ion. In this cha pter, th e
focus
is
m ain ly on
d iscernm ent .
In
accordance w i th
the
theory
p ut
forward
in
chap-
ter 1 , we argue that a cer tain w ay of learning, of unders tand ing or "seeing" a
part icular phenomenon, means that certain cri t ical features must be dis-
cerned a nd held in our awareness s imul taneous ly . Hence , the possib il i ty for
the
learner
to
discern
o r
focus
on
these
features is a
necessary c ondi t ion
fo r
lea rn ing som eth ing in a cer tain w ay. W e i l lus t rate th is theory us ing different
examples
from
mathematics lessons.
DISCERNMENT, E X P E R I E N C E ,
AN D
M E A N I N G
In
chapter 1 , exam ples w ere given that i l lus t rated how different profess ion-
als m ust pay at tent ion or mu st be sensit ive to cer tain aspects o f a s i tuat ion in
order
to
handle
the
s i tuat ion
in a
cer tain w ay.
T he
ability
to
handle
a
si tua-
t ion
c ou ld be descr ibed in terms o f the w ay in wh ich the s i tuat ion is seen or
exp erienced ; in other wo rds, the origin of
pow erfu l
w ays of ac ting is power-
fu l w a y s o f seeing.
The w ay in w hich a s i tuat ion is seen or experienced depends on the fea-
tures of the situation that are discerned. In every situation, we can attend to
all
the
different aspects
of the
si tuation . How ever, this
is not
wh at happens .
W e
do not at tend to al l these asp ects and w e do not at tend to them at the sam e
t ime . Ins tead, we pay part icular a t tent ion to some aspects—that i s , some
63
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64 R U N E S S O N AND MOK
features
of the si tuation are discerned, w herea s othe rs are not . Th e features
that w e discern are in the fore of our at tent ion, or put differently, they are
held
in our
focal
awareness; and
they
are
held
in our
awareness
at the
same
t ime.
W e can say
therefore, tha t
a
certain
w ay of
exp er iencing could
be
cha r -
acterized in term s o f the aspects that a re discerned s im ul tane ous ly .
T he
par t icular
way in
w h i c h
the individual
experiences
a
s itua t ion— or
a
phenomenon—is
the way the
individual unders tands
it.
E x p e r i e n c in g
im -
plies experiencing the object as som eth ing , t hus experiencing a m e a n in g .
When
we use the
concept
a way o f exper ienc ing someth ing and
describe
how
som eth ing
is
experienced,
w e
describe
the
m ean ing t ha t t h i s som eth ing
has for the individual. That w hich appears to be the same thing could have a
different
mean ing
for
different
individual s .
It
could also have
different
mean ings for the same individua l at different t im es . W ha t m ean ing it has for
the individual cou ld be unders tood in terms of wh ich aspects of the object
are
discerned
and
held
in the
focal awareness s im u l t aneous ly .
One way of
experiencing impl ies the s imu l t aneous d i s ce rnmen t o f cer tain features ,
w hereas another w a y o f exper iencing im pl ies th e s imu l t an eo u s d i s c e rn m e n t
of
other features .
W e
leam to experience by discerning aspects of the object to w h i ch w e
direct
o u r
aw areness.
In
order
to
gain
a
cer ta in un ders tan ding
o f a
p h e n o me -
non ,
w e
m u s t
be
able
to
discern cer tain cr i t ical features . Fo l low ing this l ine
of reasoning, if w e, as educators, w ant our students to gain a p ar t icular w ay
of unders tanding, o r to develop a par t icular ca pabi l i ty , w e m u s t m a k e it pos-
sible
f o r
them
to
discern feature s that
are
cr i t ical
fo r
tha t par t i cu lar l earn ing .
D I S C E R N I N G C R I T I C A L F E A T U R E S
O F WHAT IS TAUG H T
Wh a t
do we
me a n
by
crit ical features '?
And how can d i f ferent
w a y s
of
h a n -
dling
these cr i t ical feature s
in the
l earn ing s i tua t ion provide
d i f ferent
possi-
bilities
for
learning? Learning what
a
square is—and what
it is
no t—for
instance, takes
the
di scernment
o f the
cr i t ical featu res
o f
that geom etr ical
shape. Consequent ly , if the teacher a im s a t m a k in g the learner un ders tan d
wha t
a square is, he o r she
mu s t start wi th w hat
it
takes
to
know
and recog-
nize
the
cri t ical features
o f a
square,
in
order
to
m ake learn ing poss ib le .
In
this case,
the
cri t ical fea tures
are the
size
of the
angles ,
th e
n u m b e r
o f
sides,
and the relat ions betw een them , and i t m ust be possible for the learners to
discern these features . How ever , s im ply po int ing
ou t
these cr i t ica l features
to the learners is not enough .
W e i llus t rate th is po int w i th a t hou gh t experimen t . Le t us i ma g i n e tw o
dif ferent c lass rooms wi th
tw o dif ferent
t eachers , bo th in tending
t o
he lp
their students learn w h a t a square is. They both ta lk about the characteris-
t ics of a square and refe r to a pictu re of a square. In that respect the lessons
a re
s imi lar .
But le t us
im ag ine t ha t
th e first
t eache r s im p ly po in t s
to the an -
gles, stating that they are four righ t angles; po ints to the fou r sides, show-
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3. D I S C E R N M E N T
A N D
" W H A T
C A N B E
L E A R N E D ? "
6 5
ing the
relat ion be t w e e n
th e
sides ( i .e. , equal);
an d
f inal ly g ives
a
defin i t ion o f a
square .
T he
second teacher s imi lar ly points out—or
fo-
cuses on—the ang les ,
th e
sides
and the
re la tion be tween them,
b u t
also
in -
t roduces a variat ion of these aspects . F or ins tance, she draws a pictu re of a
rhombus bes ide
the
square
an d
draw s
th e
s tuden ts ' a ttent ion
to the differ-
ence be tween th e angles o f the square and the angles o f the r h o mb u s re -
spect ively. Next she compares the number o f s ides in a square wi th the
number of ' s ides
in a
t r i ang le .
In the
same way,
she
con tras ts
the
re la t ion
betw een the opposi te s ides of a square and a rectan gle. F inal ly , the teac he r
points to squares of d i f ferent sizes.
I f w e
take
a
closer look
a t how
that w hich
w as
t augh t
w as
handled,
and
w h a t
i t was
po ssible
to
learn,
w e
find
that
the
same cr i t ical features
of the
square w ere fo cuse d on in both lessons (ang les , num ber of s ides , and the re-
lat ion
betw een them ). How ever, w hereas
the
second teacher indica ted that
the
size of the angles, the num ber of sides, and the relat ion betwee n the sides
cou ld be different be tween what is a square and w h a t is not a square, her
counterpart
did
not .
In
th is way,
a
variat ion
of the
cr i t ical features
w as
broug ht to the at tent ion of the s tudents by m eans of contras ts . The teache r
also gave exam ples
o f
different squares ( i .e., squares with different area) .
In
this
way ,
the
geometrical shape
w as
con stant,
but the
size
of the
shape
w as
varied. In the lesson taugh t by the
first
teacher, how ever, such variation w as
no t in t roduced. I t w as not possible for the learners to experience the fact that
the
size
of an
angle c ou ld vary. N either
was i t
possible
for
them
to
experi-
ence the
fact
tha t the same shape could have
different
sizes, but still be
cal led
a square .
Accord ing
to the
theoret ical f ramework laid down
in
chapter
1 , tha t
w h i c h varies
is
likely
to be
discerned.
F or
ins tance ,
it is
necessary
to
know
w h a t
a
right angle
is
no t ,
in
order
to
learn w hat
i t
ac tua l ly
is. And it
takes
the
experience
of (at
leas t )
tw o
different
examples
of
squ ares ( i .e. , variat ion
of
the area)
to
unders tand what
a
square
is. So, in
other words ,
the
space
of
var iat ion
afforded
o r
const i tu ted—part ly wi th
the
learners—is cr i t ical
fo r
the po ssibil i ty to discern these cri t ical fe ature s. A certain pattern o f varia-
t ion is
necessary
fo r a
certain learning
to
happen .
So , in
answer
to the
ques-
t ion , "How can learning best be promoted for m y studen ts?," w e w ould say ,
"Take
as yo ur point of departure the ca pab i l it ies you wa nt them to develop.
W hat do you w ant you r students to learn? W hat is cri t ical for th is learnin g
and fo r
this
way o f
u nders tanding? Make
it
po ssible
for the
learners
to
dis-
cern those features that
are
cri t ical
for
that learning."
However , we
must s t ress that
we a r e no t
say ing tha t what
is
t a u g h t
is
necessa r i ly w hat i s learned by the s tuden ts . From our point of view, there
is no
cau sa l i t y be tween t each ing
an d
l earn ing . That
is ,
there
is no
gua ran-
tee
t ha t a par t i cu lar l earn ing w i l l t ake p lace s imply beca use t eachers ac t in
a ce r ta in way , o r s t ructure th e learning s i tuat ion in a par t icu lar w ay . B ut ,
w h a t
t eache r s
can
accom pl i sh
is to
create
t h e
pos s ib i l i ty
o f
learn ing som e-
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66 R U N E S S O N AND MOK
thing in a cer ta in w ay. It is not
possible
to say co nc lus ive ly how the t e ache r
af fects what s tudents
leam
s imply by looking a t the way in which the
teacher teaches th e
lesson.
How ever , it is po ss ib le to say w ha t s tuden t s are
afforded
to learn in that pa r t icula r learning si tuat io n to acc ou nt for
d i f fer-
ences in pos sibi l i ties for learning , and to show h ow th ese are ref lec ted in
what s tudents ac tua l ly lea rn .
STUDENTS'
A C H I E V E M E N T S
AN D POSSIBILITIES FO R L E A RN I N G
In 1992, Stevenson and St igler published some rem arkable findings in their
book, The
Learning
G a p.
These findings indicated more or less tha t previ-
ous
specula t ions— tha t
is ,
tha t
a
lea rner 's achievem ent
is af fected by differ-
ences
in
w h a t
it is possible to
discern—seem ed
to be
correct .
In tw o
studies,
Stevenson and St igler (1992) com pared achievem ent in m ath em atics in pr i-
m ary Grade 1 and pr imary Grade 5 s tudents from a num ber of schools in
Sendai, Taipei,
and
M inneapolis ;
and in
Sen dai , Taipei , B e i j ing ,
and
Chi -
cago, respec t ive ly . Al though the Amer ican s tudents a l ready se r ious ly
lagged behind the Asian s tudents in pr imary Grade 1 , by the t ime they
reached primary Grade
5, the gap had
w idened
so
m u c h
tha t
there
w as
bas i -
cal ly no overlap; the per form ance in the bes t A m er ican schools w as w e a k er
than the perform ance in the w eakest o f the A sian sch ools .
Several other comparative studies (e.g. , the Third In te rna t iona l M athe-
ma t i c s and Science Study [TIMSS], 1999; see M u l l i s et al , 2000) hav e
demon stra ted that Japanese s tudents ,
and
Chinese s tudents
from
H o n g
Kong and Ta iwan, do m uch be t te r in m athe m at ics than Am er ican s tudents .
There
were ser ious a t tem pts to acco un t for such dif ferences . On e of these
was the TIMS S-video s tudy, in w hich a great nu m ber of ma them at ics les-
sons in Germany, Japa n, and the Un ited Sta tes were recorded and in tense ly
scrutinized. Stigler and Hiebert followed up The Learn ing G ap (Stevenson
&
Stigler, 1992)
by
publishing their book, The Teach ing Gap,
in
1999
(Stigler
&
Hie bert, 1999). Th eir
w a y o f
describing
the
typic al Japan ese les-
son and the typical A m erican lesson offers a potent ia l exp lana t ion of the ob-
se rved d i f f e r ences in ach ievement be tween Japanese and Amer ican
students.
In a typical Japanese lesson,
af ter
having reviewed the previo us lesson,
the
teacher introdu ces
the
problem
of the
day:
a
p rob lem comp lex enough
to
be used as a f ramework for the entire lesson and for e labora t ing d i f ferent
ideas and procedures. A s a rule, the students first work on the problem indi-
vidual ly
and in a num ber of different w ays , and then cont in ue the wo rk in
groups. Eventual ly different groups present their solut ions
and
these
are
compared . T he t e ache r—and the s tudents as w e l l — c o m m e n t on the
strength an d weakn esses of dif ferent approaches. Final ly , the teacher sum-
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3.
D I S C E R N M E N T
A N D
" W H A T
C A N B E
L E A R N E D ? "
6 7
m arizes the work and points to the most pow erfu l ideas that have come up
during the lesson.
In a
typical Am erican lesson,
the
teac her also starts
by
review ing
the
pre-
vious
lesson.
Then
the teacher m ay int roduce
definit ions,
term s and, above
all , a method for solving a certain k ind of problem . Af ter the dem ons t ra tion ,
the
s tudents are given a relat ively large num ber of problem s of the same
kind
to pract ice on. After they have prac ticed these, another type o f pro blem
m ay
be
in t roduce d.
T he
m ethod
fo r
solving this kind
of
problem
is
demon-
strated
by the teacher, and the students are given a further set of problem s of
this
other kind
to
pract ice
on .
M a t h e m a t i c s lessons
in
China have been described
in
s imi lar terms
as
Stigler
and
Hiebert
described
the
Japanese lesson
(see
Stevenson
&
Stigler,
1992).
An d to a
certain extent ,
it
wou ld
be
true
to say
that
th e difference s
j u s t
i l lustrated could potent ial ly provide an explanation of the differences in
achievement
between Asian
and
American s tudents .
If w e
s impl i fy th ings somewhat ,
we can
argue that
an
im por tan t differ-
ence betw een Chinese an d Japanese m athem at ics lessons on one hand, and
Amer ican
lessons
on the
other,
is
that
in the
former,
the
s tudents most ly
face
one
problem
to
w hich they
are
asked
to f ind different
solut ions , w hereas
in
the latter, the students are presented wi th one method fo r solving one kind of
p rob lem,
which they then prac t i ce
by
solving
different
problems
of the
same kind.
In
each case ,
t he
s tudents were af forded dif ferent poss ib i l i t ies
fo r
w h a t
cou ld b e
learned.
In one
type
o f
lesson, s tuden ts w ere given
the
poss ibi l i ty
to
learn
how to f ind
solut ions
to a
p rob lem , w hereas
in the
other , they w ere
af forded the po ss ib i l i ty to learn ho w to m ake use of a pa r t icula r solut io n.
In
these s tudies , comparisons were made using lessons wi th
different
mathemat i ca l
co ntents . Thus, the comparison w as m ade o n a general
level.
In
the
fo l lowing
example ,
tw o
lessons tha t aim ed
to
teach
the
same
specific
conten t are
com pared
in
relat ion
to
w h a t
w as
possible
to
learn.
L E A R N I N G
TH E OPERATOR
ASPECT
O F TH E FRACTION AL
C O N C E PT
R une sson (1999) s tudied f ive m a them at i c s le s sons , a ll t each ing f rac t iona l
num bers an d percen tages . In many respect s , the l essons w ere very s imi lar .
F o r
i n s t ance ,
four o f
them used
the
same textbook,
and the
c lass room
w ork was orga n ized in a very s imi lar way . The a im of Ru nesso n ' s s tudy
w as to
invest igate
th e
var ious ways
in
which teachers handle conten t ,
in
th is case, f ract ional n u mb e r s
an d
percen tages .
Le t us
take
a
closer loo k
a t
tw o of the
teachers.
In both lessons, the content being taught was the operator aspect o f the
fract ional co ncept (e.g. , how to f ind 1 /3 of 12). In both cases, the discussio n
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68
R U N E S S O N
A N D M O K
took place
in a
whole-class
setting. The lessons were audiorecorded and
transcribed verbatim.
T he
d ia logue
is
p resen ted a longs ide
o ur
analys i s :
3.1
[Mathematics
Lesson
/
F ract ions/
Secondary Grade
1 ]
Teacher
A
T: OK. Here I have a piece of
string. It's
90
cent imeters long.
[Teacher holds up a piece of
string] Three people have
to
share that equally. How do you
go about that? Fair share? Tell
m e,
Sylvia .
S 1 :
Wel l ... divide by three.
T :
Yeah, each
o ne
w i ll
get a
th ird .
B ut let's say one of them wants
to have more than the others .
The str ing is
stil l
90 cen t ime-
ters long and I want 2/3. H ow
cou ld we f igure tha t out? 2/3 of
a
piec e of str ing tha t is 90 cen-
timeters long?
Thomas?
S 2:
[ inaud ib le]
T:
R ight. First
you
f igure
out the
length
o f a
third
and
then take
another
one . . . and
together
that makes
... ?
W h a t
d id you
say?
60
cen t im eter s? Yes.
So,
first you
have
to figure out the
length of 1/3. Measure that,
an d
then t ake ano the r one .
[The teacher
first
marks 1/3 ,
then 2/3 of the whole length o f
the str ing] .
T: OK.
Let ' s take
a
look
a t
th is
piece
of
string. [The teacher
is
hold ing up a
shorter piece
o f
str ing] This is on ly 40 cent i-
meters long. I would l ike to
have
one fifth of 40
cen t ime-
ters . [Wri t ing on the b l ack -
board: 1/5 of 40 cm]
The teacher introduces the
problem.
A man ipulative aid is
used.
A
s trategy
fo r
solving
the
p r ob l e m (1/3
of 90) is
intro-
duced.
The
nom inator is changed; 1/3
is changed to 2/3 (2/3 o f 90).
The
teacher elucidates the
strategy an d illustrates with
the manipulative aid. (1/3 o f
90 = 90/3 = 30)
A
ne\v
problem
(1/5
of 40) is
introduced. A manipulative
aid is
used.
Writ ten
representation
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D I S C E R N M E N T A N D " W H A T C A N B E L E A R NE D ' . ' "
69
S 2: 8 cen t im eter s .
T :
Yes, each fifth is 8 cen t ime-
ters .
B u t le t 's s ay we wan t 3/5.
How do you f igu re that out?
Tell m e, L i s a .
S 3: Th r ee t imes 8.
T : O K . Firs t w e m u s t f igure out
how m u c h 1/5 is. So, you di-
vide 40 by 5, and you get 8.
A n d
three f i f ths m ust be three
t i m e s
a s m u c h .
Three
s u c h
p i e c e s . Th at ' s 24. B ut le t 's say
t ha t the piece of str ing is 60
c e n t i m e t e r s in s t ead . [Wr i t e s
60 cm on the board] . One of
y ou
should have 3/5,
and an-
other o n e
2/5.
H o w m u c h w i l l
the person w h o gets 3/5 have?
...
O K . H o w d o w e g o abou t
th is? T h e w ho le p iece o f string
is
60.1 shou ld have 3/5, then
I
m u s t
f i g u r e s o m e t h i n g
o u t
f i rs t , w h a t .. . ? M ar tin .
S4: 5 d ivided by 60
T : Wel l , now you said it the other
w ay
around— 60 d iv ided by 5.
W hat ' s t ha t?
S5: 12
T : OK. 12 . So now we know tha t
1 /5 is 12. Then how m u c h is
3/5?
The
n o m i n a to r is changed (3/5
of 40). The
teacher asks
for an
appropriate
s t ra tegy.
The teacher elucidates
the
s tra tegy .
The
who le
is
changed
(3/5 o f
60).
W ri tt en represen ta tion
The
teacher asks
for the ap-
propria te s t ra tegy.
I f we
an alyze this data
in
term s
o f the
aspects focus ed
on , it is
apparent
tha t
the
focus
was on the
strategy
fo r
solving
the
problem ( i .e . , calc ulat ing
the
length of a fractional part of a piece of str ing) .
This
is the aspect that the
teach er tr ied to draw the students ' at tention to. B ut only one strategy or proce-
dure
wa s presen ted, and hence the strategy w as not varied. This particular as-
pec t was foc use d on, but w as kept invariant. However, the teacher did chang e
the param eters in the problem . After introducing the first problem and pre-
senting an appropriate solving strategy, the teacher ch anged the length of the
piece of siring (i .e. , the wh ole) a s we ll as the size of the fractional part (1/5 o f
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7
R U N E S S O N
A N D M O K
40).
In the fo l lowing
example ,
the
num era to r
w as
changed (3/5
o f
40),
an d fi-
nally in the last example, the who le ( i .e ., the length of the string) w as changed .
Thus, the
strategy
w as
invariant , while
the
numbers var ied
in a
sys tema t ic
way.
(1 /3
of 90, 2/3 of 90, 1 /5 of 40, 3/5 of 40, 3/5 of 60)
Let us now contrast th is approach w i th that o f Teacher B , wh o se t each in g
also deal t wi th
th e
operator aspect
o f f rac t ional
n u m b e r s .
Th e day
be fo re
this lesson, the
students
had been working on a
p ar t icu lar
problem in
w h i ch
they had to mark 3/7 of a recta ng le w i th a size of 7 x 8 squares , as shown in
Fig. 3.1 .
3.2 [Ma them at ics /Frac tions /Pr im ary Grade 6 ]
Teacher B
The
rectangle
is
shown
on an
O H T T o
begin w i th
the
teacher
asks Lena to
tell
the class how
she
marked
3/7 of the
rectangle.
SI: If you just take seven squares
from the
whole,
and
then take
three of those ... If you count
"one, two, three,"
and
mark them.
T:
W h y ?
SI: Well it is 3/7 of the small pile.
And then
I
continue: one, two,
three, four,
five,
six, seven,
go on
like that.
I
keep counting
to
seven
and
m arking three of them .
A
manipulat ive
aid is
used .
In each group of seven squares ,
three are m arked .
The teacher asks
fo r an
argu-
ment.
The s tudent i s explaining her
s tra tegy .
FI G. 3 . 1 . T he grid fo r m a r k i n g 3/7 of 56.
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3. D I S C E R N M E N T A N D
" W H A T
C A N B E
L E A R N E D ?"
71
T: Oh yeah . I unders tand You
counted one, two, three,
four,
five six, seven, and then you
marked th ree
o f
t h e m.
A n d
t hen one , two , t h ree , fou r ,
f i v e ,
s i x , s e v e n , a n d y o u
m arked them . In o ther words ,
you do it
l ike this [pointing
a t
the pro jec t ion on the board]
one, two, three, four, five, six,
seven.
You can
ma r k
the
las t
ones l ike tha t . How do you go
on? In the same w ay?
S I: Yes .
T: Wel l did anyone do it differ-
ently?
Did you all do it like
that?
Ss: N o.
T :
Well what about you ...
Sophie?
S 2:
We l l ,
I
j u s t d iv ided
it
in to
seven parts .
T: OK. You
jus t counted
all the
squares and divided them into
seven. OK, Maria what about
you?
S 3: Wel l I tried
different
numbers
like that unt i l I got seven parts .
The teacher e lucidates Lena 's
s tra tegy.
A manipula t ive aid is used .
The
teache r asks for a l terna-
t ive s tra tegies .
Another
s tudent expla ins
her
strategy, which
is
different
f rom the
previous
o n e .
The
teacher asks for a l terna-
t ive s tra tegies .
Yet
another s tudent exp la ins
her
s tra teg y, which
is different
f rom the prev ious one .
Here, Teacher
B
focused
on the
solving strategy
in a
s imi lar
way to
Teacher A. Thus, the foc used aspects w ere the same in both lessons . B ut , w e
can
observe that Teacher B asked the students to come up with
different
solving strategies to the sam e problem (3/7 of 56). The variation in the stu-
den ts ' solving s t rategies was m ade exp l ici t w hen the teacher asked: "Did
you al l do i t
l ike that?"
T he
studen ts ' responses show ed that they
h ad
c o me
up w i th different w ays of solving the problem. Lena solved the problem by
count ing seven squares in each column and then marking three of them.
So phie divided the 56 squares into seven parts (and m ult ipl ied six by three ).
A nd f inal ly,
M aria tried
different
num bers, which m ul tip l ied
by
three equ als
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72 R U N E S S O N A N D M O K
56. So, in B 's lesson, the solving strategy varied, w hereas the param eters o f
the problem were the
sam e
(i.e., 3/7 of 56), and hence were invar iant .
T he
different w a y s
in
w h i c h
the
studen ts chose
to
solve
the
problem
im -
ply
that
they had
differe nt interpretations
of the
operator aspect
of fractional
num bers. Th e way tha t Lena solved the problem im plie s that she interpreted
3/7 of 56 squares by a rranging the 56 squares in to groups of seven an d then
taking three ou t of seven in each group (s tre tcher /shr inker interp reta t ion ;
B ehr, Harel, Post, & L esh, 1993) as i l lus trate d in Fig. 3.2.
The other two stra tegies both imp ly another interpreta tion, na m ely divid-
ing 56 squares in to seven group s and then tak ing three groups out of the seven
groups (dup licator/partit ion -reducer interpretatio n) as
illustrate d
in F ig. 3.3.
In
Lesson
B , the
var ia t ion
in
so lving stra tegies that were presented
by and
to the
s tudents a lso in volved
a
var ia t ion
in the
sem ant ic in te rpre ta tion
of the
operator aspect o f f ract ional num ber s . Thus , in th is s i tua t ion , a var ia t ion o f
the semantic interpreta t ion of the concept was introduced.
N ow le t us take a c lose look a t the two lessons. W hat is the m ain differ-
ence be tween the two teachers ' w ays of dea l ing wi th the same conten t ( a
FI G. 3.2. Le na 's strategy for f ind ing 3/7 of 56.
F I G .
3 .3 . A no the r s tud e n t ' s s t ra t egy fo r f i n d i n g 3/7 of 56.
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3 . D I S C E R N M E N T AND "WHAT CAN BE L E A R N E D ? " 73
strategy
for
solving a/b
of c)?
Teacher
A
introduced
a
m e thod
for
com put ing
the fraction of an integer that basically involved dividing the integer by the
denomina tor
and
m ult iplying
the
quot ient
by the
nominator . This method
w as
first
applied
to one
problem, then
to
another,
and
finally
to a
th ird, tha t
is, the method w as the same but the problem s
differed.
Teacher B offered the students one problem only but invited them to find
different ways of solving i t . Three different students found three different
w ays of solving the same p roblem. Hence, the problem w as invariant but the
solving strategy varied. This w as the oppo site of w ha t w e observed in the
case of teacher A , w here the me thod w as invariant and the problem varied.
A com parison of the tw o lessons is i l lustrated in Table 3.1.
From Table 3.1,
it is
apparent that there
is a
system atic
difference
in the
aspects that the two teach ers varied and those they kep t invariant. Som e as-
pect s varied in one lesson, w hereas they w ere invariant in the o ther and vice
versa.
In the first case (T eacher A ), w e find a variation in the a lgo rithm ic so-
lu t ion,
w hereas
in the
second case (Teacher
B ),
there
is a
variation
in the se-
mant ic interpreta tions o f fraction numbers as operator.
Seeing
the two
lessons
in
terms
o f
possibi l i t ies
for
d iscernment (i .e.,
w h a t m i g h t be discerned), the two lessons are also different; different n u m -
bers are plugg ed into the formula in one lesson, and different wa y s o f inter-
preting and solving the problem, in the other lesson.
Focused Aspects an d D i m e n s i o n s of V a r i at io n
For every aspect of the ob jec t o f learning , there is a corresponding dimen -
sion of
varia t ion.
B y
that
w e
mean tha t
a
part icular aspect co uld
b e
some-
th ing
different . For instance, in the exam ples ju s t c i ted , the calcula t ion
a /b
o fc could be done in different ways , and thus the ca lcula t ion corresponds to
a dimension of variation in the solving strategies. One way of solving the
problem is a
"value"
in the dimension of solving s t ra tegies , whereas an-
other way of solving is another
"value"
in the same d imens ion. When
TABLE 3 .1
The Space of V a r i a ti o n
Constituted
in Lesson A and
Lesson
B,
R e s p e c t i v e l y
S o l v i n g
s t ra tegy
Paramete rs o f ope ra t ion
Rep r e s en t a t i o n
S t ude n t s ' unde r s t a nd i ng
Semant i c in t e rpre ta t ion
Teacher A
Inva r i an t
Var i ed
Var i ed
Invar ian t
Invar ian t
Teacher B
Var i ed
Inva r i an t
Inva r i an t
Var i ed
Var i ed
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74
R U N E S S O N
A N D M O K
studying the lessons f rom the po in t of view of how the "enacted object of
learning" is con stituted, w e find that the aspect focus ed on in each lesson is
varied
and we
describe tha t
in
term s
of the
opening
o f a
d imens ion
of
varia-
tion
o f
that par t icular aspect .
F o r
instance,
in
Lesson
B ,
w he re
the
focus
w as
on the solving strategy, and different solving stra tegies w ere dem on stra ted,
a
dimension
o f
tha t aspect ( i .e ., m etho ds
o f
so lv ing)
w as
opened.
In
addi-
t ion ,
we saw
that
the
teacher presented different in te rpre ta t ions
of the
con-
cept and different w ays of un derstan ding , and thu s that these aspects were
also opened
as
d im ensions
o f
var ia t ion.
In
other wo rds,
the
solving strate-
gies , the interpreta t ion of the concept , an d the s tudents ' unders tan ding were
dimensions of var ia t ion that were a l l opened in Lesson B. In Lesson A,
other
aspects
varied (i.e. ,
the
parameters
o f
op era t ion
and
representa t ion) ,
and therefore other dimensions
o f
var ia t ion were opened (see Table 3.1) .
Thu s, the spaces of var ia t ion con st i tuted in the lessons w ere di f fe rent .
DISCERNING PARTS
AN D
W H O L E S
So far in
this chap ter ,
w e
have discuss ed
how dif ferent
aspects
o r
fea tures
of
an object of learning are discerned. B ut the ob ject of learning is a lw ay s s i tu-
ated in a context , a nd it has to be discerned
from
tha t par t icu la r context in
order to re la te i t to other con texts and to other instan ces and by doin g so dis-
cern
its
fea tures . Fur therm ore ,
the
ob jec t
o f
l e a rn ing
is a
whole and .
as a
rule , dis t inct par ts within i t can be discerned.
These
par ts can also be de-
scribed in te rms o f their features, their re la t ions to each o ther and to the
whole , and in term s o f their parts.
In chapter 1 , re fe rence w as made to Svensson (1 976) who s ta ted that the
ent it ies , or the phenomenon (we w ould say the ob jec t of lea rn ing ) w e en-
counter m ust be del im ited ( i .e . , d iscerned) by the sub ject and they can be de-
l imited (or
discerned)
in
different
w ays . Such
d i f ferences
accou nt par t ly
fo r
the reason wh y we al l see t h i n g s
differently.
T he exam ple g iven in chapte r 1
w as the
deer
in the
forest ,
bu t
these dif ferences
are
present
in all
cases wh en
somebody is learn ing something . In the exam ple s g iven in th is chapte r , w e
can a lso see tha t m athem at ica l problems in the c lassroom have to be d is-
cerned f rom the con text . At very least , the s tuden ts m us t be able to dist in-
gu i sh be tween wh en the pa r t i cu la r p rob lem i s d i scussed and w hen
something e lse is ta lked about . Fur thermore, if the problem is the w h o l e,
there a re generally also parts that can be
identif ied,
such as separate ar i th-
metic operat ions,
and the
m eaning s tha t derive from
the
p rob lem .
Let us look again a t the c i ted exam ple , in w h i ch tw o dist inct ively
differ-
ent way s of dealing w ith the operator asp ect of the
f ract ional
concept were
described. According
to the
m e thods used
in the
first example (Lesson
A )
the s tudents cou ld ident i fy and learn to use an a lgor i thm for the ca lcu la t ion
a/b of c, by
carrying
ou t the
division c /b
and
thus ob ta in ing lib
of c, and
then
mul t ip ly ing
by b to obta in
a/b.
There w ere four subprob lems :
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3. D I S C E R N M E N T
A N D " W H A T C A N B E
L E A R N E D ? "
75
Answer
1. 2/3 of 90 30
2. 1/5 of 40 8
3.
3/5 of 40 24
4. 3/5 of 60 36
W hen deal ing with this part icular kind
of
problem ,
the
students
had to
del imit this sequence from the context of the lesson. By doing so, they be-
came poten t ia lly capable of relating it to sim ilar kinds of problem s in the fu -
ture.
The
sequence could then
be
considered
as a
part
of the
lesson,
but
also
as
a whole in which the
four
subproblems could be discerned as parts.
Within the subproblems, the three kinds of components—numerator , de-
nominator , and the whole—could be discerned and re la ted to each other
within the
same subproblem,
or to
corresponding par t s wi th in o ther
subproblems.
A s
w e
show
in the first
example
in
chapter
4,
this process
of
del im ita tion
also
appl ies
to the
process
o f
reading
a
text . W hen reading texts ,
the way in
which the
reader
delimits the whole and the
parts,
and
relates
them to each
other is of vital importance for unders tanding.
L E A R N I N G
A B O U T
P R O B L E M
S O L V I N G —
T H E
POSTMAN'S ROUTE
Th e secon d ma in data set to be used in this chapter is "the p ostm an 's route,"
which gives
a
further i l lustration
of the
thesis presented
in
chapter
2. In the
Ch inese
lesson that we describe, the teacher carefu l ly planned the lesson
and
fo l low ed th e lesson p lan accordingly. W e f irs t present a summ ary of the
lesson fo l low ed
by an
an a lys i s.
S u m m a r y of the Les s on
This lesson w as a demon stra tion lesson con ducted a t the N at ional C onfe r-
ence
for
Open-Ended
Que stions
held
in
Shanghai
in
N ovem ber, 1998 (the
data w as d iscussed in M ok, 2000, 2002). Dem onstra t ion lessons, in w h i ch
an
expert teacher is invited to teach a class in front of an audience , are a
com m on prac t ice in schools in the
Peo ple 's
R epu bl ic of China. The c lass-
room w as a room m uch la rger than a normal c lass room. The front section o f
the room had the normal c lassroom set ting w ith a teach er ' s po dium , and the
back section
w as
l ined w ith about
50
chairs
fo r the
audience.
For the
dem -
onstrat ion lesson u nder discussion here , the audience w as made u p of par-
t ic ipants
of the N at ional Con ference. Despi te the demonstra t ion natu re of
the lesson, i t w as a real 40-min . prim ary Grade 4 lesson, co ndu cted during
the norm al school t imetab le . There were 28 studen ts and they sat in g roups
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76 R U N E S S O N AND MOK
of four. B efore the lesson, the teacher gave the au dienc e a one-page lesson
plan . It w as s ta ted in the plan tha t the obje ct ives of the lesson w ere to de-
velop students ' problem-solving stra tegies by so lv ing a pos tman 's prob-
lem, and to develop stude nts ' creat ivi ty and divergent th ink ing via problem
solv ing.
In the
lesson plan ,
i t w as
exp l ic i t ly s ta ted tha t
the
t e ache r wo u ld
ap -
proach the problem by asking students to design rou tes for the postm an in a
real-l i fe context . Fol lowing th is , the t e ache r wou ld he lp s tuden t s to con-
sider th e problem in a m athematical context , by asking them to look for reg-
ular i t ies exhibi ted in the routes th at they had com e up w ith , and to thin k
about the possible transform ation of the
shapes.
(The routes becam e shapes
once the direct ion arrows w ere taken aw ay.) To beg in wit h, the teache r ex-
plained
the
problem
by
holding
up a
sample worksheet (see Fig. 3.4). Here
is a transla t ion of the problem sta teme nt that w as show n on the black bo ard
and explained by the teacher verbal ly:
There are nine dots on the paper. The dot surroun ded by a t r iangle in
the left u pper comer represents the post off ice. The pos tman needs to
start at the post
office
deliver a letter to each of the e igh t p lace s , and re-
turn to the post off ice . W hat could be the po s tm an 's route?
T he
lesson consisted
o f
four phases
in
w h i c h
the
teach er he lped
the
s tu-
dents to tackle the problem according to the lesson p lan . Th e
four
p arts are
now illustrated:
Part
1:
Students Designing Their
O w n Routes .
The
teacher asked
th e
students to work in groups an d exper iment w ith as m any routes as possible .
Each student designed his/her ow n route o n the pieces of paper provided by
the
teacher,
and the
designs
o f all
group m embers w ere
put in a
p i l e .
T he
s tu-
den ts w ere very
eff ic ient
and
only ta lked w i th the i r ne ighbors occas iona l ly .
W hen they h ad f in ished al l the papers o n the i r desks , they ra ised the i r han ds
for more . T he act ivi ty lasted about 1 0 m i n .
F IG .
3.4.
T he workshee t .
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3.
D I S C E R N M E N T
A N D " W H A T C A N B E L E A R N E D ? "
77
Part 2:
Evaluating
Their O wn D es igns Selectively. During this phase, th e
teacher resumed the at tention of the whole class. She posted some of their
designs
on the
blackboard
and
asked
the
class
to
j udge
whether the
designs
w ere correct . One group produ ced 18 designs and the teache r asked the stu-
dents to discuss with their group members whether this group's designs
were correct (see Fig. 3.5).
After the discussion, the whole class agreed that a ll of the designs were
correct . Then the teacher pointed to a faulty design produced by another
group,
and
asked whether
i t w as
correct (see Fig. 3.6).
Th e s tudents pointed o ut that the arrows w ere m iss ing from this design,
and that there w as no indicat ion of how the postm an cou ld return to the post
office .
Fol lowing this,
the
teache r asked
the
class
to
think
o f
w a y s
t o
deter-
m ine wh ich design w as the best . After a few exchanges of ideas between the
class and the teacher, they agreed that the shortest route w as the best . Then
the
teacher guided
the
class
to
compare
the
n u mb e r
of
straight
a nd
d i agona l
F I G .
3.5. The 18 rou te s .
FI G. 3 .6 . The w rong route .
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78
R U N E S S O N A N D M O K
segments
in the
designs,
an d to
determine
the
shortest rou te based
on
this
in-
formation
(see Fig. 3.7).
The teacher removed the longer routes, leaving
seven
on the
board.
Part
3:
Group Interchange
in
Order
to
Supplement Additional Best Routes
After
this, the teacher asked the students to supply more of the shortest
routes f rom their own piles of designs. They handed in 5 m ore, w hich made
a tota l of 12 on the blackb oa rd. The teacher g uided the class to remove the
repe titions and to disregard the arrows. E ven tua lly only 8 designs rem ained
on
the
board (see Fig. 3.8).
Stra ight
segments
Diagona l
segments
F IG . 3.7.
T h e
four pat terns
and the
n u m b e r
o f
l ine segments .
F I G . 3.8. The 8 pat terns
after
neg lec t ing the a rrows . N ote tha t (1 ) has the m iss in g
part fac ing left
w he r e a s ( 2) has the m i s s ing pa rt
fac ing
up .
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3.
D I S C E R N M E N T A N D "W H A T C A N B E L E A R N E D ? "
79
Part 4: Converting a Practical
Problem
Into the
Mathematical Problem
of
Categorizing th e Routes
A ccording
to
Th eir
Shapes.
Once th e arrows were
discarded, the designs of the routes becam e geom etric shapes. In this part of
the
lesson,
the
teache r asked
the
students
to
catego rize
the
shapes acco rding
to the way
they
saw the
relationship between them. There w ere very l ively
class discussions, and the students gave a lot of suggestions, such as how to
rotate
the
shapes (see Fig. 3.9)
or
flip them over (see Fig. 3.10).
Consequently, the students had different ideas about the number of cate-
gories, for example, infinity, 2, 8, and 16.
Toward the end of the lesson, the teache r invited the class to th ink abo ut a
related problem, which
had the
addit iona l constraint suggested earl ier
b y a
student, that
is,
wha t
the
postman would
do if
there
w as an
urgen t letter.
Ana l ys i s of the
L e s s o n :
T h e P oss ib i li ty of D i s c e r n m e n t
i f f e r e n t Solutions to the Same Problem. At the outset, the teach er asked
th e students
to
work
in
groups
and
experiment w ith
as
many po ssible rou tes
as
they
cou ld think
of. It is
significant that
th e
teacher asked
for as
m any routes
as possible instead of the best route. This demand for as many solutions as
possible created
a
dimension
of
variation
in the
possible routes. W hen
the de-
signs were pu t on the board, the oppo rtunities for discerning alternative rou tes
became m anifold because each student had to consider not only th e routes
proposed
by
their group m em bers,
but
also those suggested
by
mem bers
of
other groups.
F I G.
3.9.
A
ro ta t ion .
F IG . 3.10. Ref l ec t ions .
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80 R U N E S S O N AND MOK
Possible
Versus Impossible Routes .
In order to help students discern the
critical features of a possible rou te, the teacher del iberately focused the stu-
dents' attention o n a faulty design
(i.e.,
an
im possible route),
and
asked
the
class wh ether this design
w as
correct (see F ig. 3.6).
In the
di scussion about
w hether the route was correct or not , one s tudent pointed out that the arrow s
were missing, and another student pointed out that the route did not lead
back to the post
off ice.
In other w ords,
by
juxta po sing poss ib le rou tes wi th
an
im possible route,
the
teacher
w as
able
to
help stu den ts discern
tw o
cri t ical features
of a
possi-
ble route. One is tha t to con st i tu te a route, there has to be an indic at ion of the
direction of the route, and using an arrow to indicate direction is im portant.
T he
other
is
tha t
the
rou te needs
to
reach
a
pa r t i cu l a r des t ina t i on .
In
th is
case, the pos tm an needed to be able to go back to the post office
af ter
del iv-
ering the letters. Discerning these tw o critical features helped the class to
cons ider
t he
designs th at they
had
come
up
w i th
and
e l imina te
the
imp oss i-
b le
rou tes .
Possible
Routes Versus
Bes t
Rou tes.
Af ter
this , the teacher raised th e
quest ion
of how to
dec ide wh ich design
w as
best .
T he
fol lowing
is an ex-
cerpt from
the
di scuss ion .
3.3. [Math Lesson/Primary Grade
4]
T: How
should
w e
decide wh ich design
can be
called
th e
best design?
S3: Use the
shortest route?
T: "Use the shortest route," goo d. A ny others?
S 4:
Do n ' t repea t
the
rou te .
T :
Good,
"Don't
repeat the route." A ny others?
S5: If
there
is an
urgen t le t ter that needs
to be
del ivered
first,
w h a t
should we do?
T: Goo d, "If there is an urg ent let ter." V ery good. An y others?
[N o
m ore su ggest ions . ]
T :
Let ' s
first put S5 s
problem aside
an d
assum e tha t there
are no ur-
gent letters.
A ll
let ters
are
eq ual ly im por tan t. Then , w hich
is the
best design?
S6: The shortes t route.
B y
asking the s tudents to th ink about w ha t const i tu ted a
"best
route," the
teacher w as trying to ge t the students to revis i t the routes that they had de-
signed
f rom a
different perspective: that
is,
w h a t
is
possible versus what
is
best. The s tuden ts 'judg m ent of the best route w as at f irs t s imp ly an intui t ive
judgm ent w i th re ference to the postman's prob lem . The c ri teria for the best
route were
no t
form al ized. Subsequent ly ,
the
teacher g uided
the
students
to
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3. D I S C E R N M E N T
A N D
" W H A T
C A N B E
L E A R N E D ? "
8J_
coun t the
number
of
straight line segments (horizontal, vertical,
and
diago-
na l ;
see Fig. 3.7). A t this point, the teacher w as in fact guiding the students to
scrutinize
the
routes from
a
m athem at ical perspective.
U p to this poin t in the lesson, the teacher had taken an open problem , p re-
sented at a level very close to the students' everyday experience (design ing as
many paths as possible from the postman's perspective), and deliberately
guided
the students to twice revisit the designs that they prop osed: first to pick
the correct routes a nd then to pick the best rou te. In this way, the students not
only had the
chance
to see
that
the
problem
w as
open,
b ut
also
to see
that there
w ere m any possible solutions. In other words, the problem w as the invariant
in
the
lesson, w hereas
a
dimension
of
variation
w as
created
in the
m ethods
of
solving th e problem . Because of the variation created, students were
given
oppo rtunit ies to see various aspects of the problem— the m any po ssible solu-
t ions to the same problem; the difference between possible and impossible
solutions; the difference between possible and best solutions; and that th e cri-
teria used
m ay
vary between
an
intuitive choice
and a
mathemat ica l ly
grounded ch oice.
Categorization
of
Shapes:
Rotat ions and Reflections. In the
fourth par t
of
the lesson, the tea che r asked the class to discern the regu lari t ies exh ibited
in the eight shapes that rem ained on the board, an d to catego rize the shapes
(see F ig. 3.8). This task gene rated
a
very l ively wh ole-class discuss ion.
T he
fo l lowing
is an
excerp t from
the
discuss ion:
3.4 [M ath Le sson/Prim ary Grade 4]
T: N o w ,
we are not
going
to
consider di rect ion anymore. Look
at
these shapes . I w ould l ike you to use different m e thods to ca tego-
r ize
them. [Referr ing
to
Fig. 3.8.]
S 1 1 :
There are eight
shapes.
A ccording to the direction in w hich the
miss ing part
is
fac ing, there
are four
categories. There
are two
shapes for each category. Eight altogether.
S I 2 : Move
the
second shape [referring
to
shape
6 in
Fig. 3.8]
on the
second
row
aro und, then
i t
becomes
th e
third shape [shape
7] on
th e second row. [The teacher then moved the shape acc ording to
th e
student 's instruction.]
T: Very
good.
S he
found
tha t
af ter
ro tat ing, these
tw o
shapes
[6 and
7],
become the same. Any m ore sugges t ions?
S12 : M o v e
the
third shape
[7] on the
second row,
it
then becom es
the
third shape
[3] on the first
row.
T :
Let m e f irs t label these patterns. One, two, .. . eight [Students
said
the num bers aloud and the teacher wrote the num bers under
the patterns.]
SI 3 : [ inaudible]
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82
R U N E S S O N
AND MOK
T: S13
said that rotating
the
sixth shape
[6]
w i l l resul t
in the
eighth
shape [8]. What next?
SI 4:
[ inaudible]
T: S1 4 said that rotat in g the eighth shape [8] w il l aga in resu lt in the
seventh shape [7]. [The teacher wrote "6-8-7" on the board.]
S15: Turn the f i f t h shape [5], and turn again . It
wi l l
resul t in the eighth
shape [8]. Turn
the
third shape
[3]
upward.
No, flipping it
over
wil l resul t
in the fifth
shape [5]. [Flipp ing
the
shape w i l l produce
an image by ref lec t ion; see Fig . 3.10.]
T: W e started by sugg esting rotat ion . No w S1 5 sugg ested flipping
over
the
shapes.
A re
there
any
more suggestions? [The teacher
recorded the fl ipping in another row on the boa rd; see Fig. 3.1 1 .]
After
labeling the shapes 1 to 8, students became very active in pu tt ing
forward
thei r ideas for rotat ing them . The teacher put down a record of the
rotat ions
(6, 8, 7, and
later
5)
that
th e
students suggested (see Fig. 3.11).
How ever, rotation wa s not the only w ay to move the shapes a bou t . Som e s tu-
dents
found that they could also
obtain
matching images
by flipping
over
the shapes vert ical ly or ho rizontal ly ( i .e . , by r ef lec t ion; see Fig . 3.10) . The
students suggested altogether 1 8 rotations and seven reflections.
Let us exam ine w hat happ ened in th is excerpt . The f i rs t student (SI 1)
suggested that the eight different shapes could be put in to four
categories
according
to the
direct ion
in
w h i c h
the
"miss ing
part" w as fac ing,
t ha t
is ,
whether it faced
left
or right , up or down. This s tudent w as looking at the
shapes as static
f igures.
Af ter th is , ano ther s tudent ( S I2 ) sugges ted tha t
moving
the
second
on e on the
second
row
(i .e. ,
6 in
F ig. 3.8) wo uld resul t
in
the third one in the second row (i .e. , 7). This app roach sug ges ted seeing the
shapes as dynam ic by m oving them and looking for a m atch ing image by ro-
tat ion.
In
other words ,
in
th is exam ple ,
the
seve nth shape could
be
seen
as an
image of the sixth shape af ter a c lockwise ro ta t ion . In a s im i lar way , ano ther
FI G.
3 .1 1 .
T he
t e ache r ' s symbo l ic
r epresen ta tions .
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3. D I S C E R N M E N T AND " W H A T CAN BE L E A R N E D ? " 83
student (S14)
saw the
eighth
and
seventh shapes (i.e.,
8 and 7) as
images
of
the sixth shape after consecutive rotat ions. By doing this , the shapes were
no
longer
different,
they were s imply
different
orientat ions
of the
same
shape resul t ing f rom rotations and ref lect ions . In other words , the shapes
con sti tuted a dim ension of variat ion in the orientat ion of an invariant shap e.
The discernm ent of the equivalence between the shape an d i ts m atching im -
age was m ade poss ib le w hen the teacher rotated and f l ipped over the shapes
on
the
board fol low ing
the
students ' suggestion (see Fig. 3.9).
It
is clear that th e students' focus , in this p art of the lesson, was on the
t ransformation
( rotat ion and ref lect ion) of the shapes . They im agined the
shape turning in thei r mind s and m ade suggest ions to the teacher . W ith trial
and error, it was no t
difficult
for some students to see that there were two
possible m eans of t ransform at ion, that i s , ro tat ion and ref lect ion , and that
the rotat ional im ages could
be
categorized into
tw o
types . This categoriza-
tion
becam e ex pl icit w hen the teacher asked a new quest ion, near the end of
the
lesson, tha t requ ired the s tuden ts to think abou t their obse rvations at a
higher level o f ab straction. The fol low ing is an excerpt from th e discussion:
3.5
[Math lesson/Primary Grade 4]
T :
Let's
first
look at 1 ,2 ,3 ,4 , these
four
shapes . W hat do w e not ice?
[Referring to Fig. 3.8.]
S33: [If we] keep rotating [the shape], eventually it wi l l becom e the
first again .
T:
How abou t 5, 6, 7, 8? Does the sam e ru le app ly?
Ss:
[ inaudible]
T : Now , can we tel l how m any categories there are al l together?
S33:
E igh t .
S34: Infinitely many .
T: "Infinitely
many"
refers to the designs. Bu t we said at the begin-
ning there are eight best des igns . I f w e go back to the problem of
the postma n del ivering let ters , how m any categories of bes t de-
signs are there?
S35:
Infinitely
many .
S36: Two.
S37: Eigh t .
S38: 16.
T: W h y ?
S36: B ecau se there
are
eight shapes.
Af ter
changing
the
directions
(of
the routes), there wil l be 16.
T: Good. Then, how did S36's suggestion of " two" come up?
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84
R U N E S S O N
AND MOK
S38: Because all these shapes can be obtained by rotating tw o
differ-
ent
shapes.
T : Good.
These
are the different w a y s o f categor izat ion. Here , w e
conclude
f rom the
simple problem
of the
postman.
There
were
1 6 best routes. In the earlier part of the lesson, S5 suggested th e
problem of an urgen t letter . Teacher gave yo u this to think about
as a postlesson problem. If we
need
to
send
an
urgent
letter to the
third
poin t , how m any types o f best design are there? Don't for-
get to
tell
the
teacher you r
findings.
This
is the end of the
lesson.
Bye, c lass [Class dismissed] .
In the above excerpt, the teache r requested the studen ts to
ref lect
o n the
rela t ionship between shapes,
and
asked
for the
n u m b e r
o f
categor ies
o f the
shapes. When the s tudents were u nable to come up wi th the correct answ er,
the
teacher brought
the
c lass back
to the
everyday context
of the
pos tman .
A s we can see, this con textual
shif t
enabled som e s tuden ts to come up w ith
the correct an sw er. It is hig hly likely that as soon as these sh apes w ere seen
as
the postman's routes , the cr i t ica l features of possible routes and best
routes th at were discussed ear l ier in the lesson, that is, the
indica t ion
o f di-
rect ion and shortest distance respectively, came to the
fore
of the s tudents '
awareness. The fact that there were eight shortest routes and tha t the post-
m an cou ld e i ther go c lockw ise or cou nterc lock w ise , as po inted out by S38,
led to the answ er of 16 routes . Here w e see tha t the s tude nts ' answ ers w ere
once again focused on the
postman's
routes, bu t that this t im e the answers
were enr iched wi th
a n
u nde r s t and ing
of the
m a t h em a t ic a l m e a n i n g s .
Contextual
Variation. When w e look back at the lesson as a w h o l e , it is
no t di ff icul t to see tha t th e problem w ent through a shi f t o f context from real
life
to ma the m atica l , and vice versa (see Fig. 3 .12) . Th e problem w as f i rs t
introduced in a real-l i fe context tha t w as eas i ly access ib le to the s tudents .
T he
different solut ion s were exam ined
in
te rm s
of
fea s ibi l i ty ( w h e t h e r
the
routes were correct
o r
not )
and the
o p t im u m r e q u ir e m e n t ( w h i c h
one was
the best) . In both cases, the use of the postman's route as a con text for under-
standing
possible rou tes a nd best rou tes was a
power fu l
one . I t was easy f o r
students
to
re la te
to the
possible routes
and the
best routes
from the
post-
m an's perspect ive: that is , he m us t be ab le to re turn to the s tar t ing po int , the
post
office,
and he
should
be
able
to finish his
m ail delivery
a s
eff iciently
as
F I G . 3 .1 2 . C o n t e x t u a l
va r i a t ion .
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3 . D I S C E R N M E N T A N D
" W H A T
C A N B E L E A R N E D ? " 8 )
possible, that
is, no
part
of the
rou te should
be
repeated unne cessari ly.
T he
teacher shifted into
a
mathem at ica l con tex t
b y
invit ing
th e
students
to
cate-
gorize the routes . The s tudents then examined the
different
solutions and
thei r
relat ion s, using rotation and reflect ion. W hat is interest ing is the way
in w h i c h
the
teacher exploited
the
contextual shift back
to the
pos tman ' s
rou te when
the
students
h ad diff icult ies
coming
up
w i th
the
correct answ ers
fo r
c atego rizing the routes. Even m ore im portant , the teach er referred to the
postm an's problem again at the end of the lesson, and co ncluded the discus-
sion by
aff i rming that there were
1 6
best ro utes.
This
conc lusion
w as
buil t
on the comparison between the m any po ss ibil it ies , different rotat ions and
ref lect ions , an d the
directions
of the
routes .
A t the end o f the
lesson,
after the
various stages of explorat ion, the way in which the students discerned the
postman's problem
w as
u ndoubtedly different from thei r unders tanding
o f
this
problem at the outse t of the lesson. T he lesson provided a rich ex peri-
ence o f problem solving reinforced by the teacher wi th
careful
p l ann ing .
However ,
the
s tudents also played
a
cru cial role
in the
con st rual
o f the
ob jec t
of
learning. For exam ple, when the class wa s discuss ing the best route, one
s tudent
imagined the si tuation of an urgent letter. This show ed tha t the stu-
den t 's reflec t ions on the solution
were
very m uch in areal- l i fe context a t th is
stage.
T he
teacher skillfully kept
the
s tudents ' focus according
to her
or igi-
nal
p lan ,
and put
this nove l idea aside
fo r
that par t icular m om ent . However ,
after
examining
t he
solutions
of the
problem
f rom a
m athem at ica l perspec-
t ive, the idea of "an urgent letter" became a m ean in g fu l al ternat ive problem .
T he
problem
was the
same type
of
problem
as the
original one,
bu t
w i th
a
var iat ion,
and as such, it w as an opp ortunity for the students to put w h a t they
h ad
ju s t experienced into pract ice.
This example provides
a wonderfu l
illustration
of the way in
w h i ch
a
t eacher
can
provide studen ts w ith
a
rich un ders tanding
of the
ma n y
facets o f
problem solving even with the use of one single problem. The lesson also
suppor ted th e teacher 's lesson objective "to enhance s tudents ' p rob-
lem-solving abil i ty
and
strategies"
in an efficient and
s t im ulat ing wa y.
WHAT
C O UL D BE L EARNE D?
W e
s tar ted this chapter by saying that unders tanding something as some-
th ing
im pl ies discerning features ,
o r
aspects,
o f
that which
is
experienced.
Certain learning takes the s im ul taneous di scernm ent o f certain c ri t ical a s-
pec ts of the o bjec t of learning . That is , the cri t ical asp ects are held in the fo-
cal aw areness a t the sam e t im e. How ever, an aspect can on ly be discern ed if
it
is expe rienced as a dime nsion of variation. From this assum ption, we ar-
gue that those dim ensions of variat ion that are presen t in the learning en vi-
ronm ent are cri tical for learning w ha t is possible to learn . In other words, i f
an
aspect is presented as a dim ension of variat ion to the learners, i t m ake s i t
poss ib le
fo r the
learners
to
discern tha t pa rt icular aspe ct .
And i f
several
di-
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86
R U N E S S O N
A N D M O K
mens ions
o f
variat ion
are
open s imul taneous ly ,
it
ma k e s
it
poss ib le
for the
learners to discern al l of these aspects s im ul tan eo usly . So, wh at i s varying,
w h a t
is
invariant,
and
w h a t
is
varying
at the
same t ime
are
impor tan t
fo r
w h a t
is
po ssible
to le a m .
W e
have an alyzed three m athem at ics lessons f rom the point of view of
the pattern of variat ion that was consti tuted during the lesson, and have
identif ied the pattern of variant and invariant aspec ts in the three lessons re-
spectively.
From this w e can draw
some
co nclusio ns about the poss ib i l i t ies
to leam that were provided for the learners.
In the f irst tw o
exam ple lessons ,
in
w h i c h
th e
object
o f
learning
w as f rac-
t ional
n u m b e rs
as
operator,
w e can see
tha t there
was a dif ference in
w h a t
it
w as possible to learn . Teacher A provided the learners w ith the possibili ty to
leam
to
solve
different
p rob lem s w i th
the
sam e strategy, w hereas T eacher
B
provided the learners w ith the possibil i ty to leam to solve the same p roblem
wi th different strategies. In Teacher A 's lesson the chang ing of the parame-
ters
in the
operat ion opened
a
variat ion
of different
examples , whereas
in
Teacher B 's lesson, the param eters were invarian t and the s t rategy varied
(F ig . 3 .1 ) . In addi t ion , in Teacher B 's lesson, the learners had the po ss ib i l i ty
to
discern
a
semant ic aspect
of fractional
numbers ; th i s
did not
occur
in
Teacher
A 's
lesson.
On the
o ther hand,
the
s tudents
in
Teacher
A 's
lesson
were presented w i th
a
variat ion
of how a f ract ional
num ber cou ld
be
repre-
sented,
and
thus
the
possibil i ty
to
discern this pa r t icula r aspect .
It
is
obvious that these
tw o
lessons were very s im i lar
on one
level ,
for in-
stance in the t each ing me thods and the a r r angem en t of the l earn ing s i tua-
t ion.
How ever,
o n
an other rather m ore su bt le level (but
one
t ha t
is
im por tan t
from
the
po in t
of
view
of the
s t uden t s ' po t en t i a l
fo r
l earn ing) , they were very
different. W hen com par ing tw o lessons as we ha ve done here, i t seems na tu-
ra l
to ask, "W hich one is the best?" However, there can be no gen eral answ er
to
tha t ques t ion .
T he
answer
to any
assessm ent
o f
th i s k ind
wi l l
a lw ays need
to take into con siderat ion th e ca pab i l i t ies the t eache r wan ted th e s tudents to
develop,
and
t hus
the
in ten ded object
o f
learning .
The lesson on the postman's routes showed how the teacher very
though t fu l ly , and j o in t l y w i th her s tuden ts , con st i tu ted a pa t tern of variation
that w as
very
rich in
several aspects.
T he
learners ,
in the
s ame
way a s
those
in Teacher B 's lesson, were
afforded
the opportunity to discern that there
can
be
many poss ible solut ions ( routes)
to the
s ame p rob lem .
A s
we l l
as
this ,
they were provided
the
opportunity
to
evalua te ( scru t in ize)
th e
so lu-
t ions
in different
w a y s ,
in an
everyday contex t
and a
m a them at i ca l con t ex t ,
and
in
term s
of
w he ther
the
solut ion s were feas ib le (poss ib le
o r
impo ss ib le)
and
optimal (best) . They were also required to discern the character of a
shape
by the
variat ion
in the
o r ientation
of the
sam e shape
af ter
rotat ion
and
ref lect ion. Tha t is ,
w i thin
th e
m athem at ica l con tex t ,
th e
same shape
c an
pro-
duce many different possible routes by rotat ion o r ref lec t ion. Rotat ion and
reflection were tw o
w a y s
b y
w h i c h
the
s tudents cou ld
see
os tens ib ly differ-
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3.
D I S C E R N M E N T
A N D
" W H A T
C A N B E
L E A R N E D ? "
87
ent shapes
a s the
same. Fu rther,
th e
students w ere able
to see the
sam e prob-
lem a nd its solutions differently, before and af ter scrutinizing the solut ions
in
a m athem at ical context.
A l though our
focus
has been o n the impo rtance of the ob ject of learning,
w e do not wish to imply that c lassroom arrangemen ts are unim portant . A s
w e have seen in two o f the examples (Teacher B 's lesson and the Chinese
demonstrat ion lesson)
the
students contributed very much
to the
co nst i tu-
t ion and the widenin g of the space of variat ion. It is reasonable to assum e
that
this variation
w as a
resul t
of the
group discussions that took place
b e-
fore the w hole-class sessions. In both of these lessons, the studen ts w ere al-
lowed, and even enc oura ged, to discuss the problem w ith their peers. Th us a
certain
arrangement (group work)
facilitated
th e
opening
of
variation. How -
ever, w ha t w e w ant to stress is that i t is not a certain arrangem ent in i tself that
m ake s a certain learning possible, but rather that the possibil i ty to learn is
provided
by
w h a t
it is
possible
to
discern.
In th is chapter w e have fo cu sed on the poss ib i l i t ies to learn, rather than
w hat the s tudents actua l ly learned. W e have also descr ibed the en acted ob-
j e c t
o f
learning
as a
po ten t ia l
fo r
s tudent learning seen
from the
po in t
o f
view
o f the researcher. How ever, we w ould no t a rgue tha t what w as poss i -
ble
to
experience
w as
indeed wh at
th e
s tudents actual ly experienced.
It is
l ikely tha t
th e
s tuden ts learned d i f ferent t h ings . W ha t
w e do
argue
is
tha t
is
l ikely that the s tudents learned cer tain th ings in one lesson, and other
th ings in another .
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4
Simultaneity and the Enacted
Object of Learning
P a k e y
P . M . C h i k
M u n L i n g L o
In the
three previous chapters,
the
im portant role
of
variation
in
opening
up
possibil i t ies for a
particular learn ing
(or the
deve lopmen t
o f
certain cap abil-
i t ies) to
take place
w as
described
and
exem pl i f ied .
W e
also i l lustrated tha t
the way in
which
w e
experience
or
understand som ething depends
on
which fea tures of it we are aware of and can discern s im ultaneously. Thu s,
w h e n different
aspects
of the
same th ing
are
discerned
and
focused
on ,
d i f -
ferent
ways of understanding wil l resul t . More powerful ways of under-
standing a m o u n t
to a
s imul taneous awareness
of
those fea tures tha t
are
crit ical to
ac hieving certa in a ims.
In
this chapter ,
we
pr im ar ily focu s
on
describing
one of the two
fo rm s
of s im ul t ane i ty d i scussed
in
chapte r
1 :
synchron ic s imul tane i t y , w h i c h
r e fe r s
to
expe r i enc ing d i sce rned fea tu re s
at the
sam e time , w he re
th e
dis-
cerned features
may be
he ld
in two
differe nt types
of
re la tionship. W hen
th e
d isce rned fea tu re s a re seen a s aspec ts o f s o m e t h in g , w e r e f e r to re l a -
t i onsh ips
o f
th i s k ind
a s aspect-aspect re lat ionships. F o r
e x a m p l e , w h e n
we see a person
w ri ting
an
essay
on a
com pute r,
we may
exp erience
it as
som eone eng aged in an ac t of essay w ri t ing as we l l a s an ac t of word pro-
ces s ing .
T h e other re la t ionsh ip invo lves see ing t h e discerne d parts of the
wh o l e ,
and the
whole tha t
is
del imited from
a
context ,
at the
same t ime .
For exam ple , one may d isce rn the eyes , m uzz le , and l im bs a s d i f fe ren t
p a r t s
of the
body
o f a
deer , which
is in
turn de l imi ted f rom
th e
w o o d s
(Mar ton & B ooth, 1997). The kind of l inkag es
established
between an
ob jec t or a phen om enon and it s pa r t s be ing d iscerned a re re fe r red to as
part-whole re lat ionships.
89
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90 C H I K A N D L O
Things m ight or migh t not be experienced s im ul tane ou sly , and in teach -
ing, various things
m ay o r m ay not
come
to the
fore s imu l taneo usly .
In
this
chapter,
w e
compare lessons that
differ in
this respect; th at
is, the
in tended
object
o f
learning
is the
same,
but the
enacted object
differs,
as
does
w h a t
the students leam (i.e., the
l ived object o f learning) .
Let us, however, start with a study in which th e learners were facing the
sam e situation, but the w ay they discerned and experienced the relation s be-
tween
parts, an d
wholes
differe d. Saljo
(1982)
carried out a study to investi-
g a t e t h e d i f f e r e n t w a y s i n w h i c h u n i v e r s i t y s t u d e n t s i n S w e d e n
comprehended the same text . He
found
tha t a l though these s tudents were
reading
the
same text (w hich was,
by the
w ay, about
different
perspectives
of
learning),
the
students
saw
different
meanings
in it. Tw o
dis t inct w ays
of un-
derstanding
the
text were identif ied.
In the first
way ,
th e
students
saw the
text
as
having
a
sequential s tructure, with
different
perspectives
o f
learning being
described,
but
bearing
no
relationship
to
each other.
In the
second way,
the
students discerned
a mam
t hem e
(the
f o r m s of learning) i l lustrated
b y a
n u m -
ber of
subthemes ( d i f f e r e n t
perspect ives o f learning) .
They
saw the
text
as
having a
hierarchical structure w ith clear
part-part
relat ionships (between
the
subthemes) and part-whole relationships (between th e subthemes and the
m ain theme).
In
both w ays
o f
com prehending
the
text ,
all the
parts contained
in the text were distinguished, but these
parts
w ere seen as occupying differ-
ent structural positions. S aljo (1982) also found that th e students w ho under-
stood
th e text in the hierarchical way had a
more
organized and m ean ing fu l
understanding, and were better able to grasp the mam idea of the text than the
students
w ho
understood
the
text
in the
sequent ial way.
It is not
diff icul t , therefore,
to
i ma g i n e
w hy i t is
tha t
in any one
par t i cu lar
classroom si tuat ion, d i f ferent s tudents w i l l have
d i f ferent
levels o f under-
s tanding even thou gh they all are given the sam e presen ta t ion by the teacher .
W hat s tudents
gam
from
a
lesson,
and how
w el l they unders tand tha t l esson ,
depends
on the w ay
they com prehend
the
s t ructure
of the
presen ta t ion ; th i s
in turn dep ends on w ha t t hey focus on and w hat recedes to the background
(or is
taken
fo r
granted) w hen they
try to
unders tand
the
lesson. Some s tu-
dents w i l l
see no
relat ionsh ip between
the
different par ts
of the
p resen ta tion ,
whereas others w i ll be able to comprehend the presentation in m ore power-
fu l
ways (especial ly
if
they
can
s im u l taneous ly
see
c lear re la tionsh ips
be -
tween the parts and the way in which these parts are related to the
presentat ion
as a
w h o l e ).
It
then fo l low s tha t s tudents wi l l leam m ore
effec-
tively if the teacher is able to consciously structure the presen tat ion in such a
w ay as to
bring
out
clear ly
the
cr i t ical features
of the
ob jec t
o f
learn ing ,
as
w ell as
thei r relationships
to the
object
o f
learning
and to
each o ther.
In
other
words , the way the lesson is structured w il l have a n impor tan t inf luence on
s tudent learning .
W e
now
provide three sets
o f
c lass room data—compri s ing
six
pa i rs
of
lessons—to i l lus t rate th e w a y s in w hich teachers can s t ructure the i r lessons
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4.
S I M U L T A N E I T Y
A N D T H E
E N A C T E D O B J E C T
O F L E A R N I N G 9 ±
to
enable their students
to
discern
the
aspect-aspect
( or part-part) and part-
w hole relat ionships of various fe atures o f the object o f learning. I n par t icu-
lar,
we look at w hat i t is possible to learn regarding
specific
obje cts of learn-
ing
(i.e.,
enacted objects of learning) and w h a t is actual ly learned by
studen ts ( i .e. , l ived objects o f learning ).
The
first pair
of
mathemat ics lessons
is
drawn
from
Runesson 's (1999)
study
and is
used
to
i l lustrate
the
aspect-aspect relat ionship.
The
second
and the
third pairs
o f
lessons
are
taken from
a
2-year research p roject un der-
taken
by a research team in Hong Kong,
1
and involve a pair of primary
Grade
2
Chinese language lessons
and a
pai r
of
pr imary Grade
1
E ngl i sh
l anguage lessons , respect ively ( for detai led informat ion and discuss ions
abo ut other aspects
o f
these
tw o
pairs
o f
lessons,
see
C hik, 2002;
L o &
Ch ik ,
2000, and M ok et al ., 1 999). These three p airs of lessons wil l be m ain ly used
to
i l lus t rate part-whole and
aspect-aspect
relat ionships . Each pai r o f les-
sons was o n the same topic, but taug ht by two different t eachers .
The
analysis
is
based
on the
audio
o r
video recordings
of the
lessons
and
the subsequent transcript ions. In order to explore the impact of the struc-
tural
difference s
between the lessons on s tudent learning outcom es, the les-
son
analyses
of the
second
and
thi rd pai rs were also com pared against
the
student data , w hich include the w orksheets c om pleted by the s tudents im -
media te ly
after
each lesson.
A P A I R O F
MATHEMATICS LESSONS
The two m athem at ics l essons focused on teach ing two
different
aspects of
fractional numbers : the part-whole aspect and the division-quotient as-
pec t , where
the
former aspect involves adding
up
parts
to a
w hole (e .g . ,
1 2
qua rters add up to 3) and the lat ter involves dividin g up a who le in to par ts
(e.g. , 1 2 divided by 4 is equal to 3). The different w ays in w hich these two
aspects and thei r relat ionsh ip are s im ul taneo usly brough t to the s tuden ts
1
focal
awareness
are
com pared .
Des cr i p t i o n
of L e s s o n A
This lesson con sists of three main e pisodes. In Episode 1, the teacher drew
the
students ' at tention
to the
part-whole
aspect
of
fractional
numbers .
S he
used an ico nic represe ntat ion to show six pieces of 1 /3 of a pizza and invited
the s tudents to represent th is wi th mathemat ical symbols
2
( i .e. , symbolic
represen tat ion) . The fol low ing suggest ion was arr ived at by the s tudents :
— or 2
3
(6 pieces
of
pizza, each
1/3 of a
whole, equal
2
whole p izzas)
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92 C H 1 K A N D L O
In Episode
2, the
teacher focused
on the
division-quo tient aspect
of frac-
tional
numbers
(6 divided by 3), and asked the students, "How can this be
represented by (mathem at ica l ) sym bols?" The same represen tat ion w as ar-
rived
a t
again
by the
students:
— = 2 (6
divided
by 3
equa l s
2)
T he teacher further illustrated this with an example of dividing 6 by 3
(e.g., 6 p ieces of pizza are divided am ong 3 persons) :
In
Ep isode 3, the teacher broug ht the two aspects together by ex pla inin g
to the
class:
T: ... the resu l t is the same, but it is said
differently.
Somet imes I
will say. "20 divided by 4" and som etimes I w ill say, "20 quar-
ters"
. . . the resul t i s 5 anyway. But you should know that a l -
thoug h these are actual ly qu i te different [concepts] , the r e su l t is
th e same.
Des cr i p t i o n o f L es s o n B
This
lesson can also be divided into three m ain episodes. In Episod e 1, the
teacher drew a picture of 12 apples on the b lackboard. H e sa id that 3 per-
sons were to share them equ al ly ( the divis ion-quot ient aspect of f ract ional
num bers w as fo cuse d on) , and asked the class to th ink in s i lence how m an y
apples each person would get .
Meanwhile ,
he
drew
a new
picture—a bowl with
a lot of
triangles
in it
(where each triangle was supposed to be 1/3 of an app le)— and asked the class:
...
If you
have
to
pick
up as
man y p ieces
o f
apple
from the
bowl
as you
have there (m eaning the same as the total of the problem ju s t g iven) ,
how
many p ieces
of
apple
do you
have
to
p ick
up?
Again ,
the
students were instructed
to
th ink abo ut
the
answer
in
si lence.
In th is way, the teacher in t roduced both the divis ion-quo t ient aspect and
the
part-whole
aspect
by
usin g icon s ( i.e.,
the
p ic tures
of
apples)
a nd
m a d e
the difference
between
the two aspects visible by asking the students to
m ental ly solve two p roblems that resul ted in the sam e num ber ( i .e . , 4) .
In Episode 2, the teacher referred back to the first example (12 apples
shared
equally
by 3 persons) and
asked
h is
s tudents
to
represent
it
u s ing
mathemat ical symbols . He also asked for the resul t of the operat ion. The
teacher then wrote
the
student 's suggestion
on the
b lackboard:
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4.
S I M U L T A N E I T Y
A N D T H E
E N A C T E D O B J EC T
O F
L E A R N I N G
93
12
— =4 (apples)
N e x t ,
the teacher referred to the second example ( th i rds of apples) and
asked , "How m any thi rds
of an
apple
did w e
need
to
pick
u p, and how
could
that
be wri t ten w i th symbols?" T he teache r wrote dow n wh at the s tudents
sugges ted :
12
— (i.e., 12 x 1/3 apple)
A g a i n , both aspects w ere focu sed on s imu l taneously in th is episode.
In
Ep isode 3, the teach er asked the stu den ts to consider and com pare the
tw o
examples . After
som e
questions
and
comments f rom
the
students,
the
teacher
f inal ly conc luded:
.. .
1 2 divided by 3, and 12 thirds, the resu l t is the same. So w h e th e r
you have 1 2 apples shared by 3 or you have 1 2 thirds, you w i ll get the
same resu l t .
Aga in , the teacher l inked the two aspects of fract ional num bers by con c lud-
ing tha t they corresponded to the same nu m ber (4).
Thus,
thro ugh out this lesson,
the
teacher
ha d
kept
the two
aspects toge ther.
Aspect-Aspect R e l a t i o n s h i p
S h o w n
in D i f f e r e n t L e s s o n
O r g a n i z a t i o n s
A lthough bo th lessons were teaching the same content , the part-whole as-
pect
and the
divis ion-quot ient aspect
of
fract ional
num bers , t hey
differed
signif icantly in term s o f wha t
aspects w ere
kept in focu s, w hat varied, and
whethe r
the aspec ts were varied at the sam e t im e (see Fig . 4 .1) .
In Lesson
A, the tw o
aspects
of fractional
num bers were b rough t
up one
after
the o ther ( i .e. , f i rst, the
part-whole
aspect and then the division-quo -
t ient
aspect ) . I t was only in the last episode that the two aspects were
b r ough t together
as two
aspects
of a fractional
num ber . Thus ,
a
consc ious
effort
to set up the
condi t ion
for the
s tudents
to
discern
th e
a spect-aspect
re-
la t ionship
betw een the two aspects s im ul tane ously was observed in the f inal
F I G .
4 . 1 .
The focused
a spec t ( s )
i n
d i f f e ren t e p i sode s
o f
Lesson
A and
Lesson
B .
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94 C H I K AND LO
episode of Lesson A. In comparison, the teacher of Lesson B
focused
on
both aspects in each of the three episodes. He
first
asked the class to men -
tally
work
o ut the
solutions
of tw o
problems, each po int ing
to one of the as-
pects
o f
fractiona l
num bers and resul t ing in the same n um ber (4) . Then, he
asked the students to represent their solutions in term s of m ath em atic al
symbols.
He
concluded tha t
the
same num ber could
be
arrived
at by
m e th -
ods
that reflected
the different
aspects
of
fractional num ber s.
In
th is way .
the
relationship between the two
aspects
perm eated the who le lesson and the
condition for the exp erience of the relations hip w as co nsciou sly created all
through the lesson. This is an exam ple of the pat tern of variation refe rred to
as
us ion
in
chapter
1 : The two
aspects vary together
to
br ing abo ut
a
s imu l -
taneous awareness
of
both
in the
learners.
The two lessons il lustrate how two aspects o f the sam e direct object of
learning
(fractional
num bers )
can be
brou ght in to students '
focal
awareness
simultaneously .
In the
fol lowing sect ions,
we try to
invest igate
how
stu-
dents ' learning outcom es are affected by the w ay in w h i ch a lesson is struc-
tured—from
the point of view of the part-whole relationship s.
A P A I R O F PRIMARY GRADE 2
C H I N E S E L A N G UAG E
L ES S O N S
Tw o pr imary Grade 2 Chinese langu age lessons tau gh t by two different
teachers from
the
same school were selected
for the
study. B oth lessons
were th e first of a senes o f lessons dealing w ith th e teach ing of vocabulary
in a
text. Both classes
(2 A and 2B)
consisted
o f
s tudents
w i th
s imi lar
abili-
ties.
T he
title
of the
text
was "A
polite l i t t le guest."
T he
com ple te tex t
is
translated into E nglish and reproduced in Table 4.1 .
Description of Lesson 2A
The lesson can be roughly divided into
four
episodes. In Episode 1, the
teacher introduced
the
main them e
of the
text
as
"being polite." This
w as
TABLE 4.1
The
Text Used
in
Both
Lesson 2 A a nd Lesson 2 B
Lesson
10: A
Pol i te Li t t le Guest
Father intended
to
visi t
a
fr iend w i t h
us. He
asked , " W h a t m u s t
on e do to be a
pol i te
little guest?"
M y
y o u n g e r sister said, "When
we are
ea t ing,
w e
should
no t
turn food over
again and again to select food in the dish." M y elder sister said, "W e should look at the
person
we are
ta lk ing
to, no t
look from side
to
side.
W h e n
other people
are
t a lk ing ,
w e
should not
interrupt ."
I
said,
"On
leaving,
we must say
goodbye." Father
w as
very
pleased after
hea r ing these , he prom ised to give us the c ha nc e to show ourse lves to be a
pol i te guest .
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4 . S I M U L T A N E I T Y
A N D T H E
E N A C T E D O B J E C T
O F
L E A R N I N G
95
done by asking the students to first nom inate the classmates that they con-
sidered
to be
poli te,
to
give their
reasons, and
then
to
read
the
text
in
si lence
to f ind out w h a t w as mean t by being poli te.
In
Episode 2, the teacher taught the at tributes (e.g. , forms, pronuncia-
t ions,
and me anings) of seven words
3
that had been p re-iden tif ied
from
th e
text. M any teaching aids were used to show the m eaning of each word (e.g. ,
drawings
and
real objects) . References were also made
to
show
how the
mean ings
o f
these wo rds con tributed
to the
t hem e
of the
text— being pol i te .
With each word they studied, the teacher posted up on the b lackboard the
corresponding word card.
In E pisode 3, the teacher asked the students to f ind the sen tence in the text
where
each word that
they
had
studied
w as
used,
and to
read
the
sentence
out loud.
The
sentences were then p osted
up .
W hen
all the
sentences (each
involving on e or tw o of the
w ords) were found,
the
teacher told
the
students
that
if
they
did all of the
th ings that were described
in the
sentences, they
wou ld
be
po l i te chi ldren. The phrase "polite children" [ ^ = f ̂ |^ ^j ̂ -f- ]
w as
a l so pos ted
up . The
s tudents
w ere
then asked
to read the
text together .
In th is way, the teacher focused the s tudents ' a t tent ion on the words as
parts
o f the
sen tences , w hich were
in
turn parts
of the
text
an d i ts
them e
of
"being poli te."
In Episode 4, the teacher taught the students how to write some of the
characters .
4
Des cr i p t i o n
o f L e s s o n 2 B
There are five m ain episodes in the lesson. In Episode 1, the teac her gave
the stud en ts an overall idea of w hat the text w as abou t by asking a few ques-
t ions
to
in t roduce
the
content
of the
text .
In E pisode 2, the teacher foc used on teaching the form s of a num ber of
charac ters that she thoug ht her s tudents migh t f ind
difficult.
Individua l stu-
dents were invited
to
come
o ut and try to
w ri te each character
o n the
b lack-
board.
T he
other students were required
to pay
at tention
and to
j u dg e
whe the r the character was correc tly writ ten or no t . I f not , the teacher w ould
invite othe r studen ts to try unti l the charac ter was co rrectly writ ten. In some
cases, the
teacher also posted
up a
word card highlighting
the
structure
of
the character.
In E pisode 3, the teach er identified a set of w ords
from
the text and taug ht
the m e a n in g
of
each wo rd. From t im e
to
t im e,
the
studen ts w ere invited
to
give a verbal explanation of a certain w ord o r to act out i ts me an ing.
In
Episode 4, the teacher focused on teaching the pronunciat ion of the
words in the text. This w as done b y asking different groups of students to
take
turns reading them. Ins tant feedback
w as
given when
the
students
could not pronounce the w ords correctly.
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96
C H I K . A N D L O
In
Ep isode 5, the teacher introduced a m a tch ing game . In th i s gam e, the
teacher showed the students three phrases one by one and asked them, in
grou ps, to m atch the phrases by finding a w ord in the text tha t convey ed the
same meaning.
Part-Whole
R e l a t i o n s h i p i n t h e H i era rch i ca l S tructure
of Lesson
2A
Lesson
2A was
structured
in a
hierarchical
w ay
that showed clear
part-
whole re la t ionships between the word a t t r ibutes (each as an aspect of a
charac ter), the ch aracters (each as part of a wo rd), the w ords (ea ch as part of
a
sentence),
th e
sentences
(each
as
part
of the
text)
and the
text
(a s
con tribut-
ing to the u nderstanding of i ts them e). Figure 4.2 i l lust ra tes the part-who le
re la t ionships in the hierarch ical organ izat ion o f Lesson A .
For
example,
th e
character that
has the
meaning
o f "insert"
[}ff
] w as first
learned on i ts own wi th a part icular form, pronuncia t ion, a nd m e a n i n g . It
w as
then referred
to in the
context
of the
word "interrupt"
[} §
* % ] , which
is
m ade up of two characters ,
"insert"
[}fj] and "m outh" [°%]. The charac te rs
now took on a different m e a n i n g in com bina tion . In th is wa y , their re la t ion
w as
such that they were
no
long er
tw o
separate p arts
pu t
together,
bu t
con-
stituted a
who le,
in
w hich each
was a
part . Hence, w hen
the
wo rd "interrupt"
[ t§ "H ] was focused on, the characters "insert" [ ̂ ] and "mouth" [ °% ], as
w ell as their relatio n to each other , w ere broug ht
s imul taneous ly
to the s tu-
FIG. 4.2.
A n
i l lus t ra t ion
of the
part-whole re la t ionship shown
in the
h ie r a r ch ica l
structure
of Lesson 2A .
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H H
den t s ' focal awareness . Nex t , the word was seen again in a sentence, "W hen
others
are
ta lk ing
to
each other,
w e
should
n ot interrupt"
[}fj
*$].
Here
the
word, w hich com pr ises tw o ch aracters , becomes part of a sentence on po-
l i teness
th at contributes
to the
learning
of
poli tene ss. Thus,
the
part-whole
relat ionships between the characters and the word, as w e l l as the word and
the
sen tence, become clear . Fina l ly
the
sentence, which involved
the
word
as a part, wa s seen in the con text of a text . Together w ith al l the other sen-
tences
identified from the text , i t also con tributed to the und erstan ding of the
theme of the text. A gain , w hi le focu sing on the text , the sentence, the w ord,
and the charac ters were s imul taneous ly focused on to
facili tate
the discern-
m e n t of the
par t -w hole
relat ionships as we l l as the relat ionships betw een
each par t .
In this w ay, Lesson 2A dem onstrated h ow the parts (e.g., different attrib-
utes of a charac ter , an d
different
characters that m ake up a word) were em -
bedded in the wholes (e.g. , a character is embedded in a word; a word is
embedded
in a
sentence) . Therefore
it
provided
the
s tudents w i th
a
s imu l ta -
neous
experience (and hence, discernment)
of
these
par t -w hole
relat ion-
ships throu gh ou t the lesson. The s tudents cou ld refer to the word ca rds, the
sentence
stops,
and the text throughou t the lesson, thus making
possible
the
discernment
through synchronic s im ul taneity .
Part -Whole
R e l a t i o n s h i p
i n t h e
Seq uent i a l S truc ture
of L es s o n 2 B
T he teacher of Lesson 2B spent m ost of the
class
t im e o n vocabulary teach -
ing,
w hic h she organized unde r the three at t r ibutes of w ords ( form , pron un -
cia t ion, and m eaning ) and presented in a sequ ent ial m anner (see Fig . 4 .3) .
In this lesson, the
different
attributes of a character were taugh t in differ-
ent episodes, but no at tempt was made to relate the different at tributes of
each character
to one
another ( the aspect-aspect relat ionships) .
A s a
resul t ,
some s tudents m ay have unders tood the characters as to tal ly discrete ent i -
t ies.
Let us take fo r exam ple, the word "interrup t" [$| °^], which consists o f
two cha racters , the first one m eaning "insert" [ j j ] , and the second m eaning
"mouth" [°^]. Instead
o f
teaching
the
form s
of
these
tw o
characters
at the
F IG . 4.3.
T he
se quentia l organizat ion
of
Lesson
2B .
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98
C H I K A N D L O
TABLE
4.2
A
Comparison of the Structures of Lessons
2A
a n d 2B
Lesson
2A
Lesson
2B
Word 1 -»
form;
p ro n u n c i a t i o n ;
m e a n i n g
Word 2 -»
fo rm;
p ro n u n c i a t i o n ;
m e a n i n g
Word
3 -» ...
form;
p r onunc i a t i on ;
m e a n i n g
Form •>
w or d 1 ;
word 2;
word 3;
P r o n u n c i a t i o n ->
w or d 1 ;
w o r d 2;
w or d
3;
M e a n i n g
w or d 1 ;
word 2 ;
w o r d
3;
same t im e
as
teaching
the way in
w hich they combine
to
form
the
wo rd ' 'in-
terrupt" (as the teacher in Lesson 2A did) th e teacher of Lesson 2B taught
the
form s
of the first
character
on i ts ow n in
Episode
2, and the
p r o n u n c i a -
tion
of
this character
as part of the
word
"interrupt" in
Episode
4.
F urther-
m ore in Episode 5, the word "interrup t" w as given a
defini t ion
(" joining in
others ' conversation" [fa ̂ #J A ^ |£ f£ ]) tha t was ne i ther s i tuated in
the
con text of being po li te, nor re lated to the text .
Thus,
in
each
of the
three con secutive episodes
of
Les?on
2B, one o f the
word at t r ibutes ( form, pronunciat ion,
or
m e a n i n g )
w as
kept invariant ,
and
thus became superordinate , whi le the characters /words tha t varied were
used to illustrate the attribute. B y con trast, the words were the focus of Les-
son 2A, and each w ord becam e supe rordinate w hi le the three at t r ibutes (or
aspects) varied at the sam e t im e, in order to enhance th e s imul taneou s expe-
rience of the w ord at tributes. This is ano ther exa m ple of the pattern of varia-
t ion called
fusion.
A m a jo r
difference
be tween the two classes is w h e t h e r
at tr ibutes or w ords were supe rordinate , as determ ined by the different w a y s
in
w h ich
th e
lesson
w as
structured (see Table 4.2).
The
quest ion
w e
need
to ask is,
does th is
difference
have
an
i mp a c t
on
students ' learning outcomes?
Des cr i b i ng L ea rn i ng Outcomes
Af te r each lesson,
the
s tudents
in
bo th c lasses w ere reques ted
to
com ple te
a worksheet . Thi r ty worksheet s were co l lec ted from Class 2A. and 31
from
Class
2B. The
workshee t con t a ined
tw o
par t s .
In the first
par t ,
the
s tudents were asked
to put
down w ha t they thoug h t
w as the
mos t impor -
tan t th ing tau gh t and/or l earned in the l esson . The second pa r t requ i red the
students to
com ple te
a text by fil l ing in b lanks wi th ap propriate words tha t
had
been t augh t
in the
lesson (see Table
4.4 for the t ex t ) .
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4. S I M U L T A N E I T Y
AND THE
E N A C T E D O B J E C T
OF L E A R N I N G 99
What W as
Taught
and Learned From the S tuden t s '
Perspective?
In an-
sw er ing the first par t of the quest ion, some s tudents put down m ore tha n one
response . A s shown in Table 4 .3 , the responses of both c lasses fel l in to two
m ain ca tegor ies . Som e s tudents r eported tha t they w ere taug ht the them e
(e .g . , "how to be poli te," "being a pol i te guest") and sub them es o f the tex t
(e.g.,
"When others are
talking
to
each other,
we
should
not
interrupt."),
and
som e repor ted that they were tau gh t vocabulary. How ever,
dif ference s
wer e
observed in their pat tern of responses .
More students from Class 2A reported the main theme of the text or the
subthem es as the
mo st important thing taught.
In
co ntrast,
a
higher prop ortion
o f
Class 2B considered vocabulary th e m ost important thing taugh t in the lesson.
W hen w e look a t the b reakdown of the s tuden ts ' r esponses , we can see
tha t
the answers of the students in
Class
2A covered all subthemes of the
text , w hereas the answ ers o f the s tudents in Class 2B o nly covered two of the
sub themes .
With
regard
to the
learning
o f
vocabulary,
th e
students
of
C lass
2B
m os tly
descr ibed w ha t they had learned in m ore general terms (e .g ., "using w ords to
m a k e
sentence s," "reading w ords," etc.) . B y co ntrast , a high er proportion of
the
s tudents
in
Class
2A
wrote down specific wo rds tha t they
h ad
learned .
What
Were
the
L ea r n i n g O u t c o mes ?
T he
r esu l t
of the
secon d par t
of the
w orksh eet is shown in Table 4 .4 . To assess the ap propr iate use of wo rds, the
s tudents ' answe rs w ere m arked cor rec t even i f they had ma de m inor mis-
takes in the w r i tten form of the words. W ith respe ct to the w ords " inter rupt"
and
"pol i te ," wh ich
had
been g iven specia l emp has is dur ing teac h ing
in
bo th
c lasses , we can see tha t Class 2A per formed much bet te r in us ing these
words
to
com ple te
the
given text
(30 out of 30
correct
for
C lass
2 A, and
only
9
out of 31 for C las s 2B ) . Rega r d ing the ch arac ters
("insert"
[^|] and "ap-
p e a r a n c e "
[ f f e ] )
w hose form s bo th teachers h ad spen t time teach ing , again
th e
s tuden ts o f C lass 2 A were be t te r ab le to w r i te these charac ter s than the
s tudent s
f rom C lass 2B . Only one m is take (on "insert") was m ad e in C las s
T A B L E 4.3
The
S t u d e n t s '
Responses
S h o w n
in the
First Part
of the
Workshee t*
What is the
mos t impor tan t th ing
Genera l Ques t ion:
Class
(N - t o t a l n u mber of r e sponse s )
1
. The m a i n t h em e a nd s u b t h e m e s of the text
2. V o c a b u la r y
3.
I r re l evan t
r e sponses
taught/ learned
in the
le s son?
2 A ( W = 3 5 ) 2 E ( W = 3 9 )
18 10
5 22
12 7
*Some students
put down
more than
one response.
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TABLE 4.4
Th e Students Performances as S h o w n in the Second Part of the W orksheet
Second Par t : Complete
th e
fo l low ing tex t wi th appropr ia te words /phrases
y ou
ha ve
learned in the lesson.
O u r teacher often te l ls u s t ha t w he n w e mee t teache rs an d c la ssmates in school , w e have
to greet
3
t h e m . In the c la ss room, when th e teache r is t a l k i ng w i t h other c lassmates , do
not in te r rup t a s one l ikes ; w hen the teac he r ta lks to you , do no t look from s ide to s ide .
c
Afte r
school , we have to say goodbye to our teachers and c lassm ates . Then we can be
counted
as
good students
who a re
po l i t e .
d
[English translation]
2A 2E
1 . Use of words
1
. 1
A ppropr ia te
for all
b lanks
30 9
1 .2 One to t h r e e b l a nks m i s s ing / ina pp r op r i a t e — 22
2. Form
of
cha rac te r s
W r o n g l y w r i t t e n
N ot t a ugh t in the le sson :
T a ugh t in the lesson:
" M o u t h "
"Wave"
"Watch"
"West"
"Insert"
"Appearance"
8 4
1
1 —
— 1
1 7
—
4
Note .
a
T he
word
"greet" [^J
% Q °^-]
i s m ade up of
three Chinese characters , "beat"
T ], "wave" [ j£ ], and "ca l l" [ *f-].
word " in te r rup t" [ | j |
° ^]
is ma de up o f two C hin ese cha rac te r s , " inse r t" \ f f i j
]
and
" mou th"
°The word
" look
f rom s ide to s ide" [ Jt ^ \3j St ] '
s
rnade up of four Ch ine se c ha r a c t e r s ,
"east" [ Jt ],
"open"
[ ̂ ],
"west"
[ gj ], and "watch" [ 5t ]•
d
The word
"pol i te" [^ffe]
is
ma de
up of two
Ch ines e cha rac te r s , "po l ite"
[^] and
"appearance
100
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4.
S I M U L T A N E I T Y
A N D T H E E N A C T E D O B J E C T O F L E A R N I N G 1 01
2A ,
w hereas
1 1
m istakes w ere noted
in
Class
2B (7 on
"insert";
4 on
"ap-
pearance") .
Simultaneity
and the
Possibility
fo r
Learning.
In
order
for the
s tudents
to
be ab le to use the w ords learned in the lesson to f i l l in the blank s o f a given
text,
i t w as not enough for them simply to know how to w ri te the form of the
characters that made up that wo rd. T he students also had to understand the
meaning of the words, and be able to use them in an appropr ia te context .
That
is,
they
had to be
able
to
discern simu ltaneously
the
form ,
th e
meaning,
and the usage of the w ord. Lesson 2 A w as s tructured in such a w ay as to a l-
lo w
the
students
to be
simultaneously aware
of the
w ord attributes (form
and
m e a n i n g )
that are cr i t ica l to the words being used appropr ia te ly. Corre-
spondingly,
w e
fo und that
the
students
in Class 2A
were better able
to
dis-
cern these a t t ributes s im ultan eou sly than the s tude nts of Class 2B.
In Lesson
2B ,
a l thoug h
the
s tudents were a lso taugh t
the
same w ords ,
the
cr i t ical a t t r ibutes o f each word were taug ht in different episodes, and there
w as no a t tem pt to he lp the s tudents link these aspects together . A lthou gh the
form of the charac te r meaning "insert" was taught in Episode 2, and the
m ean ing of the word " interrupt" (w hich consists of the two ch aracters " in-
sert"
and
"mouth")
w as
t a u g h t
in
Episode
3, the
s tudents were
no t
m a d e
aware s imul taneous ly
of
these
tw o
attr ibutes (form
and
m e a n i n g )
of the
character "insert,"
and may
have considered them
as two
different, unre-
la ted ent i t ies . In oth er wo rds, even if only three words were taug ht in the les-
son, if the three different attr ibutes of each word were taught as unrelated
en t i t i es—ins tead
of
present ing them
as
three attr ibutes
o f
three words—
some students m ay perceive these attributes as nine unrelated e ntit ies to be
learned. The l a rge numb er o f un re la ted ent i t ies m ight cause some s tudents
to be
confused, whereas others m ight
not be
able
to
cope w ith
so
m a n y
n ew
th ings in a
shor t t ime . This
m ay
accoun t
for the
fact
th a t a l thoug h
the
teacher
of Lesson 2B spent mu ch t ime teaching the s tudents how to cor rec t ly w r ite
the forms of the words "insert" and "appearance," many students still got
them w rong. Of course , some s tudents m ight still be able to exper ience the
at t r ibutes s imul taneously
because o f p rev ious exper iences . How ever, the si-
m u l t a n e o u s exper ience
o f different
a t t r ibutes
was no t
b rough t abou t
by the
co n sc io u s effort of the teacher , un l ike in Lesson 2A , whe re the teacher con-
sc ious ly s t ruc tured the learning exper ience s to facil i tate such an exp er ience .
A P A I R O F P R I M A R Y G R A D E 1
E N G L I S H
L A N G U A G E
L E S S O N S
In this section, w e further i l lustrate o u r point by looking at two double peri-
ods of E ng l ish languag e lessons taken from tw o pr im ary G rade 1 c lasses
(Class IB and Class IE ) that were taught by two dif ferent teachers in the
same schoo l . B oth lessons w ere
on e of a
series
of
lessons
on
"Food
in the
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1 02 CHIK A N D L O
superm arket ." B efore this lesson, both c lasses of s tud en ts had a lready
learned the n a m e s o f several i tem s o f food a nd d r ink . Bu i ld in g o n th i s
pnor
knowledge , the teachers a im ed to develop the s tu dents ' abi l i ty to use differ-
ent langu age i tems to describe food and drink (n oun s: e .g., c r isps , m ilk;
partitives: e.g., a bottle of, a pa cke t of; and adjectives describin g size: e .g. ,
large, small), as wel l as their ability to extract spec if ic inform ation (prices
of food and drink) through the use of d ia logue ("How much is it?" "It is
dollars.").
The two
classes
were of similar ability and most of the students were
quite good
at
E ngl ish
as far as
speaking
and
listening were concerned.
Des cr i p t i o n
o f
Lesson
1 B
This lesson consisted
of four
m ain episodes, each
focus ing on an
objec t
of
learning.
In
Ep isode
1, the
teache r revised
th e
names
of
e igh t kinds
o f
food
and
drink that
the
students
had
learned
in
previous lessons. Pictures
and
word cards were shown.
In Episode 2, the teacher introduced th e phrases "a bottle of and "a packet
of to describe th e attributes of some of the food and drink item s shown in Ep-
isode
1. She
explained
to the
class that there were some
food
i tems that
needed
a
partitive
and
some that
did
not .
She
represented
th e
phrases
in
pic to-
rial, spoken, a nd written fo rm s. A lso, w hen she exp la ined the wo rd "packet,"
which was new to the students, the teacher made re fe rence to the more
famil-
iar
word "bag" that earned the sam e mea ning as "packet."
In Episode 3, the teacher expla ined the use of the words "large" and
"small" to
describe
different
sizes
of the
sam e kin d
of food/drink for ident i -
f icat ion purposes—in
her
words ,
"so
that peop le know w hich
one yo u are
ta lking about ." A gain, pic tures
and
word cards were used .
The
m e a n in g
of
the word
"large"
was also exp la ined in term s of another word ,
"big,"
w h i ch
w as
more fam iliar
and has a
s imilar mean ing
to "large."
Finally in Episode 4, the teacher used the context of a supermarket to in-
troduce
the
dialogue, "How m uch
is
it?"
" It is
dollars," w hich
w as
then
posted
on the
blackboard.
T he
students practiced
the
dia logu e
in tw o
differ-
ent
tasks:
guessing the prices of different food and drink i tems, and
role-playing the act of buy ing in a superm arke t. In both tasks, the teacher
did the ques t ioning w hi le the s tudents w ere invi ted to respond by g iv ing the
"i t is" s ta tem ent e ither on a w ho le-class or individual bas i s .
Descript ion
o f
Lesson
1 E
This
lesson
comprised
three interrelated
episodes. In
Episode
1, the
teacher
introduced
the
m ain theme
of the
lesson, "Buying food
in a
supermarket."
Specifical ly,
the
teacher focused
on two
ma in aspects , nam ely
the
food
and
drink tha t could be fo un d in the superm arket, and the dialo gu e used to ask
for the prices of food and drink.
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4.
S I M U L T A N E I T Y
A N D T H E
E N A C T E D O B J E C T
O F L E A R N I N G 1 0 3
In
Ep isode 2, the teach er began by asking , "What kinds of food a nd dr ink
can
we find in a
superm arket?"
Then, the
teacher used pictures
to
in troduce
eight pairs
o f
food
and
drink i tem s
one by
one. Each pair consis ted
o f two
dif ferent-s ized
vers ions of the same kind of food/dr ink (e .g ., one large and
one
sm all bot t le
of
w ater ).
The
teacher required
the
s tudents
to
n a m e e a ch
pai r of i tem s (e .g . , "a large bo ttle of water" and "a sm all bot t le of water"). In
th is way,
the
wo rds describ ing s ize,
the
p arti tives,
a nd the
n a m e s
o f
par t icu-
lar k inds of food and dr ink were presented to the class s imultaneously .
In Episode 3, the teacher to ld the class, "Well , here are some k inds o f
food and dr ink tha t we can f ind in a supermarket . I f we w ant to buy them ,
w h a t
should
we say?"
Then ,
she
pos ted
up the
d ia logue "How m uch
is
it?"
"It is dollars," and in t roduced i t as a way of f inding out the
price
o f
food and dr ink i tem s in a superm arket . T he s tu dents then pract iced the d ia-
l o g u e
by engaging in
different
tasks , such as gue ssing the pr ice of cer tain
i t ems of food and/or drink and pretending to buy thing s in the sup erm arket .
Part-Whole R e l a t io n s h i p s in D i ff e r e n t
Lesson
O r g a n i z a t i o n s
A l t h o u g h
the lessons bo th deal t wi th s imi lar teach ing conten ts , the two
teache rs used
d i f ferent
w ays of s t ruc tur ing the i r l essons , and henc e the re la-
t ionsh ips es tab l i shed s im ul tane ou s ly be tween
the
ob jec ts
o f
learn ing w ere
also d i f ferent . In Lesson IB , the teach er p resen ted the ob jec ts o f learn ing
( n o u n s
fo r
descr ib ing food
and
dr ink; adjec t ives descr ib ing s ize; par t i t ives
used
in con junc t ion w i th uncoun tab le nouns ; and a d i a logue pa t te r n ) in a se-
quent i a l w ay (see F ig . 4 .4) . For ins tan ce, in order to foc us on "small," the
t eacher
showed many exam ples
o f
sm al l i tem s
of food and
dr ink. Then ,
in
order to foc us on "large," she showed m any ex am ples o f la rge item s of food
and
dr ink.
A s a
resu l t , despi te
th e
fact tha t
th e
s ame examples
o f
food
and
dr ink
were used th roughout the lesson , on ly one ob jec t o f learn ing was
b r o u g h t to the fore in each ep isode . This ob jec t o f learn ing w as then left in
the
backg round in the nex t ep isode w hi le som eth ing e lse w as
h i gh l igh t e d .
Episode 1
Introduction
of
the nouns
for different
foods
and
drinks
b,
Episode 2
Introduction
of partitives:
"A
bottle of
and
"A
packet of
^
Episode 3
Introduction
of
adjectives
fo r describing
size:
"Large" an d
"Small"
Episode 4
Introduction
of
a dialogue
used to elicit
prices:
"Dollars"
"How much
is
it?"
FIG. 4.4. T he
sequent ial s t ructure
of Lesson IB .
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1 4
C H I K A N D L O
In comparison, the teacher of Lesson IE focused on each kind of
food/drink as an object that had different attributes (nam e, size, packaging,
and price), and set up the l earn ing wi th the them e o f buy ing in a supermar-
ket . For ins tance, the food and drink i tems (which have thei r own name,
size, and packag ing) were presented a s the th ing s tha t can be found in a su-
permarket (whole)
and
also
as the
objects being referred
to in the
b u y i n g
ac-
tivity. In
th i s way ,
th e
same
set of
nouns , adjectives, par t i t ives ,
and
d i a logu e
were organized in a m anner tha t re la ted them to each other as a t tr ibutes of
certain food/drink i tems,
a s
w e ll
as to the
them e
o f
buy ing
in the
superm ar-
ket as a
w hole . Lesson
IE can
t hus
be
described
as
h a v i n g
a
h i e ra rch i ca l
o r-
ganization (see Fig. 4.5) that ma de
it
possible
for the
students
to
experience
both the
part-whole
relat ionsh ips between thin gs and the aspect-aspect re-
lationships betw een at tributes sim ultaneo usly (see also Table 4.5).
E
pisode 1 : Introduction of the theme, "Buying in a supermarket"
Episode 2: Introduction of food an d drink that can be foun d in
su
dr
pennarket [name, size, and packaging of a certain kind of food and/or
ink]
Episode
3 : Introduction of the buying activity in supermarket
["Dollars,"
"How mu ch is it?" " It is dollars."]
FIG.
4.5.
The
hierarchica l s tructure
of
Lesson
1 E .
TABLE
4.5
A C omparison o f the Structures o f Lesson IB and L esson IE
Lesson
IB
Lesson IE
N o u n s
Adject ives
descr ib ing
size •> Partitives
Type
of
food/
Type
of food/
Type
of
food/
dr ink
1 -> d r ink 2 -> dr ink 3 -^ ...
food/drink 1 ;
food/dr ink
2;
food/dr ink 3;
food/drink 1 ;
food/drink 2;
food/dr ink 3;
food/drink 1 ;
food/drink
2;
food/dr ink 3
n o u n ;
adjectives
descr ib ing
size; w i t h
or
w i t hou t
part i t ive
n o u n ;
adject ives
desc r ib ing
size;
wi th
or
w i t h o u t
par t i t ive
n o u n ;
adjectives
descr ib ing
size;
w i t h
or w i t h o u t
parti t ive
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4. S I M U L T A N E I T Y A N D T H E
E N A C T E D O B J E C T
O F L E A R N I N G
105
Because of the
different foci
and organization of the lessons, the two
classes also
differed in
what came
to be
superordinate.
In
Lesson
IB, the
no un s, adjectives, and part i t ives tha t described food and drink i tem s becam e
superordinate,
as
each
w as
focused
on and
i llustrated w ith varied exam ples
of food/drink i tems, whereas
in
Lesson
IE, the
food/drink became super-
ordinate
as the
teacher focused
on each of the
food
a nd
drink
i tem s and
var-
ied the nouns and adjectives used to describe them (see Table 4.5).
In Lesson IE , how ever, w e find another example of "fusion," tha t is, di f -
ferent aspe cts (size, parti t ives) varying together. W hat is the im pac t of th is
structural difference on student learning?
D e s c r i b i n g L e a r n i n g Outcomes
To investigate the impact of structural difference on student learning, 43
students in
C lass
IB an d 45
s tudents
in
Class
IE
w ere invi ted
to
com ple te
a
worksheet immedia te ly after
the
lesson.
T he
worksheet consis ted
of two
questions. T he
first
question required the students to put down what they
perceived
as the
m ost imp ortant th ing taugh t and/or learned
in the
lesson.
The second question required them to fi l l in blanks in a dialogue (see Fig.
4.6
w here
the
expected answers
are
underl ined) .
F I G .
4.6.
T he
second ques t ion
of the
workshee t .
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1 06
C H I K A N D L O
T he Students Un ders tanding
of
W h a t
They
Learned
in the
Lesson. A s
shown in Table 4.6, nearly a ll the students in Class 1 B reported that the most
important things taught in the lesson were some language items (e.g.,
names, adjectives describing size, partitives,
and the
dialogue). Only
o ne
student mentioned that they
had
learned how
to find the
prices,"
a
concept
that should have been one of the main foci of the lesson.
T A B L E 4.6
Th e
Students Responses
to the
First General Question
of the
Written Task
1 . 1
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
1 .8
1 .9
1 . 1 0
2.1
2.2
3.1
3.2
T he
first
que s t i on :
(N =
total number o f
re sponses;
some students
gave more than o n e response)
]
.
Language items
S om e food
and
dr ink i t ems
Good s
o the r than
1 . 1
Size
Part i t ives
Size
and
par t i t ives
Dol l a r
Pr ices
of d i f f e ren t
food
and
dr ink i t ems
Pr ices
o f goods
other than food
and
d r i n k
T h e
How m u c h ?"
d i a l ogue
Learn ing Engl i sh in genera l
terms (e.g.
r e a d i ng ,
w r i t i n g
E n g l i s h ;
some
E ng l i sh w or ds )
2.
Theme
How to find the pr ices
C o n d u c t i n g
th e
d i a l ogue
o r
a sk ing
the how
m u c h ? "
ques t ion or buy ing food and dr in k in the
contex t o f supermarke t o r t e a c h i ng s i tua t i on
3.
Others
I r re levant
M i s s i n g
W h a t
was the
most
important
t h i n g
t aught / l ea rned in the
lesson?
Class
IB Class IE
(N = 50) (N = 48)
48 40
26 —
— 4
4 8
1
—
3 —
10
6
3 —
— 4
1 1 4
— 4
8
1 —
— 8
I Q
1
—
— —
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4.
S I M U L T A N E I T Y A N D T HE E N A C T E D O B J E C T O F L E A R N I N G 1 07
There were relatively fewer responses in C lass IE (40 out of 48) indicating
language
i tem s
as the
most imp ortant thing taught.
O ne
sixth
o f the
students
actually
quo ted som e exam ples from their ow n personal experience
of buying
goods
at a
supermarket; these exam ples included i tem s men tioned
in the
les-
son
(e.g.,
food or
drink)
as
w ell
a s
some
not
m ent ioned
in the
lesson (e.g.,
ap-
ples, m elons, a teddy bear). N one of the students from the other class did so.
Also ,
regarding those responses that m ent ioned the them e of buy ing
th ings
in a
superm arket,
the
responses
from
Class
IE
w ere m ost ly related
to
the context of buying in a superm arket, con duct ing the dialogue, and asking
the "How much?" quest ion, whereas , the responses
from
Class IB were
main ly abo ut el ic i t ing prices , an d the context w as seldom ment ioned.
What
Are the
Learning Ou tcomes?
The second quest ion required th e
s tudents
to first fill in appropriate words to indicate the different sizes of two
bags pr inted
on the
worksheet ,
and
then
to fill in the
m iss ing blanks
in a
s im -
u la ted d i a logue
on
buying
and
sel l ing.
In
order
to be
able
to fill in the
appro-
pr iate
w ords in the f irst section, the s tudents had to be able to different iate
large and
sm al l objects
and to use the
correct vocabulary.
In
order
to fill in
the b lanks
of the
dia logue ,
the
students
had to be
able
to
recognize
the
sen-
t ences
as par ts o f a dialogu e carr ied ou t in a buy ing and sel l ing context be-
fore
they cou ld choose
the
most appropriate words
to fill in the
b lanks .
A s
shown
in
T able 4.7, nearly
all of the
s tudents
in
both classes were able
to descr ibe the two bags w i th appropriate w ords that indicated their s ize.
This
show s that both classes
had a
good m astery
of the
words descr ib ing
size
as t a ugh t in the lesson. However, a differenc e w as observed in the two
c la sse s 'pe r fo rma nce in answer ing the second part o f the que s t ion . W hereas
m ost of the
s tudents
in
Class
IE
w ere able
to
un ders tand
the
dia logue
as be-
long ing
to a
buy ing
a nd
sel l ing context ,
a nd
comple ted
it in a
me a n i ng f u l
way,
only
o ne
third
o f
C lass
IB
could
do so.
Many s tudents
in
C lass
IB did
no t
recognize
the two
sentences
a s
cons t i tu t ing
a
dia logue ,
and
took them
as
single sentences unrelated to one another . F or ins tance, some s tudents u n-
derstood
the first
inco m plete sentence, "Good a f te rnoo n .
,
please."
in a
c lass room
context ,
and f il led in the
wo rds "sit dow n," even thou gh they
m ade sense
of the
second sen tenc e," dol lars , p lease."
in the
buying
and
se l l ing contex t ,
and f il led in the
word
"ten."
Simultaneity
and the
Possibility
for
Learning.
One
possible
way to ac-
coun t
fo r
these d i f ferences
in
learning
is the
structural difference observed
in
the tw o
t eachers ' ways
o f
handl ing
the
objects
of
learning.
T he
t eacher
of
Lesson IE
organized
the
direct objects
o f
learning
in a
hierarch ical s truc-
ture,
us ing "buying
in a
supermarket"
as a
theme. Different at tributes
( n a m e ,
s ize, pack aging, and price) o f each food/drink we re focus ed on at the
same t ime, w hich
afforded the
po ssibil i ty
of the
s im ul taneous experience
o f
those
at tributes. A s a resu lt , m ore o f the students in Lesson IE expressed
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TABLE
4.7
Th e
S t u d e n t s'
Answers to the
Sp ecif ic Quest ion
of the Worksheet
Second part :
F i l l in the blanks
(A ) A
large/big bag.
A
small bag.
IB
IE
Class
(N = 43) (N = 45)
1 Use of words to indic ate s ize:
1 . 1 Appropr ia te 39 45
1 .2
One to t h ree b l an k s m i s s i n g / inappropr ia te 4 —
(e.g.
"a
large
of
bag,"
"a
smal l
of
bag")
2.
W r o ng
spel l ing
o f
words ( large, smal l , bag)
6 1 1
(B) SI :
Good af ternoon,
a
large/big bag/any
goods.
please.
S 2: Here you are.
S3: How m u c h is it?
S4: Ten dol lars , p lease.
1. Fil l in bo th b lanks appropr ia te ly
( e i t h e r
u s i n g the 15 37
i n format ion
from
the
lesson, i .e.
the
e igh t k inds
o f
food
and
d r ink i t ems ,
o r
that provided
in the
worksheet , i .e . two bags of
different
s izes )
2. Fi l l in one of the blanks appropriately
2.1
,
please.
— 2
2.2
dollar s, please.
1 8
a
4
3. Inappro priate answers to
3.1 both
2.1 and 2.2 2
b
—
3 . 2 2 . 1
a n d
l eav in g
2 .2
b l an k
l
c
—
3.3 2.2 and
l e av in g
2.1
b l an k
2
d
—
4. Did not
respond
5 2
N o t e . I nappropr i a t e answers to 2 .1 , fo r example, "si t down," "Miss W ." " H a v e a b i scu i t . " "many
in," "you are," "teacher and,"
"good
night ," " thank you."
Inappropr iate answers to, for exam pl e , 2.1 "you," "teacher and"; 2.2 "here." "it is"
Inappropr i a t e
answers to, for example, 2.1 and leaving 2.2 blank ("many in") .
Inappropr iate answers to, for example, 2.2 and leaving 2.1 blank ("it," "it is").
1 8
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4 . S I M U L T A N E I T Y
A N D T H E
E N A C T E D O B J E C T
O F
L E A R N I N G
1 09
w hat they h ad learned in a contextual and organized w ay. In this lesson , be-
cause
th e
food
and
drink items were superordinate
to
their attributes,
it
seems that
the
students cou ld relate mo re readily
to the
fact that
the
objects
of learning w ere
the
food
and
drink items that
can be
purchased
in a
super-
market , and that the "How
much? "
dialogue w as used to inquire about price
in a supermarket . The students could hence see the relevance of wh at they
learned, because i t w as fam iliar to their daily experience. In Lesson IB ,
however , because
the
words and/or adjectives describing
the
attributes
of
food and drink were su perordinate to the food and drink i tem s, it seem s that
mos t
of the
students
not
only
had
difficulties relating these attributes (the
languag e i tem s)
and the use o f the
dialogue
to the
t hem e
of
"buying
in a su-
permarket,"
but also in
relating
them to
their
ow n
daily
experiences.
A l-
though some s tudents might have been able
to
recognize
the
relat ionship
betw een the two by draw ing on their ow n past experiences, this had been
left
to c han ce, ins tead
o f
being co nsciou sly structured
by the
teacher.
In
Lesson
1E,
on the o ther hand, the consciou s effort of the teache r to structure the les-
son using the theme of buying in a superm arket
afforded
the stude nts the si-
m ul taneou s experience of context , w hole and parts .
Because l anguage i t ems such
as
part i t ives were highlighted
and
kept
superordinate
in Lesson IB and not in Lesson IE, we w ould expect to see
some difference between Lesson IB and Lesson IE w i th respect to the s tu-
dents ' unders tanding of these langu age i tem s. That i s, we should see that
some studen ts in C lass IB should be able to
identify
these i tems as the mo st
imp ortant th ing taught
in the
lesson. This
w as
indeed borne
out by the
stu-
dent da ta: Four s tudents in Class IB m ent ioned part it ives as being the m ost
impor tan t
thing being taug ht , w hereas none
of the
students
from
Class
1 E
mentioned part i t ives (see Table 4.6).
C O N C L U S I O N S
So far, we have discussed the possible effect of lesson structures on stu-
dents ' learning outcomes. This effect might be unders tood in terms of
whe the r
aspect-aspect
and/or
part-whole
relat ionships could
be
experi-
enced s imul taneous ly
by the
learner. Usin g
th e
example
o f the
pai r
o f
m a th -
emat ics lessons ,
w e
i l lustrated
the
different w a y s
in
wh ich
the
teachers
created the con di t ions for the s im ul taneo us experience o f the two aspec ts of
fract ional
numbers . We then gave examples of two Chinese language les-
sons
and tw o
E ngl ish lang uag e lessons
to
i l lustrate
how the
teachers w ere
able
to structure their lessons to facilitate the s tude nts ' s im ul taneou s experi-
ence o f parts and w holes, and aspects versus aspects.
In the ana lysis of these tw o pairs of langu age lessons, i t w as also shown
that
the
differences
in
students' learning outcomes
are
related
to the
struc-
tural
differences in the way s in w hic h the teachers organized the objects of
learning, tha t is, to the differences in the enacted object o f learning. The in-
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1 1 0 CHIK A N D L Q
teresting fact is tha t in the case o f these tw o pairs o f lessons, the two teachers
used the same teaching material, subscribed to the same intended object o f
learning, and almost certainly believed tha t they carried out the sam e lesson
as
w el l.
W e c an
presum e that both teachers w ould have said that
the
enacted
object o f learning was, o f course, the same in both classes.
How ever, this w as not the ca se— as w e have seen. T he enacted o bject o f
lea rn ing differed sub s tant ia l ly in both ins tanc es . This i s because w ha t stu-
dents learn is not a
func t ion
of the in tended ob jec t of lea rn in g , but of the
enacted ob jec t o f l e a rn ing , and w h a t the s tudents in these tw o c lasses
learned c lear ly d i f fered . The teachers were f ound to have directed stu-
dents' a t tent ion to par t icu la r aspec ts o f w h a t w as t o be learned by s tructur-
ing the
lesson
in
such
a way
tha t
th e
chosen aspec ts were kept invar iant
and
superordinate to those aspects that var ied. B u t w h a t w as invar iant an d
superord ina te m ade a d i f fe ren ce to how w el l the s tude nts achieved the ex-
pected l e a rn ing ou tcomes .
This has s igni f icant imp l ica tions for w ays of im proving the qu a l i ty of the
teaching-learning cyc le . It is l ikely that s tuden ts w il l learn bet ter if teachers
can structure their lessons in such a way tha t s tudents are able to discern and
exper ience s im ultan eou sly par ts and w holes, and aspects versus aspects .
E N D N O T E S
'For the backg round o f th is research p roject , see the E p i lo g u e .
2
It i s impor tan t to no te tha t accord ing to the no ta t ion sys tem used in S w eden ,
6/3 has dual meanings: "s ix th i rds" and "six divided b y three."
3
W e use
"word"
here to refer to a m ean ing fu l en t i ty in the C hinese l anguage . A
m e a n i n g f u l
ent i ty
can be
s ing le -sy l labic (cons i s t ing
of one
cha r ac t e r )
o r
mu l t i -
syllabic (comprising two o r more characters) .
4
W e
u se "characters" to
re fer
to the w r i t ten fo rm s o f m o r p h e m e s in the Chinese
language. Some characters are m ean ing f u l on their ow n (s ingle-syl labic en t i t ies)
and
some need
to be
co up led w i th o the r cha rac te r s
so as to
m a k e
a
mean in g fu l
en-
t i ty (m ul t isyl labic ent i t ies) . B ecau se a l l the s in gle-sy l labic ent i t ies referred to in
this chapter have thei r ow n m eaning s , and bec ause very
of ten
the i r fo rm s o f w r i t-
ing
were deal t w i th
in the
lesson,
w e
sha l l refer
to
these
a s
"characters,"
and
re fe r
t o
mult isyl labic ent i t ies
as
"words"
fo r
easy re fe rence .
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O n
Language
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5
Questions
and the Space of Learning
Amy B M
Tsui
Ference
Marton
I d a A. C. Mok
Dorothy
F P Ng
Q U E S T I O N S
Quest ions is perhaps the most thoroughly researched area of classroom
learning.
This is probably because it is the most distinctive feature of
class-
room
discourse .
A
lesson
is a
speech event w here people com e together
and
engage in an
activity referred
to as
"learning." Lessons
are
organized
in
such a way
tha t there
is at
leas t
one
person
in the
classroom
who is the
"pri-
mary knower" (Berry, 1987) and who is responsible for d i s s e m i n a ti n g
knowledge
to the others. ' The knowledge gap between the "pr imary
knower"—that
is, the
t eache r— and
the
"secondary know er"— that
is, the
s tudents—vests
author i ty
in the
fo rm er
in
de termin ing
the
direct ion that
the
lesson
wi l l take ,
th e
act ivi t ies that w il l
be
conducted,
the
quest ions that w il l
be
asked,
and
what constitutes appropriate answers
to
these questions.
W h e n
a
teacher asks
a
que st ion,
the
purpose
is not to
obtain inform ation
that
the teacher does n ot have, but to check whether the students have the
m issing inform ation indicated
in the
quest ion. W hen
a
teacher asks, "W hat
t ime
is it,
Johnny?"
Johnny know s that he is supposed to tell the teacher the
t ime even tho ugh there is a big clock on the w all that everybody can see. If
Johnn y says, "W ell, look
at the
clock
on the
w all,"
or if he
pu ts
th e
question
back
to the teacher,
"What
does the clock
say?"
the class knows that John ny
is head ing
for
t rouble.
1 1 3
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1 1 4 T S U I E T A L .
Students also know that questions are not asked for their ow n sake, but that
they have
a
pedagog ical m otivation behind them , even thoug h
i t m ay no t be
clear
to the
students exactly what that motivation
is.
Therefore, when
a
teacher asks a series of qu estions, the students are supposed to try and answ er
each one as best they can. They are not supposed to query the purpose of those
questions
by
asking, "W hat
are you
trying
to get
at?"
or
"What
has
this ques-
t ion got to do w ith the preceding question?" at least not in A sian classroom s.
Qu estions serve a num ber of other purposes in the classroom besides know l-
edge checking. For example, questions can be used for classroom manage-
m ent purposes such as preventing th e students cha tting, getting the students to
focus
on the
lesson rather than daydreaming,
and so on
(see Tsui, 1995).
In
this chapter,
we are not
interested
in
classroom questions
per se, but in the
way the space of learning is c onsti tuted l ingu ist ical ly by the quest ion s asked
by the teacher, tha t is, the responses that can be
el ici ted,
and those that are ac-
tually elicited, and wha t th e teacher accepts as appropriate.
Q U E S TIO N S AN D FOCAL AWARENESS
Qu es t ions asked a t cruc ial stages of a lesson can focus s t uden t s ' at tent ion
on the
critical aspects
of the
object
o f
learning, c reate
the
con text that w i l l
help
students
to
make
sense
of the
object
of
learning,
and
open
up the
space
for explorat ion of an answer .
The
data that
we
look
a t in
this chapter co nsists
of
data sets
from
science
and
En glish classroom s
in
Hong Kong. Prior
to
presenting e ach data set,
w e
provide
a brief sum m ary of the classroom contexts and the objects of learning.
Physics
Lessons:
The Reed Relay
T he data set w e look at in this section con sists of two ph ys ics l essons taug ht
by the same teacher, one taught in Engl ish , w hich is a second language for
the students (referred to as EM I, Engl ish as a medium of instruction), and
one in the
s tudents ' m other tongu e, Ca ntonese ( referred
to as
CM I, Chinese
as a m edium of ins t ruct ion) . The di rect object of learning in both lessons is
the sam e: the function of a reed relay an d how it operates. (F or a deta i led de-
scription of the background of these two lessons, see Ng, Tsui , & M ar ton ,
2001.)
A
brief explanation
of the
direct objec t
of
learning
is in
order here.
T he
funct ion
of a
reed relay
is to
enable
a
w eak electric current
in an
elec-
tric c ircuit to start a m uc h stronger c urre nt in anoth er electric c ircuit by con-
nect ing the tw o w i th a reed sw i tch (see Fig . 5.1 for a picture of a reed relay) .
When a w eak electric current in one circuit
passes
through the reed relay,
a m agnet ic field is produced and the coil becomes an electromag net, caus-
in g
the two
ends
of the reed sw itch to touch one another. O nce the two ends
of the
reed swi tch touch
one
another,
th e
c ircu it that carries
a
very large elec-
tric curre nt is closed a nd the electric curre nt w i ll pass throug h and operate
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Q U E S T I O N S A N D T H E
S P A C E
O F L E A R N I N G
1 1 5
FIG.
5 . 1 .
A
reed relay.
the device tha t is connected to it (see Fig. 5.2b and Fig. 5.3b). In the ex am ple
l e s s o n s , th e t e a c h e r u s e d a d e v i c e c a l l e d a l i g h t - e m i t t i n g d i o d e
(LED)—which requires only a weak cur rent to operate (see Fig. 5.2a)— and
a motor— w hich requires a very large current to operate (see Fig. 5.3b)—to
i l lustrate
how the use of a
reed relay enables
a
weak cur rent
to
activate
a
very
large current ,
an d
cause
the
motor
to
rota te .
T he s tructures of the two lessons are a lmost iden tical . In both lessons, the
teacher
first
explained the structure of a reed relay by showing that i t con-
sists o f a reed sw itch w ith coi ls wrapped round it (see Fig. 5.1) . S he then ex-
plained
the
con f igura t ion
o f a
simple circuit connected
to an LED
(see Fig.
5.2a),
and the
conf igurat ion
of a
complicated circuit also connected
to an
L E D (see Fig. 5.2b).
Th e teacher asked the s tudents to condu c t tw o exper imen ts . In the
f i rst
expe r imen t , s tudents w ere asked
to
connec t
tw o
c i rcui t s .
O ne
c i r cu i t
w as
cont ro l led by a push bu t ton sw i tch an d conn ec ted to an L E D , and w as re-
F IG .
5.2. (a) A s imple ci rcui t , (b) A compl ica ted c i rcu i t w i t h a reed relay.
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1 1 6
T S U I
E T A L .
F I G . 5.3. (a) A s i m p l e c i rcu i t , (b) A c o m p l i c a te d
c i r c u i t
w i t h reed
relay .
ferred
to as the
s imple circuit (see Fig. 5.2a).
T he
o ther c i rcui t
w as
a lso
control led by a p u s h b u t t o n , and had a reed re lay con nec ted to it as w e l l as
an L E D .
This
c ircui t w as referred to as the
com plicated circuit
(see Fig.
5 .2b) . Th e teacher asked the s tudents to press the pu sh but ton sw i tch for
both c i rcui t s . In both c i rcui t s , the LED glowed when the c i rcui t s were
closed by pressing the push bu t ton swi tch , w h ich a l lowed an e lectric cu r-
rent to pass thro ug h. In the second ex per im ent , the teach er asked the s tu-
den t s to r ep lace the LE D w i th a mo to r, and the push bu t ton sw i tch w i th an
L D R
( l ight-d iode res is tor )
2
fo r
both
th e
s i m p l e
and the
c o m p l i c a t e d c i r-
cu i t s (see Fi g. 5.3a and F ig. 5.3b) . An L DR i s a l ig ht sens i t ive device t ha t
stops an
electric
cur rent f rom pass ing through. When l ight shines on an
L D R , its resis tance drops an d e lec t r ic i ty can pa ss th rough . T h e t e a c h e r
asked the s tuden ts to sh ine a torch on the LD R and w atch wh at hap pen ed.
T he students found tha t th e motor in the s imple c i rcui t (wi thout the
reed
r e l ay )
d id no t
move , whereas
th e
motor
in the
c o m p l i c a te d c i r cu i t ( w i t h
th e
reed re lay) did. Th i s i s beca use the e lec tr ic cur rent tha t passed thro ug h the
s imple c i rcu i t w as not b ig eno ugh to caus e the mo tor to ro ta te . By cont ras t ,
in the
c o m p l ic a t e d c i r c u i t ,
th e
cu r r en t became m uc h la rger
a f te r
p a s s i n g
throu gh the reed relay , and hence a l low ed the m otor to ro ta te .
After
the s tudents had per formed the two ex per iments , the teacher w ent
over w hat they had experienced w ith the wh ole c lass . She asked them to
tell
her w h a t happened to the LED when they
pressed
the push button switch
and they repor ted that the L ED in both c ircu i ts glo w ed. On h ear ing the s tu-
dents ' reports, the teacher posed the fo l lowing q u e s t i o n :
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5.
Q U E S T I O N S
A N D T H E
S P A C E
O F
L E A R N I N G
1 1 7
5.1 [Physics Lesson/CMI]
3
T : It
seems tha t
if
this
is the
case,
w e do no t
need
to use the
reed
re-
lay.
W hy use the com plicated ci rcui t wh en the s im ple ci rcui t can
do
the
job?
Do you
agree?
T he
teacher problematized
the
students' observation
by
pu t ting
a
hypo-
thet ical s tatem ent to them : "If this is the case, w e do not need to use the reed
relay." Here , "this
is the case"
refers
to the fact
that
the LE D
glow ed
in
both
circui ts ,
sug gest ing that there w as no difference between the two ci rcui ts .
However ,
the
teacher signaled that this hypothesis
m ay or m ay not be
con-
firmed, by
prefacing
the
statement with
"it
seems
that." This
prepared
the
ground
fo r the
fo l low ing quest ion: "W hy
use the
com plicated ci rcui t w hen
the
sim ple circuit can do the
job?"
Th e presuppo sition of this que stion is tha t
the
sim ple circuit
can do the job in the
same
w ay as the
com plicated circuit .
W hat is quest ioned is the reason for us ing the co m plicated ci rcui t . The q ues-
t ioned element focused
the
students ' at tention
on the
com pl ica ted circuit ,
and the
reason
fo r
us ing
it . Th e
jux tapo s i tion
of the fact
that
the
s imple
and
com plicated ci rcui ts could both l ight
up the L ED
created
the
need
for an ex-
planat ion (see Ogborn, K ress , M art ins , & M cGil l icuddy, 1996) and opened
up the
space
for
exp loring
the
function
o f a
reed relay.
T he
qu est ion created
th e
context
for
making sense
of the
ou tcome
of the
second experiment .
T o
put i t another way, the quest ion created the need to look for the answer in the
second experiment .
As already described, in the second experiment, the teacher asked the
s tudents to replace the push but ton swi tch w i th an LDR and the LE D w ith a
m otor in both ci rcui ts . She asked them to shine a torch on the LDR and see
whe the r
the
motor moved
in
each
of the
circuits (see Fig.
3a and
F ig. 3b).
After
the
experiment ,
the
teacher w ent over wh at
the
students
h ad
experi-
enced.
S he
asked
the
s tudents w hat
had
happened
to the
m otor
in the
c o m-
plicated circuit . The students reported that the motor rotated. She then
cont inued
as
follows:
5.2
[Physics Lesson
/
CM I ]
T :
Yes ,
h o w
about th i s s ide? [The teacher po in t s
at the
s i mp l e
c i rcu i t ] This s ide is even s impler . Now, here w e g o . S t r o n g
l i g h t sh i n e s
on the LD R, e l ec t ri c r e s i s t anc e va lue dec rea ses .
W e expec t t ha t there's an e lec t r i c cur ren t , a s t ronger e lec t r i c
cu r ren t , pas s in g th ro ug h the c i r cu i t and t he m o to r shou ld ro -
ta te , r igh t?
But i t i s
ve ry unhappy .
I t does n o t r e s p o n d . W e
n e e d
to exp l a in t h i s .
This tim e, the teach er drew the studen ts ' at tention to the sim ple c ircuit by
asking , "How about this
side?"
S he problem at ized the experience by po in t -
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1 1 8 TSUI E T A L .
ing ou t that the failure o f the m otor to respond, even tho ug h a stronger elec-
tric current
passed
through
the
circuit,
w as
contrary
to
w hat they expected.
Again she created a need for an explanation.
Let us
pause here
and
look
at why the
teacher
did not
focus
on the
reason
for
the
m otor rotat ing
in the
com plicated ci rcui t ,
bu t
ins tead focused
the
stu-
dents'
attention
on the reason fo r the m otor in the sim ple circuit no t rotating,
even tho ugh the electric resistance value decreased and the electric curre nt
became stronger.
W hy did the
teacher
do
that?
In
the first experiment, the LED worked in both circuits . If the teacher
had drawn the students ' at tention to the complicated circuit , the students
w ould have not been able to discern the
differenc e
between the two ci rcu i ts
because
in the
co m plicated ci rcu i t both devices ( the
LED and the
m o to r)
worked. B y jux tapos ing a c i rcu i t in w h i ch the motor worked (a com pl ica ted
circui t)
wi th another ci rcui t
in
w h ic h
it did no t
work
(a
s im ple ci rcui t ) ,
the
teacher brought into the students '
focal
aw areness different respon ses of the
same device, and opened up the space for exp loring the answer in the differ-
ent configurations of the two circuits.
Sub sequently, the t eacher put an a mm e te r in each c i rcui t to m easu re the
strength of its electric current. T he readings showed that the electric curre nt
in the
s imple c i rcui t
w as
m uch sm al ler than tha t
in the
com pl ica ted c i rcu i t .
T he teacher then guided the students through each circuit and helped them
to formula te the reason w hy the m otor did not rotate in the s imple c i rcui t ;
that is,
that a l thoug h
the
elect r ic current became s t ronger when
the
resis-
tance value decreased,
i t w as not
s trong enoug h
to
cause
the
m o to r
to
rotate.
The teacher did not s top here, how ever. She then w en t back to the s imp le
circui t
w i th
the LE D in
Fig .
2a and
posed
the fo l lowing
ques t ion :
5.3 [Physics Lesson/CMI/T8]
T: W hy is i t
that this circuit [ the simple
c i rcui t
connected
to an
LED ] worked?
Why was i t
[LED]
so
w el l -behaved?
W hy did i t
[LED] l igh t
up?
B y
asking these quest ions ,
th e
t eacher
w as
j ux t apos ing
the
s im ple c i rcui t
connected to an LED w ith the s imple ci rcu i t conne cted to a m otor. In other
words ,
she now
held
the
ci rcu i t constant,
and
varied
the
device,
the
motor ,
and the
LED.
T he
questions
she
asked brought into
the
students '
focal
awareness the
different
responses of the two devices, and opened up the
space for exploring the reasons. A correct unde rstanding of the reasons w as
achieved w hen o ne student explained that th e c i rcu i t w i th the LE D l i t up be-
cause the electr ic current needed by the L ED w as sm al ler than the curren t
needed
by the
m otor. This
is the
corollary
of w hy the
m o to r
did not
rotate .
Let us recapi tulate the wa y in w h ic h the teacher structured the l earn ing
experience.
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5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 1 9
First of all, in the
first
experiment , the teacher varied the con f igura tions
of the tw o circuits so that there wa s on e w ithout a reed relay (i .e . , a sim ple
circuit [Cl]),
and one
with
a
reed relay (i.e.,
a
complicated circuit [C2]),
w hereas the device that the s tudents operated was invariant ( the LE D [D l]) .
In both cases, the LED li t up.
In the
second experiment,
the
teacher changed
the
device
from the LED
( D 1 ) in the first exper im ent to the motor (D2) for both c i rcui ts . This t im e, it
w as also the device that w as invariant (the m otor [D2]), and the circuit that
varied (the
one
w ith
a reed
relay
[C1 ] and the one
without
a reed
relay [C2]).
W hat the
teacher
did is
represented diagrammatical ly
in
F ig. 5.4a .
How ever, in the second experiment , the variation tha t th e teacher wanted
the
students
to experience was not the
variation between
the two
circuits,
but
the varia t ion between w hat they experienced in the previous
conf igura -
tion (the first experiment) an d the present
configurat ion
( the second experi-
ment) , which
was due to the use of
different devices:
Dl in the first
exper iment
and D 2 in the
second experiment .
T he
teac her ' s exho rta t ion
for
an ex planat ion in the second ex cerpt (5.2) and the question in the third e x-
cerpt (5.3) foc use d precisely
on the different responses of the LE D (D 1) and
the motor (D2) . In other words, the teacher was now construct ing the s tu-
den ts ' total experience (of the two experiments) as a wh ole. S he held the cir-
cui t conf igura t ions cons tant
(in
both exper iments ,
a
s imple
and a
compl ica ted circuit w ere involved), and w hat varied w ere th e devices ( in the
first experim ent an LED was involved, w herea s in the second experim ent a
motor
was
involved).
The
structure
of the
potential learning experience
can
be represented by Fig. 5.4b, where the bolded parts represent the aspects
that
w ere held constant
in the first and
second experim ents ,
and the
unde r -
lined p arts represent
the
aspects that varied.
This structure of variation brought the
responses
of the devices into the
students '
focal
aw areness
in
relation
to tw o
contexts:
why the
m otor rota ted
in the co m plicated circuit but did not in the simp le circuit , and w hy the LE D
worked in the simple circuit but the m otor did not. If, in the second experi-
men t ,
the
teacher
had
replaced
the LED
w i th
a
motor only
in the
com pl i-
First E xpe r ime n t Cl -^ Dl C2 -»• Dl
Second E xpe r ime n t C l -*-> D2 C2
-*•
D2
C l = s im p le c i r cu i t D l = LE D ( l ight-emit t ing d iode)
C 2 = com pl i ca t ed c i rcui t D2 = m o t o r
- * • caused
device
to opera te
-*r>
fai led to
ca use device
to
opera te
F IG .
5 .4a . S t ruc tur ing learning.
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120
T S U I
ET AL.
First E x p e r i m e n t Second Expe r imen t
Cl •* D_L
C l -x->
D2
C2
•* Dl C2 •* D2
FIG. 5.4b. Stru cturin g of learning; first experim ent versus second experim ent.
cated circuit (as shown in Fig. 5.4c) both devices would have worked and
the
s tudents ' a t tent ion w ould
n o t
have been
so
sharply focu sed
o n
w h a t
it is
that
a
ci rcu i t w i th
the
reed relay
can do
tha t
one
w i thou t canno t .
C onversely, if the teache r ha d started off by us ing the m otor as the device
for
both ci rcui ts
in the
first
experiment , then
all the
s tudents w ould have
seen w as that the
m o to r
w orked only in the c i rcu i t w i th the reed relay. They
wou ld n ot have been able to see tha t the electric curren t in the s im ple c i rcu i t
w as a weak current w hich could operate an L ED , but not s trong enoug h to
operate the motor. Consequently, the main characterist ic of the reed relay
( that
it uses a smal l current to swi tch on a s t rong current) would n ot have
been so
effectively h igh l igh ted.
Wh a t
is
even more interest ing
is the w ay the
t eacher m ade
the
s tudents
see the interrelat ionsh ip betwee n the first exp erim ent and the second experi-
ment : that
the LED
needs only
a
smal l current
to
operate (w hich
is w hy i t
worked
in the
s imple ci rcui t ) , whereas
the
motor needs
a
large current
(which is why it did not w ork). In order to ma k e the mo tor wo rk , a reed relay
is
needed becau se
it can u se a
smal l current
to
start
a
very large curre nt .
The
teacher ' s e xplanat ion can be represented on fo l low ing pa ge (see Fig. 5.4d).
T h e w a y tha t the teacher s t ructured th e learning experience by posing
questions
a t
cri t ical points
in the
lesson brou ght in to s tuden ts '
focal
aware-
ness cri t ical aspects
of the
exper im ent
and
opened
up the
space
fo r
explor-
ing the
answers
to the
quest ions .
This w as
cruc ia l
in
b r ing ing about
the
s imu l taneo us aw areness of the three phenom ena ( i .e ., the sm al l current re-
quired
to operate the
LED,
the
very large cu rrent needed
to
operate
t he mo-
tor, as we l l as the w ay in w h ich t hey are re la ted) , w hich w as necessary for
the
students
to
unders tand
the funct ion of the
reed relay.
S o
far,
w e
have i l lus t rated
h ow
quest ions
can be a
pow er fu l m eans
for
bring ing cri t ical aspects
o f the
ob jec t
o f
l earn ing in to s tudents ' focal aware-
ness,
and
opening
up the
space
for further
enqui ry .
W e
have also seen
how
Fi rs t E x p e r i m e n t S e c on d E x p e r i m e n t
C 1 - D 1 C 1 - * D 1
C2-"D1 C 2 - D 1
F I G .
5.4c.
A l t e rn a t iv e s t ru c tu r i n g o f
l e a r n i n g .
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5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 21
Cl <C2
Dl
<D2
C l
- * D 1
C l -x->D2
C2-*D2
F I G . 5 .4d . Teacher ' s exp lana t io n.
the teacher skillfully structured the learning experience by posing que stions
at cri tica l junc tures
in the
lesson.
In the
follow ing section,
w e see how
different questions asked
by the
teacher
can bring different aspects of a phenom enon into students' focal awareness.
E ng l i s h Lessons:
O ld M a c D o n a l d ' s F ar m
The
data that
is
discussed
in
this section consist
of two
primary Grade
1
En gl ish lessons (Class ID and Class IE) tau gh t by two teachers w ho used
very similar materials and whose lesson object ives were the same. T he
topic o f the lessons w as "Old MacDonald 's Farm," a n Engl ish song about
farm an imals that
is
fam iliar
to
ch ildren
o f
many
different
na t ional i t ies .
O ne
of the ob jectives of the lesson w as to teach the determ iner "some" to signify
inexact
quantity.
In the
song,
the
word
"some"
appears many t imes
in the
lyrics, and for this reason, the teachers used the song as a vehicle for teach-
ing this determ iner
to the ch ildren.
B oth teachers used com puter-generated
im age s to revise
farm
anim al vocabulary and su bsequ ent ly to teach
"some."
(For a deta i led description of the backgroun d of these two lessons, see M ok,
R unesso n, Tsui , W ong, Chik, & Pow, 2002.)
Teaching "Some."
B oth teachers began
by
revising
th e
vocabulary
for
farm anim als by asking the quest ion, "W hat can you
see?"
In each case, the
pic ture
of a single anim al was presented on the com puter, and the respo nses
solicited
w ere "I can see a [name of animal]." The
focus
at this stage o f the
lesson w as the nam es of the anim als , ra ther than the num ber. The imp ortant
difference between the two lessons l ies in the subsequent episodes where
both teachers dealt with the teaching of "some."
After
the
vocabulary revis ion,
the
teacher
in ID
asked
the
students
to
guess the number of
different
kinds o f animals o n a farm. She
fol lowed
this
by showing the students different kinds of farm animals and asking how
ma n y
animals there were in each pic ture . The fol low ing is an excerpt of
w h a t
took place in the lesson im m ediately
after
the vocabu lary revision. To
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122 T S U I ET AL.
make
it
easier
for the
reader
to
fol low
the subsequent
discussion
of the
data,
the
parts
that will be
discussed
are underlined.
5.4 [English
Lesson/Old MacDonald's
Farm/Primary Grade
I / I D ]
4
11 9 T: . .. Do you know how many cows o r hens? O r how m any ho r ses ,
120 how many hens , how m any p igs a re ( there) in a
fa rm?
Do you
1 21 know? D o you k n o w ?
122 Ss: No.
123 T: OK,
let's
see
wh a t 's
in the
farm.
A ll
r ight ,
O K ,
w h i ch
one do you
1 24 w a n t to see first?
125
Ss:
Cow.
126 T : OK. you w a n t to see cows. Righ t . Guess how many cows a re there
127 in the
f a rm ?
128 S :
[ shout ing
from his
seat] Four.
129 T: How many cows?
130 S:
[shout ing
from his
seat] Four.
131 T: Yes, Leo.
132 S:
Four .
133 T:
W h a t
do you
think, Louise?
134 S: Three.
135 T: W h a t do you think, H o Seng?
136 S:
Six.
137 T:
W h a t
do you
think Elaine?
138 S: F ive .
139 T: OK , Elaine. Do you wa nt to find out? OK, come here. Let 's find
140 out how
many.
OK,
cows. [Speaking
to
Elaine] Press
the
button
141 please. [Elaine com es up to the f ront and cl icks the m ouse. A n
142
image
of a cow appears on the screen.] All right, OK. Le t 's see
143 how
many cows
in the
fa rm.
W h at
can you see
here? [Teacher
1 44
points
at the
screen. ] What
can you see
here?
145 Ss: I can see a cow.
146 T :
Good.
N ow
let's
f ind out how
m any cow s there are? [Teacher
1 47 clicks the m ouse and four more cows appear on the screen. ] H ow
1 48 many cows are there?
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5. Q U ES TI O N S
A N D TH E SPACE O F L E A R N I N G 1 23
149 Ss: Five.
150 T: Four?
151
Ss:
Five.
152 T: 10?
153 Five.
154 T: . I can s e e . . . ?
155 Ss: ... five cows .
156 T: Righ t . Or you may say ... ?
1 57 Ss: I can see f ive
cows .
158 Ss: I can see a
cow.
159 T:
W h a t ?
16 0 Ss : I can see . ..
161
T: Some
162 Ss:
Some cows .
163 T :
Some cows. Yes. There
are
some cow s here .
Is it
only one?
164
[Point ing
at the
screen.]
165 Ss: No.
166 T: There are four
cows.
You may
say,
I can see some
cows.
OK,
167
wh ole c lass.
168 Ss: I can see some cows.
169 T : A l l r ight , le t ' s con t in ue . . . . [Teacher c l icks the m ouse several times
170 and six
different
types
of
animals appear
on the
screen]
OK, do
17 1 you w a n t to f ind out how many [point ing to the pic ture o f a
1 72 duck] ducks there [are] in the fa rm? ...
In
this excerpt , the teache r started w ith the qu estion , "Do y ou know how
m any cows
or
hens?
O r how
m any horses,
how
m any hens,
how
many p igs
are [ there] in a farm?" The quest ioned elem ent i s the numbe r o f anim als ,
and it w as repeated four t im es . A s w e have pointed out previously , it is the
ques t ioned
e lement tha t
focuses
the
students ' at tention.
T he
focus
on the
n u m b e r o f
an imals
w as
reinforced when
the
teacher asked
the
s tudents
to
guess "how m any" cows there were on the farm (see l ines 126-127). A s w e
can
see
from
the stude nts ' responses, they did indeed focus o n the num ber,
and
proffered
"four,"
"three," "six,"
and "five" as answers. Af ter th is , the
teacher asked
the
students
to f ind out the
answer
for
them selves
b y
invit ing
one of them to c o me up to the com pu te r at the front of the class . The s tudent
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1 24
TS U I
E T A L .
cl icked the m o u s e and one cow appeared. T he teacher asked the s tudent
w h a t
she
cou ld see,
and the
student said that
she
cou ld
see a
cow. This
w as
fol lowed
by the
teacher showing four more cows
on the
screen
and
once
again posing
the
ques t ion , "How m any cows
are
there?"
B y
doing th is ,
the
teacher
w as
con trast ing "one" w ith "more than one." M oreover,
by
repeat-
edly asking the s tudents "how m any cows" there were , the teacher w as con-
trasting "one" with
"other
num bers," that is , w i th a va lue o f more than one ,
hence opening up a dime nsion of var ia tion in num ber . In other words, w ha t
w as brought in to the s tudents ' focal awareness was exac t num bers , w hereas
the object ive of the lesson w as to teach
"some,"
w hich i s an inexac t num ber
rather than an exact number .
T he
focus
on exac t numb er w as re inforced by the teacher sub sequ ent ly
get t ing four s tudents to guess the exact nu m ber of cows ( l ines 1 3 1 , 1 3 3 ,1 3 5 ,
and 137) . W hen the cow s were shown on the screen, the teacher
offered
d i f -
ferent n u m b e r s
to
tease
th e
s tudents
an d
de l ibera te ly suspended
th e
evaluative feedback
on the
exac t num ber tha t
the
s tude nts provided.
I t was
no t unt i l l ine 156 that the teacher t r ied to e l ic i t the determ iner "some" from
the students
b y
us ing
th e b lank -f i l ling
ques t ion :
"Or you may say . .. ?" Th e
students ' responses to this b lank-f i l l ing ques t ion were te l l ing. Some s tu-
dents sa id, "There are five cows," an d some said, "I can see a cow." Bo th a n-
swers provided exac t num bers , w hich sugges ts tha t exac t nu m ber
w as
stil l
very m uch in their focal aw areness. Th e determiner "some" was supp l ied by
the teacher and the s tudents were m ade to repeat it after her. Bu t i t is doub t -
fu l
if the
s tudents
ful ly
unders tood what
"some"
m ean t . W hen
the
teacher
m oved on to the next episode ( l ine 170), w here she showed the pic ture of a
duck, she aga in asked the s tudents whether they w anted to f ind how m any
ducks there were on the farm.
The focus on exact num ber w as a lso re inforced by the way in w hic h the
teacher introduced
the
determ iner
"some."
I n
both cases,
the
word
"some"
w as
in t roduced
a t the
very
end o f the
episode,
by
presenting
it as an
a l te rna-
tive
s ta tem ent
to an
exac t num ber,
fo r
examp le, "There
are
four cows .
Y ou
m ay say, I can see som e cow s," "There are seven d uc ks , or you m ay tell m e, I
can see
some ducks."
In
both cases
the
exact number preceded
the
inexac t
number s igni f ied b y
"some."
Le t us com pare the ju st c i ted discourse w ith the fo l low ing excerpt that
shows w hat took place in the lesson of Class IE after the teacher had fin-
ished vocabulary revision.
5 .5 [Engl ish Lesson/Old M cDonald 's Farm/Pr imary Grade I / I E ]
70 T: [Teacher cl ick s the m ouse ] A dog. [Teacher cl icks the m ouse
71
aga in ] ano ther
dog
[Teacher cl icks
the
m ouse ag a in ] ano ther dog .
72 W o w , w h a t can you see? Al ice?
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5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 25
73 S: I can see three dogs.
74 T: V ery goo d, three dogs. There are three dogs. Thank yo u. And you
75 can say that, in other w ords, w e can say that . ..
76 Ss: We can see
dogs.
77 T: Remember the word "some"?
78 Ss:
Yes .
79 T:
Thank you , very w el l .
I can see
some dogs.
Do you
remember
th e
80 word "some"?
81 Ss :
Yes.
82 T: Yes, a l l r ight . Now , another one. [Teacher cl icks the m ouse] A no ther
83 p ig . OK. Now, so we have a pig, w e' l l see OK. C o m e and press the
84
but ton.
[A
student comes out.]
85 T: Is he
finished?
Is there another pig there? Press the but ton. W ow,
86
ano ther p ig? W ha t
can you see
then?
87 S: I can see some pigs.
88 T:
V ery good
To
begin w ith, the teacher in IE showed the picture of a single an im al, a
dog , ju s t
as the
teacher
in 1D had
done. However, before
she
showed
the
p ic-
ture,
the
teacher asked,
"What can you see?"
rather than "How m any dogs
can
you
see?"
T he quest ioned element is
"what"
and not "how many."
Asking "What
can you
see?"
did not
focus
the
stude nts ' at tention
on the ex-
act
num ber. I t w as open to the students to give ex act or inexact num bers as
answers .
W h e n
the
teache r asked
the
students
to
offer
an
al ternative
fo r
see-
ing
three dog s, the studen ts said, "W e can see dogs." In other w ords, conc ep-
tually, the students were aware that one alternative was to leave out
speci fying
the
exact number ,
and to
s imply
use the
p lura l form
to
indicate
that there
w as
more than
o ne
dog.
A t
this point ,
the
teache r provided
the
l in-
guistic
support
to the
students
by
reminding them that
the
word
"some" had
been in troduced before .
In the
subsequent episodes ,
the
teacher showed
three
different
kinds o f farm anim als : p igs , duc ks and cats . In each episode,
she
varied
o ne
w i th
more
than one,
and
posed
th e
same question, "What
can
you see?"
T he
students
had no
problems responding wi th ,
"I can see
some
p igs
[some ducks , some cats]." In other words , the quest ioned element ,
"what," opened up a dimension of variation in inexact number, that is, on e
versus
some.
Af ter
successfu l ly soliciting the determiner
"some"
from the students,
the teach er w ent on to pose the quest ion, "How m any [anim als] are there?"
in the
third episode.
L e t us
consider
the fo l lowing
excerpt:
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126 T S U I ET AL.
5.6 [English Lesson/Old MacDonald 's Farm/Primary Grade I / IE ]
103 S: I can see some cats .
1 04
T :
V ery good.
O K.
W a it
a
m inu te .
How
many ca ts
are
there?
1 05 How m any ca ts a re there?
106 S: Four cats .
107 T: Is he correct?
108 S: Yes.
1 09
T :
V ery good.
Thank
you .
OK, how
about this picture? A lright.
1 1 0 [Teacher clicks the m ouse.] H o Ming, would you come ou t
111
and
press
i t for me to see
what p ic ture comes o ut?
[Ho
M in g
1 1 2 c l icks the m ouse .]
11 3
T :
W h a t
is it?
1 1 4 Ss : Ducks , ducks .
115 T: V ery good. Thanks. [Teacher asks Ho M ing to c l ick the
1 1 6
m ouse . ] A ny more ducks? [S tudent c l icks the m ouse and
11 7 some duck s appear.]
118
T : Any
more?
[Student clicks
th e
mouse again
and
some more
1 1 9 duck s appear .] A ny m ore? [Student c l ic ks the m ouse
1 20 aga in . ] No more . OK , w hat can you see now ? Hold the m ike
1 21
and
te l l yo ur c lassm ates,
O K?
122
S: I can see some duc k.
123
T:
D u c k s .
124 S:
Ducks .
125 T : Ducks .
126 S: Ducks.
127 T: OK. V ery good. How m any ducks a re there? How m any
1 28
duck s are there?
1 29 S: [same student] Five duck s.
1 30 T: Five duck s. Thank you very m uc h. Five duck s. Yes. you can
1 31
see some duck s, you can see some pigs, you can see some
132 cats,
and you can see
some
...
133
Ss: Dogs.
1 34 T : Dogs. O K . . . .
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5.
Q U E S T I O N S
A N D T H E
S P A C E
O F L E A R N I N G 1 27
Let us consider the sequence o f quest ioning
from
the p erspect ive o f the
logical relationship between inexact
and
exact numbers.
The
determiner
"some" signif ies a range of num bers or qua nt i t ies and is inclus ive of exact
num bers such as 3 ,4 ,5 ,1 0 , and so on . The teacher in Class IE
first
posed the
ques t ion ,
"What
can you see?"
fo l low ed
by
"How m any?" This
is a logical
sequence—when reques t ing in format ion ,
one
often goes
from
general
to
speci f ic—and the exact num ber is seen in relat ion to the inexact num ber. B y
contrast ,
the teacher in Class ID s tar ted wi th , "How many cows can you
see?" which is already very sp ecific, and therefore renders the use of the de-
te rminer
"some"
to describe an inexact num ber su perf luou s . Thus the pro-
duct ion
o f
"some"
becom es contrived.
W hat both teache rs tr ied to teach w as how to express inexact nu m bers
that
are
more than one. However,
the
different quest ions that
the
teachers
asked,
and the way
they sequen ced
the
questions, focused
the
students '
at-
tent ion o n
different w a y s
of
express ing nu m bers that
ar e
m ore than
o ne
( that
is , exact num ber and inexact num ber), and opened up different dim ensions
of variat ion. The enacted object of learning in one case w as an inexact nu m -
ber, wherea s
in the
other case,
i t w as an
exact number , which
w as not an in-
tended ob jec t of learning.
In post lesson interviews con ducted wi th hal f
of the
s tudents
from
each
class ,
a task w as given to solici t the use of "some" to describe a selection of
pic tures . The results showed th at students in Class IE perform ed bet ter than
students in
Class
ID .
QUESTION
TYPES,
QUESTION S EQU EN C ES ,
A N D T H E
SPACE
O F
L EARNI NG
Quest ion Types
Many studies have focused on the cognit ive aspect of questions, and vari-
ous
t axonom ies
o f
question types ha ve been proposed,
for
example ,
the
sys-
tem
of
classifying questions according
to
whether they require
higher or
lower order thinking skil ls . Our concern in this chapter is not to examine
que stion types per se. W e are interested in those qu estions tha t have been re-
ferred
to as
"open"
and
"closed"
que stions, and the oppo rtunities for learn-
ing that are afforded by these qu estions. In part icular, we are interested in
the w ays in wh ich teachers m odify and sequen ce their qu est ions in order to
el ici t
responses from s tudents ,
and
hence
how
teach ers shape their s tud en ts '
learning experiences.
In classroom research l i terature, dist inctions have been made between
closed
a nd
open qu estions. However, there
a re different
criteria
for
identify-
ing
these q uestion s. In education research l i terature, a
c losed ques t ion
has
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128 T S U I ET AL.
been un ders tood as having only one r ight answer, whe reas an open ques t ion
is one
that
has a
n u mb e r
of right
answ ers.
In
th i s vo lum e,
we use
c losed
ques t ions
to m ean qu estions w here there is only one acceptable answer, and
open
ques t ions to mean quest ions where there is a range of poss ib le an-
swers,
or a
range
of
poss ib le w ays
of
present ing
the
answer.
For
exam ple,
"Why does this motor work?" is an open ques t ion , w hereas "W hat is the
nam e given to th is m agnet?" is a closed q uest ion . W hen the teache r asks an
open question,
the
space
of
learning
is
w idened because
the
question chal-
lenges the s tudents to consider a num ber of
poss ib i l i ties ,
and to formulate a n
answer that makes sense no t only to them selves but also to the res t of the
class.
T he
formulat ion
of an
answer
is a
process
in
w h ich
the
students clar-
ify
thei r th inking
a nd
the i r unders tanding
of the
ob jec t
o f
learning.
On the
other hand, closed que st ions narrow down the poss ib le an swers to only one
choice,
or a
l imi ted number
of
choices,
and
hence al low l i t t le room
for
learners to explore answ ers .
In classrooms, it is very common for teachers to decompose a complex
open question into
a
series
o f
simpler questions
in
order
to
help students
to ar-
rive
at
an
appropriate answer. This
is
referred
to as
"piloting"
by
Lundgren
(1977). Studies
of
classroom questions have identified different sequences
of
questions u sed by teache rs, and ana lyzed them as to whe ther they were suc-
cessful
or not in
term s
of
helping students
to
answer
the
que st ion.
For
exam-
ple, among th e sequences of questions that Brown and Edmondson (1984)
identified w ere these
tw o
sequences , w hich they referred
to as
" funne lm g"
(p .
114): an open que stion follow ed by spec ific quest ions; and an open quest ion
followed by a narrowing down of this que stion to recal l facts and s imple de -
ductions.
"Funneling" is mos t com m only found w h e n the teacher has failed
to elicit a response from students w ith the ini t ial open que stion.
In c la s s room s w here a l angu age o the r than th e m o t h e r t o n g u e is used a s
a
m e d iu m
o f
teach ing
and
l earn ing (e .g . ,
in
E n g l i sh
as a
s ec o n d l a n g u a g e
classrooms), we typical ly find modi f ica t ion of wh-ques t ions ( i . e . , from
w hy ques t ions
to
what ques t i ons ) ,
and
c h a n g e s
in
ques t i on
fo rmat
(e .g . ,
f rom wh-ques t i ons to yes-no ques t i ons ) . Th i s is p r imar i l y because re -
sponding to why-ques t ions is l inguis t i ca l ly more demanding than re-
sponding
to
w h a t -qu e s t io n s ( w h i c h of ten r equ i re answers cons i s t i ng
o f
only on e or two w ords o r a phrase) . A nd responding to yes-no ques t i ons
(or a l t e rna t ive que s t ions ) i s leas t dem and ing becau se i t genera l ly involves
the
product ion
o f
ei ther
a
"yes"
o r a
"no" answ er
(o r in
some cases, m ak in g
a choice among the al ternatives provided). "Blank-fi l l ing" questions
(where
th e
t eache r p rov ides pa r t
of the
sen tence
an d
b l a n k s
out the key
word( s ) for the s tudents to f il l in) are a l so typ ica l ly found becau se t hey
lessen
the
l ingu ist ic
burden of the
students (see Tsui, 1995).
Let us
return
to the
physics lesson
on the
reed relay
a nd
consider
the
fo l -
lowing extract :
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5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 29
5.7 [Phys ics Lesson/Reed R elay /EM I/S2/T8]
1 T: . .. Oh
then surely ,
n ow
girls,
can you
explain
to m e, why
doesn ' t
2
th is m otor work?
3 Ss: [silent]
4 T : W hy does n ' t th is m otor work? Jus t because m otor m ust use ?
5 Ss:
[silent]
6 T: The current tha t is ? Large or small ?
7 S: Large .
8 T:
Large .
W e can see that the teacher asked an open quest ion and no response was
fo r thcoming .
Then the teach er provided some l ingu is tic scaffolding in the
form
of filling in the
b lanks . W hen th i s failed
to
el ic i t
a
response,
she
pro-
vided
m ore l inguis t ic help and a gain invi ted the s tudents to f i l l in the b lank .
W hen a response w as not imm ediately for thco m ing, she provided a choice
for them . This kind
of
sequen ce res t r ic ts wha t counts
as an
acceptable
an-
swer; the answer n ot only has to be appropriate in term s o f the content , but
also
has to f i t into the l ingu ist ic structure provided. In order to an swe r the
teacher ' s
ques t ion , th e s tudents had to shift their focus o f at tent ion
from
the
substantive pa rt (i .e.,
the
reason
why the
motor
did not
work),
to an
answer
tha t w ou ld fi t the syn tax given by the teacher . W hen the teacher provided
tw o
choices
to the
s tudents ,
the
cogni t ive deman d
w as
m in im al . This k ind
of
funnel ing effect reduces th e space in w h ich the students can explore variou s
possible answers for them selves , and formula te the appropriate answer. It
a lso has the de t r im enta l effect o f encouraging s tudents to gues s wha t the
teacher has in
m i n d ,
and to try to
produce
an
answer tha t wi l l meet
the
teacher's approval. T he fol low ing is
another
excerpt
from
th e
physics
lesson
on
the
reed relay taug ht through E ngl ish (EM I).
5.8 [Physics Lesson/Reed Relay/EMI/S2/T8]
T he teache r asked the students to compare the electric current re-
quired
to
operate
a
motor
and the
electric current required
for an
LED to
light
up .
1 7 T: . .. W hy
does
the LE D
work here? [Nom inate]
1 8 S :
[silent]
1 9
T: The LE D w orks, but it [Teacher points at the m otor] does not
20 rotate . It 's [a] sim ilar construction. [N om inate] Tell m e, how
21
m uch cu r ren t
is
needed
to
operate
a
motor?
22 S: [silent]
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1 30 T S U I E T A L .
23 T: How much cu r ren t is needed? It should be very ?
24 S: 200mA.
25 T : A h ,
nearly 200mA, very good, very large current .
B ut can you
26 t e ll m e how m uch curren t i s needed to opera te a L ED ?
27 S:
V ery smal l cur ren t .
28 T:
Yes, very sma ll current
is enough all
r ight . Then
can you
explain
29 to me, why does this LED light?
30 S: [si lent]
In
th i s excerpt ,
th e
t e ach e r posed
an
o p e n q u e s t i o n
in
l ine
1 7:
" W h y
does the LED
work?"
W h en the s tudent had d i f f i cu l t i e s responding to the
ques t ion ,
th e
t e a c h e r m o d i f i e d
th e
q u e s t i o n i n t o
a
m o r e
spec i f i c o n e
a b o u t
th e
a m o u n t
o f
e l ect ri c cu r ren t r equ i red
to
o p e ra te
a
motor , "How
m uch cur ren t is needed to
operate
a
motor?"
( l ines
20-21).
She then na r -
ro we d d o wn th e ques t ion fu r the r by t u rn i n g it in to a b l a nk- f i l l i ng q u e s -
tion
in
line
23, "It
shou ld
be
very
?"
w h i c h p ro v i de d
th e
s t u d e n t s
wi th the l inguist ic s t ructure of the first par t of the answer , and on ly re-
qui red them
to f i l l in the ke y
w o rd ( s ).
A s
p o i n t ed
o u t
be fo re , t h i s k ind
o f
funne l ing o f ten h a p p e n s
in
c l a s s ro o m s wh e re
th e
s t u d e n t s ' l a n g u a g e
ability
is
we a k because
i t
lessens
the
l ing uis t ic burden
on the
s tudents
to
f o r m u l a t e
the re sponse .
The use of this type of quest ioning sequence focuses the studen ts ' attention
on how they can finish the sentence in a w ay that w ill fit into the syn tax of the
partial
sentence provided, and, very
of ten, in a way
that
wi l l
also correspond
with
th e
answer
the
teacher
has in
m i n d.
In the
ju st c i ted excerpt ,
the
teach er 's
subsequent question "How m uch current is
needed?"
focused the students' at-
tention on the
size
of the
current .
The
l inguist ic
scaffolding
that
the
teacher
provided
required
the
students
to put in an
adjective rather than
an
exact
figure
(see line 23). Th e student, however, attended to the "how m uch " qu estion and
provided
the
ex act size
of the
current. Al thou gh this answer
was
accepted
by
th e teacher, she rephrased it as "very large current." W e can assum e that the
students then realized th at the teacher was loo king for a general description of
th e
size rather than
the
exa ct size
of the
current ,
if w e
look
at the
subsequent
exchange.
W h en
th e
teacher asked, "How m uch current
is
needed
to
operate
an
LED?"
(line 26), a student this tim e replied, "a very sm all current" instead
of
giving
the
ex act size
of the
current (see l ine 27).
From this discussion,
we can see
tha t
th e
types
o f
qu est ions asked
by the
teacher can
either o pen
up the space of
learning
by
encou raging students
to
explore possible answers
an d to
form ula te the i r
ow n
answers ,
or
reduce
the
space o f learning by conf in ing students to only a rest r ic ted num ber of possi-
bilities
and
even
by
encouraging them
to
engage
in
guesswork.
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5. Q U E S T I O N S AND THE S P A C E OF L E A R N I N G 131
Question Sequence
and
Focal Awareness
So
far, w e have seen that questions play a very im portant role in constituting
th e
space of learning in the classroom . They structure the learning experience
and they focus th e students' attention on
different
aspects of the object of
learning, w hether wit tingly,
or
unw ittingly,
on the
part
o f the
teacher.
In
dis-
cussing th e data from the E nglish lesson on O ld M acDonald 's Farm, we have
seen that different sequences of questions can fo cus the learners' attention on
quite different
things.
W e
also men tioned that teachers
often
decompose
a
complex question into simpler questions,
and we
focused
on the
ways
in
which such sequences could reduce the space o f learning. In this section, we
draw
the
reader's attention
to the
fact
that such sequenc es som etim es lead
to a
shift in focus, with the result
that
the intended object of learning is lost.
Let
u s
take
for
example
th e
fol lowing
tw o
paral le l excerpts
from the EM I
and the CM I
phy sics lessons, w here
the
teachers exp lained exa ctly
the
same
phenom enon : why the m otor does not rotate in the simple
ci rcui t .
5.9 [Physics Lesson/Reed relay/EM I/S2/T8]
1
T: . .. O h
then surely,
n ow
girls,
can you
expla in
to m e, why
d oesn ' t
2 th i s m otor wo rk?
3 Ss: [silent]
4 T: Why doesn't
this
motor
work? Just because motor m u s t
use ?
5 S s: [silent]
6 T : The cu r ren t tha t is ? Large o r small?
7 S:
Large.
8 T:
La rge .
1 7 T: . .. W hy does the LE D work here? [Nom inate]
18 S : [silent]
1 9 T: The LED works, but it [Teacher points at the
motor]
does not
20
rotate . I t ' s
[a]
similar con struct ion. [No m inate] Tell
m e, how
21 m uch cur rent i s needed to opera te a m otor?
22 Ss:
[silent]
23 T: How m uch current is needed? I t should be very ?
24 S:
200mA.
25 T: A h, nea r ly 200m A , very good, very large current . B ut can you
26
tell
me how
m uch current
is
needed
to
operate
a
LED?
27 S: V ery sma ll current .
28 T:
Yes, very sm all current
is
enough.
A ll
right. Then
can you
29 exp lain to m e, w hy does this LE D l ight [up]?
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1 32 T S U I E T A L .
30 Ss: [si lent]
31 T : I t [ re fer r ing to the m otor] does not ro ta t e , j u s t beca use the re ' s
32 no
large current .
The LED
wo rks jus t because
?
33 S: Because the L E D —
34 T:
U s e —
35 S: Use
smal l current
and the
m o to r
use
very large current .
36 T: All r ight , yes, your answer is so impressive. Would you please
37
repea t
it
once . I t ' s cor rec t , repea t
it
o n c e .
38 S: The LED use[s] smal l current w hi le the motor use[s] very large
39
current .
40 T : Yes , very goo d , t he L E D u s e [ s ] [a ] s m a l l c u r r e n t w h i le the m o to r
41
use[ s ] very l a rge curre n t .
A ll
r igh t ,
O K .
Here the teacher asked two open quest ions: "Why doesn' t this motor
work?"
and
"Why does
the LED
l ight
[up]?" These
qu est ions opened
up a
num ber of possible answ ers , as pointed out before . However, because the
teacher used
b lank-f i l ling
quest ions to help the s tudents to provide an an-
swer
to the
open quest ions,
th e
s tudents '
focus o f
awareness shifted from
the
reasons w hy the m otor did not rota te , and why the LE D l i t up, to the am ou nt
of cu rrent needed
by the
m otor
and the
L E D .
F or
exam ple,
in
l ines
20 and
23,
the
teacher repeated
the
ques t ion , "How m uch current
is
needed
[ to op-
erate a
motor]?"
In line 26, she asked the same q uest ion abou t the L E D . A l-
though
the
students were able
to
tell
the
teacher tha t
the LE D
needed
a
very
sm all current , w hen the teacher posed the quest ion about w hy the L ED did
not l ight up in l ine 29, there w as no response from the c lass
unt i l
she gave
them some help.
In
other w ords,
the
students ' at tention
w as
focused
on the
size of the current bu t they w ere u nab le to relate the size of the cu rren t to the
reason w hy the m otor did not rota te w hereas the LE D did l ight up .
Let us
com pare
the
a foremen t ioned exam ple w i th
the fo l lowing
excerpt
taken
from
the CM I c lass room .
5.10 [Physics Lesson/Reed re lay/CM I/S2/T8]
1 T: We find
that even thou gh
we
shone
a
strong l ight
on the
L D R ,
2
yes,
its
electric resistance value decreased.
But in fact th e
electric
3 curren t tha t w i l l pass through i s and the e l ec t r ic cu rren t neede d
4 to by the motor is . Do you kn o w w h a t I wo uld l ike you to
5
answ er? [ N omi na te ]
Y o u
try,
you t ry to
exp l a i n
w hy
n o t h i n g
6 happ ens here . N ow I sh ine a s trong l igh t on the L DR . r igh t? I ts
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5.
Q U E S T I O N S
A N D T H E
S P A C E
O F L E A R N I N G 1 33
7
res is tance
is ?
8 S: Smal l .
9 T : Yes, sm all. So there w ill naturally be an electric current com ing
10 in . Can you guess w hat the
difference
is between this electric
11 current
and the
electric current
it
ac tua l ly needs?
1 2
S : The
resistor 's electric current
is
smal ler than
the
motor ' s .
1 3 T : This means the motor needs an electric current that is ?
14 S:
L a rge .
1 5 T: N ot only large, but very large. Yes, and so . . . thank yo u, you
16 have answ ered correctly. An d so, even thoug h w e shine a strong
17 l ight on the LD R , i ts resistan ce value drops, and the so-ca lled
1 8 larger electric curren t
f lows
through the c i rcu i t . The m otor needs
19 a
very large electric current
to
rotate,
and so
this
is the difference
20
betw een th is c i rcui t
and the
other c i rcui t .
In this excerpt,
the
teac her also asked
the
s tudents
to
exp la in "why n o th-
ing
happens
here,"
m eaning
w hy the
m otor
did not
rotate ( l ines
5 and 6). She
also provided l ingu is t ic
scaffolding
to help the s tudents to provide the an-
swer ,
by ask ing them what k ind of cur ren t would pass th rough and what
kind
of
cur ren t
w as
needed ( l ines
3, 4, and 7).
However ,
after the
s tudents
had fi l led in the blanks, she posed an open que st ion once ag ain ( l ines 1 0 and
11 ) .
All the t ime, the
teacher
focused the
s tudents '
attention on the
differ-
ence be tween
the
current
needed
and the
cur ren t tha t ac tua l ly passed
th r ough
th e
c i r cu i t .
T he
mo di f ica t ions
of the
open que st ion
and the
s e q u e n c -
ing of the
closed quest ions
did not shift the
s tudents ' focal awar enes s away
from the
or iginal open quest ion.
Final ly, compare the fol lowing paral lel excerpts from the EMI and the
C M I
physics lessons where again
the
s ame phenomenon
w as
be ing
deal t
wi th ;
that is , w hat happene d w hen the l ight shines on the L DR .
5 . 1 1
[Phys ics Lesson/Reed Relay /CM I/S2/T8]
1
T: OK. [Teacher points to the com plicated c i rcui t ] W e love
2
shining
a
strong l ight
on the
LD R. Now , he re
it
conies, strong
3 l ight shines on the LD R . [Teacher shines the torch on the LD R ]
4 I' ll ask you questions step by step. For the circuit on the left side,
5
th is c i rcui t ,
the
largest
ef fect is the
e lec t r ic res is tance value ,
6 right? Strong light shines on the LDR, I 've told you before , a nd
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134
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
S:
T:
S:
T:
S:
T:
Ss:
T:
Ss:
T:
S:
T:
Ss:
T:
S:
T:
S:
T:
T S U I E T A L .
the
electric resistance value drops.
O K,
w h a t
effect
wi l l
it
have
on the electric current on this side of the c i rcu i t ? [nominate]
Electric resistance
drops.
Electric resistance
drops, the
electr ic curre nt
?
Increases.
Yes, th e
electric
current
increases,
th e electric current
becomes
larger,
r ight?
W h e n
an
electric current
f lows
through
the
c i rcui t ,
this coil
is no
longer s imply
a
coil ,
it
becomes
an
e l ec t romagne t .
E lec t romagnet s can p rod uce ?
Magnet i c f i e lds .
Yes, they produce magnet ic f ie lds. When
it
produces
an
electromagnetic field, it has a series of effects on this side [of the
circuit]. Then what? [nominate], you try and con tinue. [Pointing
to the
com pl ica ted c i rcu i t ]
[si lent]
N o w .
the
coi l
has a
m agne t ic
f ield, and the
reed swi tch
? The
reed swi tch
?
[silent]
The reed switch, the two ends do not touch each other originally,
but
now w hat happens to these tw o ends?
Touch each other .
Yes, the two ends touch each other . I f the two ends touch each
other ,
how do w e
describe this swi tch?
[silent]
The two
ends touch each other,
how do I
describe this sw itch?
Closed .
Close d, very good. Yes, thank y ou . No w, i f
this switch
closes,
then
the
elect r ic current
can
pass through th i s
c i rcui t .
Thi s motor
9
Rotates .
Rotates .
Is
tha t
O K?
Here the teacher asked four "open" quest ions (see l in es 7, 8, 1 9, 26, 28,
and 29) and four "closed" ques tion s (l ines 10, 1 5, 22, 23, 34. and 35). If we
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136
T S U I
ET AL.
1 3
T :
Should work ,
but it
does
not
rotate th is t ime .
How
a bout th is
1 4 ci rcu i t? [Teacher goes to the com plicated ci rcu i t ] Now once
15
again l ight shines
on the
L D R ,
its
res is tance dec reas efs] .
So,
1 6
cur ren t f lows through th i s c i rcu i t . N ow it's no t only a coi l
17 but a ?
18
Ss: [silent]
19
T: Now
this question again, [nominate]
N ow
th is t im e
it is not
20 mere ly a coil but a ?
21
S s: [silent]
22
T :
Artif icial
magne t , all r igh t . Do you still rem em ber [ the]
23 name?
24 S: E l ec t romagne t .
25
T : Once again .
26 S: Elec t romagnet .
27 T : Electromagnet , thank you, it becam e an electrom agnet, and
28 it produced a mag net ic field. So the sw i tch here
wi l l
close
29 and a
current [will]
pass
through this circuit ,
so the
m otor
30 rotate[s]. There is a sequence of processes] [that] occur here an d
31 i t m ake[s] the m otor rotate .
Here th e teach er asked an open question (lines 6 and 7):
"What
happens to
it [resistance] when light shine[s] on the LDR?" This q uestion, in a sim ilar
way to the qu estion posed in excerpt 5.11 , asked for a description o f the pro-
cess. W hen
the
teacher failed
to elicit a
response
from the
students,
she
posed
three blank-filling ques tions , one of which i s a repe t it ion (lines 10 ,1 1 ,1 6 ,1 7,
19, and 20), w hereas the others were c losed question s ( l ines 22 and 23) . How -
ever, in the course of
modify ing
the open question into
blank-fi l ling
ques-
tions, the blank-filling quest ions became focused on the devices and the
labels
( an
artificial
magnet
and an
electrom agnet) ,
and the
description
of the
process
w as
lost.
On the
basis
of our
observation that questions
focus
stu-
den ts ' awareness on the aspect of the phenom enon that was q uestione d, w e
can reasonably conclude that
the
consequence
of
asking quest ions about
the
devices,
rather tha n the processes, wo uld
result
in the devices being brough t
to the fore of the students ' aw areness and the processes rece ding to the back -
ground. A nd yet , it is the processes and not the devices
that
are cri t ical to the
understanding
of the
operation
o f the
reed relay.
C O N C L U S I O N
In chapter 1 , M arton, R une sson, and Tsui demon strated the central role
played by langua ge in con st i tu t ing the space of learning, and discussed at
length the im portance o f l anguage as a m e a n s o f en capsu la t ing experience ,
m aking di s tinc t ions , and m odi fy in g one an other 's und ers tandin g of the
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5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 37
world. They a lso
observed
the
function
of language in representing and
shaping
the
structure
o f
awareness
o f
participants
in a
d iscourse .
In
this
chapter , w e have foc use d
specifical ly
on the s tructure of que st ions and how
they impinge on the s tructure of awareness of par t ic ipants in a discourse .
Throughou t the lesson on the reed relay, w e demonstra ted how a teacher
w as able to help her s tudents discern the cr i t ica l features of a reed re lay a t
cr i t ical
points in the lesson, by asking qu est ions tha t focused their a t tent io n
on aspects that var ied. Throughout the English lesson, w e demonst ra ted
how the different quest ions asked by the teacher co uld resul t in s tudents fo-
cus ing on very
different
aspects of the object of learning. W e also showed
that
the way in wh ich the teacher sequen ced the quest ions co uld resu l t in a
shif t
of the
learners '
focal
awareness
from
the
crit ical aspects
of the object
o f
learning
to
aspects that
are not
crit ical.
In
other words,
the
teacher ' s
awareness
of how
ques t ions
can
shape
the
space
o f
learning ( i .e . ,
the en-
ac ted ob jec t of learning) is essential if our effort in br inging abou t power fu l
l earn ing in the c lassroom is to resul t in the convergence between the in-
t ended ,
the enacted, an d the l ived object of learning.
E N D N O T E S
'The term d issemina t ion is used in a neutral sense; it does not imply a
t ransmiss ive view o f t each ing .
2
F or an exp lana t ion of the L D R , see chap te r 1 , endnote 4.
3
In
this chap ter, data from the lesson taught in Can tonese w i l l be coded as CM I,
and data from the lesson taug ht in Engl ish wi l l be coded as E M I. T he data from the
CMI lesson is t ransla ted semant ica l ly , keeping as m uch as po ss ib le to verba t im
transla t ion.
4
A1 1 s tuden ts ' nam es
are
f ic t i t ious .
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6
The Semantic Enrichment
of the
Space
of
Learning
Amy B. M. T s u i
TH E SEMANTIC
D I M E N S I O N
OF THE SPACE O F
LEARNING
In chapter 1 , M ar ton , Runesson , and Tsui proposed that learning is the
proces s
o f
develop ing
a
cer tain
w a y o f
seeing,
an d
po in ted
o u t
tha t
d i f fer-
en t
w a y s
o f
seeing al low
fo r dif ferent
w a y s
o f
ac t ing . They a l so po in ted
ou t
t ha t in order to he lp l earners to develop a ca pab i l i ty fo r seeing things
in a
p o w e r fu l w a y ,
w e
need
to
focus
on
w h a t
is
being learned
and
he lp
learners d i scern c r i t ica l fea ture s
of the
object
o f
l earn ing .
In
o ther words ,
inves t iga t ions o f l earn ing involve s tudying h o w learners experience th e
o b j ec t
o f
l earn ing ,
and
inves t iga t ions
o f
c lass room learn ing involve anal -
yses o f the opportunit ies to experience the object o f
learning
that are af-
forded to learners . In th is sense, the space of learning is an exper ient ia l
space.
A n exp erient ial space is not an ins tan t iat ion, but rather a po tent ial
for unders tanding, seeing, and act ing in the world (see Hal l iday &
M a t t h i e s s e n ,
1999). It is in re la t ion to th is potent ial th at learners can m a k e
sense of a pa r t icu lar objec t of learning . As su ch, the exp erient ial space is
e las t i c . The tea che r can e ither widen th i s space by af fording learners op-
por tun i t i e s
to
explore
the
o b j ec t
o f
learning
in a
variety
o f
w a y s ,
o r
nar row
this space
by
depriving them
o f
such opportunities.
In
the
preceding ch apters,
w e
have seen that
the w ay in
wh ich
the
object
of
learn ing is experienced by learners depends on w hich aspects of the ob-
ject of learning are
being
focused on and discerned as critical. In this chap-
ter, it is
proposed that experiencing
an
object
of
learning—in
the
sense
of
discerning i ts cri tical aspects and experiencing the patterns o f variation—
13 9
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140
T S U I
necessar ily involves ass igning a m ean ing (or me anin gs) to i t. For exa m ple,
for a youn g learner w ho lives in a country w here high-rise b uilding s do not
exist , a "house" m e a ns a p lace where people live, as opposed to p l aces
w here a nim als live, such as
"stables."
A ho use is therefo re a choice in the se-
mantic system of accom m oda tion for different k inds of l iving th ings . How-
ever, to a you ng learner who l ives in a ci ty w here th ere are high -r ises as wel l
as houses, a house means something
different.
In this instance, "house" is a
choice in the seman t ic sys tem of accom m odat ion for people, wh ere houses
and
apar tments
are
choices .
A
house m eans
not an
apar tmen t : tha t
is. it is a
two- or three-story building, rather than a single unit within a m ul t i-s tory
building com pr is ing m any un i t s .
T he
meanings that learners assign
to the
object
of
learning depend
on a
host of th ings . The teacher can affect these m ean ings t h rough examples and
analogies , throu gh
the
stories th at
he
tel ls ,
and the
contex t s tha t
he
br ings
in .
The m ean ings wi l l also depend o n the persona l experiences that the learners
bring to bear o n the object of lear ning . Together , a l l of these m ea nin gs con-
stitute the semantic dimension of the space of learning, o f which language
plays a central role.
In this chap ter, exam ples from a variety of classroom s are ci ted to
i l lus-
t rate wha t is mean t by the sem antic dimension of the space of learning, and
the way s in whic h the learners ' experience of the object of learn ing is en-
riched semantically are discussed. T he central role played by language in
the
const i tu t ion
of the
seman t ic d im ens ion
of the
space
of
learn ing
is i l lus-
t ra ted by com paring classrooms w here r ich
l inguis t ic
resources were avail-
able, with those w here the l inguist ic resources were l imited.
CONTEXTUAL
VARIATION AND THE
SEMAN TIC
E N R I C H M E N T OF THE
SPACE
O F L E A R N I N G
It is c o m m o n pract ice among teachers , no matter what subject matter they
are dea l i ng wi th , to
shif t
f rom the c lass room c ontex t to co ntex t s ou t s ide the
classroom
(ranging
from
contemporary contexts
to
historical contexts)
in
the course of thei r explan at ions . How ever , few teachers ask why they are
doing this , and w h a t effect th i s k in d of con tex tua l var ia t ion has on l earn ing .
In this chapter, it is proposed that contextual var iat ion is a very im por tan t
and
co m m only used pract ice that help s learners to ma ke sense of and to re-
late
to the
object
of
learning.
M a t h e m a t i c s Lesson: Th e P o s t m a n ' s Ro ute
Let us t ake , fo r exam ple , the ma the m at ics l esson on the pos tm an ' s rou te
discussed
in chapter 3. To help the s tudents to see the relat ionships be-
tween pa t te rns ( as seen th rough ro ta t ion an d r e f l ec t i on ) , th e t eache r
started
by
asking
th e
s t uden t s
to
c o m e
up
w i th
a s
m a n y p a t t e rn s
as
poss i -
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6 . S E M A N T I C E N R I C H M E N T O F TH E
S P A C E
O F L E A R N I N G 1 41
ble , by c on nec t ing the dots that s tood for delivery po ints . In order to
faci l i-
tate task com ple t ion , the teacher provided the context of a pos tm an h aving
to deliver let ters to eight d ifferent places and then re turn to the post off ice.
W h e n the s tudents h ad com ple ted the task, the teach er asked the s tudents
to f igure ou t wh a t w as
wrong
with one particular design that he [the
teacher] ident i f ied , and then to dec ide wh at cons t i tu ted the best route . The
s tudents had no diff icul ty
po in t ing
o u t
tha t
the
design
in
ques t ion
fai led to
show the direct ion of the route , and fa i led to show h ow the po stm an c ou ld
get back to the pos t of f ice . They a lso had no d i f f icul ty dec id ing tha t the
best
route
w as the
shortest route.
T he tasks were n o t diff icul t for the
stu-
dents becau se the con text of a pos tm an de l iver ing mai l w as very
famil iar ,
and i t w as
easy
fo r
them
to
ident i fy
the
routes
in
re la t ion
to
w h a t
a
pos t -
m a n ' s
job
involved. On ce
the
e ight
bes t
rou te s we re
identif ied, th e
t e ache r
swi tched from the everyday context to a m athem at ica l context , so tha t the
designs took on a different meaning.
They were
no longer
routes
but pat-
terns .
T h e
c o n c e p t
o f
rou tes nece ssari ly involved having
a
d i rec t ion
a nd
being able to re turn to the s tar t ing point , w hich m ade i t very easy fo r the
s tudents to think of the cri ter ion for the best route . If the teacher had
started
the lesson by present ing the pa tte rns in a mathem at ica l con text , the
students would have ha d to think in sym bolic and abstract te rms and the
t a sk wo uld have been m ore dif f icu l t .
W hat is
interesting
is
tha t when
the
students failed
to see the
re la tionsh ip
between the e ight pat terns and hence were unable to categorize them , the
teacher switched back to the context of the po stm an's route , wh ich im m edi-
ately m ade
the
task easier.
The
students were then able
to see
that
th e
eight
routes w ere re la ted in two different ways: rota t ion and ref lect ion. In other
words,
the
studen ts w ere able
to
draw
on
their everyday kno w ledge
to
m a k e
sense of what the pat terns m eant .
E ng l i s h as a Second L a n g u a g e ( E S L )
Lessons:
W e a t h e r
an d Seasons
In a
s tudy
o f p r imary E S L teaching, Chan (2002) s tudied the p r imary
Grade 4 lessons taug ht by two teachers , in which the d i rec t ob jec t of lea rn-
ing
w as weather, c lothing, and
seasons.
In the first
part
of an 80-minute
lesson, both teachers used p ic tures
to
e l ic i t
th e
vocabula ry
fo r
w ea the r
a n d
c lo th ing .
Hav ing establ ished that there
w as
shared kno w ledge
o f
di f ferent
w e a t h e r con di t ion s and the corresponding types of c lo th ing , both teachers
in t roduced "seasons" and asked s tudents to deduce the season from the
clothing that they showed them .
In so
doing , both
teachers
w ere trying
to
he lp the i r s tudents see tha t w ea ther and c lo th in g w ere re la ted in m eaning-
ful wa y s . W e cou ld say tha t the teachers were t rying to establ ish a s e m a n -
tic
f ie ld w i th two sem ant ic dom ains : wea ther and c lo th ing . Su bsequen t ly ,
both teachers in t roduc ed a fur ther semant ic domain of
"seasons,"
h e n c e
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1H42
T S U I
wea the r , an d c lo th ing ) w ere unders tood no t on ly o n the i r own , b u t also in
relation to
each other.
In the
latter part
o f
each lesson,
th e
teachers used
a
story
a s the
context
fo r
recycling the vocabulary i tem s introduced, a nd for reinfo rcing the students '
unders tanding of
wea the r
and
seasons.
T he
stories that
the two
teachers
told, however, were very different.
Teacher A to ld a s tory abou t a poor little gir l , M ary, w h o w a s driven o u t
of the house by her
s tepmother
in the
w inte r wh en
i t w as
cold
a nd
snowing.
T he s tepmother sa id tha t she w o u l d not le t Ma ry b a c k in un le s s she
brought back some beau t i fu l f lowers . Mary walked up the h i l l and
fell
as leep wi th ex hau s t ion . Four brothers ,
th e
four
sea sons , c am e
to her
res-
cue. Brother Spring waved
a
mag ic w and
and the
w ea ther became w arm
an d
ra iny . M ary
w as
then able
to ge t
f lowers
for her
s tepm othe r .
B u t
w h e n
Mary brought
the
f lowers home,
h er
s tepmother would
no t le t her in and
told
her to ge t
some app le s . Th i s t ime Bro the r Su m m er cam e
to her
re scue ,
and the w ea ther becam e h ot and sunny so tha t M ary could p ick some ap-
ples . T h e
s to ry con t inued
and a l l four
b ro the rs cam e
to her
re scue
in
tu rn ,
each t ime
the
greedy s tepmother m ade unreasonable dem ands
fo r
some-
th ing tha t cou ld not be f ound in tha t pa r t i cu l a r sea son .
L e t us
c o n s i d e r
the
s e m a n t i c d i m e n s i o n
of the
s p a c e
of
l e a r n i n g
t h a t w a s
o p e n e d
u p
w i t h t h i s s t o ry . P r i o r
to
t e l l i n g
th e
s t o r y ,
th e
t e a c h e r had a l ready e s t ab l i shed the r e l a t i o n b e t w e e n two s e m a n t ic do-
m a i n s ( s e a s o n s
a n d
w e a t h e r )
b y
s h o w i n g
h o w o n e i s
r e l a t e d
t o t he
other . The story p ro v i d e d the c o n t e x t not o n l y for m a k in g
sense
of the
r e l a t i o n s h i p b e t w e e n w e a th e r a n d s e a s o n s , b u t a l so fo r i n t r o d u c i n g
a n o t h e r s e m a n t i c d o m a i n r e l a te d
to
w e a th e r
a n d
sea son , t ha t
i s ,
p l a n t s
a n d
f r u i t s .
W h i l e p l a n t s a n d f r u i t s w e r e p a r t o f t h e s t u d e n t s '
e x i s t i n g
k n o w l e dg e , i t w a s th e t e a c h e r w h o b r o u g h t th e r e l a t i o n s h i p o f t h i s d o -
m a i n w i t h s e a s o n s
a n d
w e a t h e r i n t o
th e
s t u d e n t s '
f o c a l
a w a r e n e s s .
W h a t
is
i n t e r e s t i n g
is the way the
t e ach e r va r i ed
the
r e l a t io n s h i p s
be-
t w e e n s e a s o n s , w e a t h e r , an d p l a n t s an d f r u i t s . S h e s t a r t e d w i th a n e g a -
t ive re l a t ionsh ip b e twe en them
by
g e t t i n g
the
s t u d e n t s
to see \vhat
could n o t b e found i n a p a r t i c u l a r s e a s o n , a n d s h e h e l p e d t h e s t u d e n t s
to make
sense
of t h i s n e g a t i v e r e l a t i o n s h i p t h ro u g h the c h a r a c t e r of
th e s te p m o t h e r , w h o m a d e im p o s s i b le d e m a n d s o n l i t t l e M a r y . L a t e r , a
p o s i t i v e r e l a t i o n s h i p b e t we e n t h e s e d o m a i n s
was
e s t a b l is h e d w h e n
e a c h
o f t h e f o u r
b r o t h e r s c a m e
to
M a r y ' s r e s c u e
b y
c h a n g i n g
th e
sea-
son and the w e a t h e r so t h a t the p l a n t or the f r u i t d e m a n d e d by the s t ep-
m o t h e r c o u l d b e
f o u n d .
As the lesson progressed, there was a
gradua l w idening
of the
semant ic
f ield f rom w e a th e r an d c lo th ing , to inc lude sea sons , p l an t s , an d fruits . T he
fol lowing
excerpt
is an
example
of how the
teacher related
one
semant ic
do ma i n
w i th ano the r.
H
idening the semantic field so that the three semantic domains seasons,
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6.
S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 43
6.1 [English Lesson/P4/Weather and Season]
T :
Mary's mother
says, "No.
I don't
want you.
Go away." Her
m other says, "Okay,
you ask me to let you
come back,
b ut
unless
you get me some
beau tiful flowers
(I
won't)."
Can you get some
beaut i ful
f lowers
in
w inter?
Ss: N o.
T: Outside it is .
Ss :
Cold
and
snowy.
T :
Can M ary get some f low ers?
Ss : [loudly] N o
T he readiness w ith
w hich
the students
responded
to the teacher
when
she
asked if M ary co uld get flow ers in the w inter when i t w as cold and snowy
show ed that they w ere able to make sense of the story an d see the relation
be tween the semant ic domains.
Teacher B also told a story
after
introducing all the vocabulary i tem s for
w eather, clothing,
and
seasons.
T he
story
w as
about
a
little boy, B illy,
and
w h a t he did on each of the seven da ys of a w eek and wh at the we ather w as
like. For
example,
on M onday,
when
it w as
raining,
Billy watched televi-
sion;
on
Tu esday, when
i t was
sunny, B illy play ed basketball ;
and so
forth.
The students were asked to learn the days of the w eek, and to say w hat B i l ly
did
and wh at the weather w as l ike . The w ay in w hich the teacher tr ied to re-
late the three sem antic doma ins was largely arbitrary. A ltho ug h certain ac-
tivities w ere logically related to the w eather co nditions (e.g. , "swimm ing"
and
"sunny w eather"), there were others that w ere not (e.g. , "w atching tele-
vision" and
"rainy
w eather").
A ctivities
and
days
of the
week
are of
them -
selves
no t
log ically related either. When
the
three sem ant ic dom ains w ere
taken
together, they
did not
form
a
sem ant ic
field. T he
story therefore
did
not serve as a
meaningfu l
context to w hich the stude nts could easily relate,
nor did it
help
th e
students
to
make sense
o f
each
of the
sem antic dom ains
in
relation to the other two . In other w ords, the s tuden ts ' un derstanding of the
relat ionship
betw een the three dom ains was not enriched sem antical ly by
the story.
If
anything,
the
story confused
the s tudents '
u nderstanding
be-
cause of the
arbit rary re la t ionsh ip that
the
teacher
had
tried
to
establ ish.
S c i e n c e L e s s o n : N e u t r a l i z a t i o n
To further i l lustrate what
can be
achieved
by
contextual variation,
let us
take a look at an example of a secondary Grade 2 level science lesson
(Hoare ,
2003). The object of learning in the lesson was "neutralization."
The teacher first introduced the concepts
o f acidi ty , alkal ini ty ,
an d the use
of the/?// value s cale to measu re the strength of acids and alkalis. Sh e also
asked
the
students
to find ou t the
acidity
and
alkalinity
o f
som e acids
an d al-
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144 T S U I
kalis
by
using
pH
paper .
Af te r
this,
she
asked
the
students
to
test
the pH
value of several h ouseh old substances , su ch as lem on ju ice , vinegar , tooth-
paste , baking soda, b leach ing ag ent , and a canned soft dr ink. The fo l lowing
is
an excerpt
from
the classroom.
6.2 [Science lesson/S/Neutral izat ion/EMI]
T: . . .
Okay, now,
in our
dai ly l i fe
w e
have ,
um, we
com e in to con-
tact
wi th many things , r ight? For example, toothpaste , lemon
juice, e tc . . Do you k n o w w h a t is the pH va lue o f th i s? I s th is a
strong ac id?
Is it a
weak ac id?
Is it a
strong
a lka l i o r
weak a lka l i?
W e
don ' t know. S o in the fol low ing I w a n t you to do [the] experi-
m e n t
on
page
.
S:
167, 167.
T :
167,
is
th at right?
A nd
then
w e
have
to
test
the pH
va lue
of
lem on
juice, bleaching agent, baking soda, detergent, glass cleaner,
toothpaste , 7-Up™, but don' t drink it [s tudents laugh ] , m i lk o f
magnes ia ,
sea
w a te r
.. .
S : I[ ' l l] drink it .
T : Do n' t dr ink it.
S:
Why?
T: I [wi l l] have to call the am bulan ce. So, you do the same. Use the
pH
paper.
H ow
ma n y
o f
t hem?
S: Those 7-Up, change [them]
to
Coca-Cola™
ah
[Meaning
re-
place 7-Up with Coca-Cola]
T:
Yes.
S :
Ten...
S: Those 7-Up chang e [ them]
to
C oca-Cola .
T: Yes, you know that there is C oca-Co la there.
S: [inaudible]
T: Yes, sorry, ah, maybe 7-Up w as
diff icult
to buy.
S: A h I don ' t . .. I can go to the 7-11 ™ to buy i t.
T :
Okay , after this lesson. Okay
w e
change [ them]
to
Coca-Cola.
B ut
don't
drink
it.
Remember.
[Students co nduc ted the experiment and recorded the pH values
of the
substances.]
T: Now
okay look here. Lemon juice
is of pH ...
S: Three.
T: So we
cal l
it .
Ss: Strongly acidic, strongly, strongly acidic.
T: How do we describe it?
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6.
S E M A N T I C E N R I C H M E N T OF THE S P A C E OF L E A R N I N G 145
Ss:
[silent]
T : Yes, it is a strong acid, so it is s t rongly ac idic . . . .
Prior
to
this experiment, al though
the
s tudents were famil iar wi th
th e
household substances listed
by the
teacher, these substances m eant n othing
more than things that they found
in
supermarkets
and
k i t chens .
In
other
words , the meanings of these substances were interpreted in the semant ic
domain
of the
supermarket
or the
ki tchen,
an d the
level
at
w h ich
the
students
were operat ing when they thought about these objects was the level of ev-
eryday knowledge. However, when the teacher asked the students to do an
exper iment
on
hou sehold substances ( i .e., w hen
the
s tudents w ere engaged
in
f inding
o ut their pH values and using tech nical langu age, su ch as "acid,"
"alkali ," and "strongly acidic" or "weakly acidic" to describe these sub-
stances),
the
household substances were recon strued,
not in the
semantic
dom ain of everyday items, but in the dom ain o f chem icals . A t th is point , the
level at w hich th e students were operating changed from the level of every-
day
know ledge
to the
level
o f
scientific
(or
technical ) knowledge. What
is
interesting
in the
jus t m entioned excerpt
is
that
w e can see the
students
and
teachers operat ing at both know ledge levels and in both sem ant ic dom ains .
In
other words ,
we may say
that
the
semant ic dimension
is
enriched
in the
sense that there
is an
addi t ional layer
of
mean ing .
Having established the con cep ts of alkalinity and acidity, the teach er in-
t roduced the
concept
o f neutralization by
asking
the
students
to mix an
acid
(hydrochlor ic
acid) with a n alkal i (sodium hydrox ide) unt i l they obtained a
pH value o f seven, a point a t wh ich t he so lut ion becom es nei ther acidic nor
alka l ine .
T he teacher explained that neutral izat ion is a process by w hich an
acid is added to an alkali unti l the result ing solution is salt a nd water . A f te r
the s tudents had done the experim ent , the teacher t r ied to help them to m ake
sense
of
neu tralization
by
shifting
from
the
science laboratory context
to an
everyday context . She used a num ber o f exam ples to explain the app l ica-
tions
of
neutralization.
O ne
example
w as
that
of
using toothpaste
to
brush
our
t ee th .
S he
explained that
the
ac id produced
after
eat ing food causes
o ur
teeth to decay, and that toothpaste neutralizes the acid. Another example
was the use of
m i lk
o f
magn esia
to
neutral ize excessive acid produced
by
food
in the stomach, and thus al leviate stomachache. Yet another example
w as the use of ointm ent con taining alkal i to neutral ize the acid produc ed by
m osqu i to b i tes .
In
this section
of the
lesson,
w e see the
reverse process
of
contextualizat ion happening. Previously, neutral izat ion
w as
m ere ly
a
labo-
ratory process in w hich ch em icals were m ixed together . Here, neu tral iza-
t ion
w as presented as a process that takes place frequen tly in our everyday
lives. Ac ids
and
alkalis were
no
longer un derstood on ly
a s
chem icals
in
sci-
ence laboratories
but as
chemicals that could
be
found
in
ma n y
different
substances outside the laboratories. Once again, there were two levels of
knowledge
operating, and also tw o
semantic domains
in
wh ich neutral iza-
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146 TSUI
t ion w as unders tood: a scien t if ic process dom ain, and a dai ly life process
domain. The fol lowing excerpt shows that as soon as the teacher explained
the toothpaste as an example of neutral izat ion, the s tudents were able to
make sense of neutral izat ion in another daily
life
contex t— the use of m ag-
nesia to neutral ize ac ids in the s tomach.
6.3 [Science lesson/N eutralization/S2/EM I]
T:
A h, toothpaste is alkaline, and it neutralizes the acid in our
mo u t h af ter w e have taken some
food
. . . . A nd n eu t ra l iza tion
takes place there so that we can ha ve hea l thy teeth . Okay. Sec-
ond,
I
know some, m any, people w ould like
to
have m any— a full
lunch . . . . W hen
you
have taken
a lot of
food,
and
som etimes
you
find
that this part
is not
okay . S tom ach
?
S : S tomachache .
T: You have s tom achache . Oka y . . . . W hen you have taken a lot of
food, yo ur s tomach w i l l g ive
out
acid
to
m a k e
the food
in to sm al l
pieces so that you can take in the food, okay? . . . So at that t im e
w hen your stom ach gives out a lot of acid, you find that it is pa in-
f u l . . . . S o what should you do a t
that
t im e? Some peop l e w ou ld
like to
take some tablets. O kay this
is one of the
tablets .
W e call it
m ilk of m agnes ia . . . . H as anybody taken th is before? W hen you
have s tomachache, you can take one . . .
. .. W hy do w e have to take one?
S: Neut ra l ize .
T : Y e s , . . . the reason is tha t it ne u t ra l izes the acid f rom o ur s tom ach
so
tha t
y o u
becom e peace fu l . . . .
A s in the previou s excerpt (6.2), we may say that by varying the con text,
the sem ant ic dim ension w as enriched and the teacher w as able to help s tu-
dents ass ign an addi t iona l layer of m ean ing to the ob ject of learning .
COLLABORATIVE E N RI CH M E N T O F TH E SE MANTIC
D I M E N S I O N
BY
LEARN ERS
So
far,
the
exam ples examined w ere classroom exam ples w here
the
teacher
enriched
the
sem ant ic d imen s ion
by
br inging
in
stories
o r
con texts outs ide
the classroom and the laboratory to help learners to m ake sense o f the object
of learning. In this section, w e look at examples in w h i c h the learners
brought
in
their
own
experience
to
assign m eanings
to the
object
of
learning
and
see how the space of learning w as enriched se m ant ical ly by the collab-
orat ive construction o f m ean ing among the learners.
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6 . S E M A N T IC E N R I C H M E N T
O F T H E
S P A C E
O F L E A R N I N G 1 47
C h i n e s e
L e s s o n :
The S lo th
The data presented here com e from a prim ary Grade 3 Chinese langua ge les-
son, "The
Sloth,"
th e
background
of
which
has
already been introduced
in
chapter
2. W e
shall
now see how the
learners assigned meanings
to a
video
that they watched together,
how
they collaboratively constructed
a
written
representation
of the
video,
and how the
space
of
learning
w as
enriched.
In
th e
lesson
on the
sloth,
the
object
of
learning
w as to
w rite
a
descript ion
of the appearance of a youn g s loth , and a story about its search for a new
h o me
af ter
it lost its m other and had ea ten all the leaves on the tree where i t
lived.
T he
teacher provided
a f ram ework for
describing
an
animal that
w as
based
o n the
de script ion
of a
panda that they
had
studied
in the
previous les-
son.
The
teacher used
the
word "appearance"
as a
hyponym
for
body
or
t runk, head (brain),
four
l im bs and color (of the
fur
or skin). Then he po inted
out to the class that it w as also necessary to describe w hat the anim al was
like wh en i t was in m ot ion. For example, the movem ent of a panda is very
c lumsy. He also pointed o ut that i t w as necessary to describe the slo th 's eat-
ing h abi ts and character. After p roviding the f rame wo rk, he showed a video
of the
story
of a
sloth.
O ne
striking featu re
o f
this lesson
is the w ay in
w h i c h
the
teacher repeatedly showed
the
video,
at
first with narrat ion
and
later
wi thou t
narration, each t im e showing a
different
segment of the tape w ith a
different
focus.
This repeti t ion not only rei terated the content , but also
opened up the space for students to explore the ways in which they could
m ake sense
of the
features
of the
sloth. Students w ere then asked
to
work
in
groups
and
produce
a
writ ten text
to
describe what they
had
seen.
In the
fo l low ing di scuss ion ,
w e
exam ine some
of the
t ex t s p rodu ced
b y
the s tudents , and the discuss ion data that led to the product ion o f these
texts .
W e see how the
s tude nts ass igned m eanings
to the
video,
and how
their
cons t rua l
of
wha t they
had
seen enriched
the
semant ic aspect
o f the
space of l earn ing .
Sloth s Head a n d
Body. The fol lowing is a w ritten descript ion produ ced
by Group 2: '
It is a
s lo th ,
it s
head
is
l ike
a
b ig
chicken egg, it s
body
is l ike a
b ig
os tr ich
e gg ,
very
long , and the
th ree c laws
on its
fo r e l imb s
are
pa r t icu la r ly long .
Its
co lor
is
b l a c k ,
wh i t e , gray, brown. Very
short
tai l . T o
look
for food and a
home ,
the s loth
s low ly
c l i m b e d
d o w n the tree, and swam frees ty le . It crawled to the shore . A s soon as it
r eached
th e
shore ,
it
g lanced
to the
east
and the
west . V ery
soon,
it found a
tree.
It fi-
nal ly found
a new home .
Let u s
focus
for the
m o me nt
on the
s tudents ' desc ription
of the
head
and
body
of the
sloth. Although most groups s im ply m ade
u se of the
teache r's
suggestion that the sloth 's head w as like a m onkey 's head, this group felt
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148 T S U I
tha t us ing another an im al
to
describe
the
sloth
w as no t
adequate ,
and
tha t
they ought to use something else for comparison. T he fol lowing excerpt
shows
how the
students explored
the
descript ion
of the
s loth ' s hea d.
6.4 [Chinese lesson/P3/The Sloth/Group Discuss ion/Group 2]
296 S: W ha t 's i t [ the hea d] l ike?
297 S:
Like
a
monkey ' s head .
298 S* This is not s ay ing any th ing .
299 S: They are both an im als .
300 S : I ts h e a d . . .
301 S: Is l ike a chicke n egg.
302 S: Is l ike an oval chick en egg .
303 S:
Ju st l ike
a
ch icken
egg is
okay.
304 S: No need to say tha t it is oval as w e l l.
305 S:
Just [put t ing dow n] chicken
egg is
o k a y ?
306 S:
Like
a
ch icken
egg is
okay.
307 S:
Ch icken eggs
are
a lway s oval .
308 S:
It 's
got to be
b igger than
an
egg. It ' s
no t
t ha t sm a l l .
309 S: Th at 's r ight , chick en eggs are very sm al l .
310 S: That's right .
3 11 S :
Wha t ' s
it
l ike again?
312 S: Like a big chicken egg.
313 S: A big
ch icken
egg is not
tha t b ig .
314 S:
That's
okay.
Y ou
describe
the
head
...
315 S: A big goose egg .
316 S: A big goose egg is fine.
31 7 S: A big
ch icken
egg is f ine.
318 S: How do I
w rite
the
word "egg"?
319 [The studen ts helpe d each other w rite the word
"egg"]
320 S: Le t 's see, w ha t 's a big ostrich egg like. L et 's say a big ostrich
321
egg,
is
that okay?
322 S:
Okay, ostrich egg .
323 S: Ostr ich eggs are very big?
324 S: Okay, let's describe the body.
325 S: [ reminding the s tudent who i s w r it ing] B ig ostrich egg.
326 S: Ostr ich egg.
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6. S E M A N T I C
E N R I C H M E N T O F TH E S P A C E O F
L E A R N I N G
1 49
From this discuss ion (6.4),
we can see
that
tw o
cri tical features w ere
be-
ing
explored by the students: name ly, shape an d size. Of part icular interest
is the
ini t ial com parison
of the
sloth's head w ith
the monkey's
head
by one
student
(line 297), the reject ion of this com parison by another student ( l ine
298),
and the just if icat ion of the reject ion by a third ( l ine 299). What was
happening in that section of discourse? Why did the second student say,
"This is not saying anything," m eaning tha t com paring the s loth 's h ead wi th
a m onke y 's head w as not informa t ive at a ll? For the f i rst s tudent , w hat cam e
to
the fore of his awareness w as the comparison of the sloth with other an i-
mals .
T he
dimension
of
variation
w as
"heads
o f
anima ls" (wh ich
w as
also
w h a t the teacher had previously i l lustrated). However, for the second and
th i rd s tudents , w hat cam e to the
fore
o f their aw areness w as not to compare
the
sloth w ith other anim als, as can be seen from line 299. Their subsequent
discourse shows that it w as the shape that was in their
focal
awareness , and
t hus
they acce pted the analogy of a chicken egg that m ade the shape im m e-
diately
apparent .
"Oval" was a
shape tha t
w as
considered
by the
group
to be
a critical feature o f the shape of the sloth 's hea d. The s tuden ts w ere trying to
decide
w h ich
w as the
best a nalogy
to use to
describe
the sloth 's
head
a nd i ts
body. The de bate about whe ther i t w as necessary to specify oval when u sing
a chicken
egg as an
analogy
is
interesting both
at the
conceptual level
and
the l inguist ic level . Conceptually, oval
can be a
feature that
is
qu i te inde-
pende nt of an object . For exam ple, a table can be oval , roun d, or square.
Specify ing
the shape of an object presupposes that there are shapes other
than
that which
is
specified.
From the
discuss ion,
it is
clear that
for
some
students , oval was considered to be an inherent feature of a chicken egg,
w h i c h
rendered
the use of the
adjective
"oval" to
describe
the egg
redun-
dant . This is a fairly sophist icated level of unders tanding that the s tudents
w ere able to reach throug h col laborat ive ta lk . Lingu is t ical ly , "chicken egg"
w as
used to describe the shape, and "chicken egg" took on a m ean ing
that
w as
synonym ous w i th oval.
T he
other feature
is
size,
bu t
here
we see the
opposi te happening.
A l-
though
there
are
chicken egg s that
are b ig and
those that
are
sm al l,
th e
varia-
t ion
implied by describing the sloth 's body as a "big chicken egg" (as
opposed to "chicken egg" for its
head)
w as considered inadequate because
even b ig
chicken eggs were thought
to be too
small . Instead,
the
s tudents
proposed the
k ind
of egg as a dimension of variat ion. Thus they proposed
goose egg an d ostrich egg as a variat ion in size, and finally dec ided on os-
tr ich
eg g. Here
w e can see
three term s
in the
students ' semantic system
of
size:
chicken eggs , which are smal l ; goose eggs , which are b igger than
ch icken
eg gs; and o strich eggs, w hich are biggest of al l three. In the final
draf t tha t the students produced, they added the adjective "big" in front of
ostrich
eg g to describe the
size
of the
body.
B y
doing this ,
the
students have
added o ne m ore term to thei r sem ant ic sys tem of s ize to m ake f iner dis tinc-
t ions in
size.
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150
T S U I
Th e collaborative co nstrual of the appe arance of the sloth is evide nt in the
way the
students questioned each other 's contribution
and
then cam e
to a
consensus on the most appropriate descript ion.
Sloth s Eyes. Le t us now cons ide r th e desc r ip t i on p roduced by an-
other g roup , Group 4. When desc r ib ing th e a p p e a r a n c e o f the s lo th , o n e
s tudent in Group 4 said that the
sloth's
eyes were b lack . However , the
o ther g roup me m bers im m edia t e ly po in t ed ou t t ha t eve rybody knew eyes
were black, imp ly ing t ha t this
piece
of i n fo rmat ion was supe r f l uous .
How ever , ano the r s tuden t po in ted ou t tha t the eyes o f a rabb i t were spe-
c ia l , and ano the r s t ud en t ch ipped i n and sa id t ha t r ab b i t s ' eyes w ere r ed .
In
t h i s d i s cus s ion ,
w e can see
t ha t i n i t i a l l y
for th e
s t u de n t s ,
a ll
eyes were
b l a c k and t he re fo re t he re was on ly one t erm in t he sys t em o f m ea n in g o f
color
of eyes.
How ever ,
as
soon
as the
color
of
rabbits' eyes
was
b rough t
in , t he mean ing o f t he co lo r o f eyes changed . B l ack was no l onger a
given, but a
choice
in the system of c o l o r— w h i c h at tha t par t icu lar po in t
in
th e
d i scou r se cons i s t ed
o f
b l a c k
and no t
b l a c k ,
t h a t is ,
red .
In
o t h e r
w ords , we co uld say tha t the co lor o f the eyes was an aspe ct t h a t w a s n o t
d i s ce rned
in i t i a l ly
(a t l eas t b y s o me of the s t u de n t s ) . I t was t a k e n fo r
gran t ed . How ever , w hen
a n
a l t e rna t ive
ey e
co lo r
w a s
e xp l i c i t l y b r o u g h t
u p , a d imens ion o f var ia t ion in co lor w as o p e n e d u p . Di sce rn ing t ha t th e
co lo r o f the s l o th ' s ey es i s b l ac k imp l i e s a d im ens io n o f v a r i a t ion w i t h a t
least
tw o
poss ib le value s : b lack
an d no t
b lack . De scr ib ing
th e
eyes
of the
s lo th a s b l ack m ean t t ha t co lo r was i n t he f oc a l aw aren es s o f one o f t he
s tuden ts . I t w as by
va r y i n g
th e
co lo r
o f a
s l o th ' s eyes ( and
a
r a b b i t ' s e y e s )
t ha t s t uden t s w ere ab l e
to
d i s ce rn t ha t ha v in g b l a ck eyes
w a s a c r i t i c a l
fea tu re o f t he s l o th ' s appea rance .
Sloth s
Body.
A l thou gh m ost groups described
the
body
of the
sloth
a s
"roundish,"
p lu m p , o r like a big ostrich egg (as Group 2 did), Group 5 de-
scribed the slo th 's body as very thin . Th e fo l lowing excerp t shows the m ean-
ing that Group 5 a t t ached to th is descr ipt ion.
6 .5 [Chinese Lesson/P3/The Sloth/Group Discuss ion/G roup 5]
S : Now , i t ' s bod y [shape]
...
S: I t 's body [shape] , i t 's body is qui te b ig , huh ?
S:
Thin
S :
Thinnish
...
Looks l ike
he is
un dernour i shed.
S: N o
S:
Thin
He is
very thin
S : H is body shape ...
S: In fact, it was his fur that covered it up.
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6. S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 51
S: Oh no
S:
The fur
covered
it up
S : His body shape . . .
S:
Yeah
S:
In fact he is
very plump
S:
He is
very thin.
S : Yeah, th ink about th is . Plum p because o f the fur, his fur covered
up his body.
S:
Because
his fur is
long
This debate wen t on for quite a w hi le and finally the students agreed to put
down "thin." What happened here was that this
group's
construal of the
sloth's
appearan ce w as m ade in the con text of the narration that said that the
sloth's mo ther ha d died, that it w as alone, and tha t the leaves on the tree w here
it lived had all been eaten up. For this reason one of the studen ts said that the
sloth
was "undernourished." In order to reconcile the discrepancy between
what they saw on the video and
their
understanding of what his
appearance
should
be,
they cam e
u p
w i th
an
interesting explana tion: that
th e
sloth looke d
plum p only because
of its
fur. This suggests that
the
meanings that
are as-
signed by the students to the phenom enon under discussion m ay lead to a di f-
ferent construal of the object of learning.
Sloth's
Diet .
Let us
take
a
look
at an
excerpt from
the
discuss ion
in
Group 4 on the s loth ' s diet . The video narration only provided the inform a-
t ion
that
the
sloth
ate
leaves
from one
par t icular t ree:
I t [ the sloth] looks around and tries t o find a t ree wh ere i t wo uld l ike to live. The tree
should
be o f the same spec ies as the one that i t
lived
on before because wh en a
sloth
gets
used
to the taste of the leaves of a certain
k ind
of tree, it w i l l not change what i t eats .
6.6
[C hinese Lesson/The
S
loth/PS /Group Discuss ion/Grou p
4]
S :
It
eats
... it
only eats leaves.
S:
It
does
not eat
anything else,
it
only eats leaves.
S:
Ea ts leaves.
S :
E a t s le aves , i f . . . i f . . .
S: Like a big bear, it's pin sihk
2
(C antonese) [ $| ^ ] ("a
fussy
eater").
Like
the
panda ,
it's
p in
sihk.
S : He y . .. there's m ore
S:
It ' s
a.pin sihk
an imal .
S: It
does
not eat
me a t
and . . .
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1 52 T S U I
S: I t
does
not eat
meat
and
does
not eat fish.
Does
it eat fish?
Ss:
N o
S: N o, i t also says . ..
S :
When
it
gets used
to the
taste
of one
k ind
of
leaf ,
it
wi l l
not
e a t . . .
S: That 's why [ I said]
ii'spin
s ihk .
In the or iginal n arrat ion , the narrator ex plain ed that the s loth had to f ind
a
tree
of the
same spec ies because
of its
p re fe rence
for a
cer tain type
of
leaves.
T he
students
in
Group
4,
however, ass igned fur ther m ean ing
to the
s lo th ' s p reference fo r l eaves . They used a s i n g l e e x p r e s si o n ,
p in
sihk
( Ca n t o n e s e )
[ ̂ ^ ], an
ad jec t iva l
ph rase
for
de s c r ib i n g s o m e o n e
who
is
a fussy eater, to describe the eat ing habits of the sloth. T he s tudents were
br ing ing in the i r own exp er ience of be ing to ld by th e i r pare n t s tha t they
should eat everything and not be
fussy
abou t the i r food ( a com m on exhor -
tat ion made by parents to their children ). T he phrase p in sihk is at a h ighe r
level of abst ract ion and general izat ion than the descr ipt ion given in the
video. Moreover ,
the
s tudents were also able
to
re la te
th e
s lo th ' s ea t ing
habits
to the
eat ing habits
o f the
panda, something that they
had
learned
about
in the
previou s lesson.
T he phrase
p in
sihk
proposed
by the
s t uden t s
has the fol lowing semant ic features : does not eat meat or f i sh , and eats
only one kind of leaves. There are at least tw o an im al m embers be longing
to
th i s ca tegory : panda s
an d
s loths .
T he
question
is, how
were
the
s tudents able
to
co l labora t ive ly cons t ruc t
such a rich text, both spoken and writ ten? How is i t that the same video
could be const rued in such a sem ant ical ly rich m anne r? How did the teacher
bring this about?
It seems
that there were tw o th ings that the teacher did that were qu i te
crucial .
The first has to do
w i th
the w ay he
varied
the
showing
of the
video
with and
w i th o u t
the
narrat ion.
Variation: Video With and Without Narration.
Wh e n
th e
teach er showed
the video for the f irs t t ime, the narrat ion w as given. B ut whe n he showed
segments of the video, he took away the n arration. The purpose of m ak ing
the video soundless w as, as the teacher told the studen ts, tha t if he pla ye d the
narrat ion as we l l , then there w ould be no thing for the s tu dents to talk about .
In
other
wo rds,
th e
narration
in the first
viewing gave
the
students
an
idea
o f
w hat the s tory w as abo ut . In a way, one c ould say tha t the narrat ion provided
the
context
in
wh ich
the
appearance
and the
m o veme n t
of the
s lo th cou ld
be
interpreted. This is most evident in the description made by one group of
students w ho described the sloth 's eyes as look ing l ike tw o teardrops. Th is
construal w as obvious ly made in l ight of the fact that the sloth h ad lost its
mother and had to struggle for survival.
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6 . S E M A N T I C E N R I C H M E N T
O F T H E
S P A CE
O F
L E A R N I N G
1 53
For the second viewing, the narrat ion w as removed in order to allow the
students to interpret what they saw in their own ways. By doing this , the
teacher opened
up the
space
of
learning.
T he
students
were free to
bring
in
their
o w n
experience
and
previous learning
to
make
sense
of
what they
s aw
on the video without being constrained by wha t w as said in the narration.
In
other words, what
the
teacher varied
was the
n arration
and
wha t
he
kept
co nstant w as the visual im ages . B y so doing, the s tudents becam e very
m u c h aw are of the lack of narrat ion, an d the fact th at they ha d to write the
narra t ion
them selves .
In
order
to fulfill the
task, they nee ded
to focus
thei r
at tent ion on the
visua l images , especial ly
the
appearance
and the
mo ve me n t
of the
sloth.
Let
u s im agine that the teacher asked the students to do the same task, bu t
re ta ined the
narrat ion w hen showing
the
video
th e
second time. W hat w ould
have happened? A s the students had been given the task of w riting a narra-
tion of the story, it is likely tha t the structure of their
awareness
would have
changed. What would have come to the fore of their awareness, or wha t
w o u l d
have been f igural , w ould be the narrat ion; wha t the narrator actu al ly
said. T he
actual
appearance and the m ovem ent of the s loth w ould have re-
ceded
to the
ground. What
the
teacher w ould very l ikely have achieved
is
tha t the s tudents wou ld have t ried to regurgitate the narrat ion rather than
c o m i n g up
w i th thei r
ow n
descript ions.
Variat ion:
Teacher-Led D iscuss ion and S tudent -Led D i scus s ion .
R e-
searchers have pointed out that wo rking in groups is natu ral ly con ducive to
making
use of
variation (see W istedt
& Martinsson's
w ork, 1994,
on
inexac t
decimal representation
of the
fraction "one third," cited
in
M arton
&
Booth,
1 997). How ever, this does no t m ean that group work w il l necessarily lead to
successful
learning. W hether succ essful learning
is
achieved
or not
depends
on
whe the r
the
teacher
has
exploited
the
conduciveness
to
variation
in the
group wo rk. Ci t ing the wo rk of Lybeck (1 981) on group w ork ( in wh ich the
t eacher
conf ron ted
the
students with variat ions
in the
concept
o f densi ty
proposed by other students, and put the variat ions und er scru tiny), M arton
(1986) observed that the teacher "funct ioned as the arch i tect of the peda-
gogical mi l ieu,
the
midwi fe
of
experience
and the
sculptor
of
thought"
(cited in M arton & B ooth, 1997, p . 69).
In the lesson on the sloth, the teacher focused the studen ts ' at tention on
th e
cr i t ical features
o f the
sloth, such
as its
appearance
(which
is
stat ic),
and
its
m ovem ents (w hich
a re
dynam ic). This teacher-led discus sion pro-
vided the
sca f fo ld ing
for the
subsequen t s tudent - led di scuss ion
i n
groups .
The teach er a l so emph as ized the co l labora t ive na ture o f g roup w ork , and
to ld th e
s tudents tha t
i t w as
im por tan t
fo r
them
to pay
at tent ion
to the
con-
t r ibut ions of other group m em bers , to th ink about these con tr ibut ions , and
to
t ry to im prove on them . These are the ins t ruct ions he gave to the s tu-
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154
T S U I
dents after
h e had put the
s truc tura l com pon ents
o f the
descr ipt ion
of the
sloth on the board.
6.7
[Chinese Lesson/PS/The Sloth]
T: A fter w atching th e video,
each
group wil l discuss among them-
selves...
. You
have
to
collaborate. D on ' t jus t write
it all by
your-
self. Y ou mu st work together and contr ibute your opinion. You
have to see whether w hat
another
member has said is right or not,
and
whether
it is
good
or
not . Af ter
a
mem ber
has offered a
[de-
scriptive] sentence, you can add you r opinion. L ike, "It w ou ld be
better
to
w rite
it
this
way
...,"
"It
w ould
be better to say it
that
way
. . . ," or "No, I disagree, I saw it [the sloth] making this kind of
movement." and you can give your own account [of what you
saw].
If everybody agrees, then y ou write it down.
B y providing the students with a detailed explanation of w h a t w as ex-
pected of them w hen they engaged in group w ork, the teacher was opening
up the
space
fo r
variat ion
in
discerning
the
c r i t ical features
of the
s lo th .
T he
data from the group discussions show tha t each group was able to bring their
ow n experience to bear on the descript ion, a nd
different
d imens ions of vari-
at ion w ere opened up .
A lthou gh the in i t i a l d i scuss ion w as t eacher- led , the l earn in g space w as
jo in t ly cons t i tu ted by the t eache r and the s tude nts in the sense tha t th e s tu-
dents offered descriptions of the cri t ical features o f appearance, such as
the hea d, the body, the color, and the four l im bs of the s loth , as w el l as it s
mo ve me n t s .
T he teacher also provided scaffolding for the group discussions by re-
m inding s tudents w hich aspects they should
be
focus ing
on in the
course
o f
the
discuss ion.
F o r
exam ple,
he
reminded
the
s tudents tha t they shou ld have
finished discussing the appearance and should be m oving on to the descrip-
t ion o f m ovem ent . A s the s tudents w ere discu ss ing the movem ents , he re-
m inded them of the various m ovem ents they should be descr ib ing, such as
sw im m ing, crawling up the r iver bank, c l imb ing up the t ree, and so on.
Table 6 .1 summarizes the contr ibut ions made by the s tudents in the
teacher-led discussion
and the
student-led discussion
in
four groups
out of
six.
T he
features
in the
s tudent- led discuss ions that were
no t
found
in
teacher-led discussion s are in i tal ics.
When the groups had finished drafting their
descriptions,
the teacher
asked each group
to
present their descript ions
as the
na rrat ion
as he
p layed
the video again. Here the teacher was further w idening the space of varia-
tion
b y
gett ing students
to
listen
to the
descriptions w ritten
by
other grou ps.
T he different
descript ions showed that
different
aspects
of the
sloth were
in
th e
focal awareness
of
each group.
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TABLE 6. 1
D escr i p t i on o f t he S lo t h i n Teacher-Led an d S t u d en t -Led D i scu ss i on s
Teacher-Led Discussion
T
M o v e m e n t
Appearance
Colo r
Head:
l ike
m o n k e y ' s
head
Ss
Slow, s lowly
c l i m b i n g
up a tree.
Furry
B r o w n ,
w h i t e
Head very ro und, very
s mal l ,
neck
is
very
long, l i m b s
ar e
very
long
Student-Led Discussion
Gro up
1
Mouth (beak)
— very
f lat,
like a duck,
very shor t
Gro up
2
Very short tai l
Grayish, whi t ish,
brownish and whit ish,
black, brown
Looks l ike a m o n k e y ' s
head , ch icken egg ,
b ig
goose
egg , b ig duck egg ,
big ostrich egg
Gro up
4
Nose: b lack , body: black,
eyes: black
(a s
op p osed
to red) , mouth: f lat ,
protruding,
b lun t
Head
is l ike a
m o n k e y 's ,
head can turn 36 0 degrees
Gro up 5
Face: whi te, eyebrows:
brown, eyes: triangular,
l i ke m onkey
's
eyes , body:
l ike a
hum an be ing , very
small , only half a year
old, like
th e
thigh
of a
baby, l ike a b ig winter
m elon
R o u n d ,
ova l
tn
in
(cont inued on next page)
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l/l
Os
TABLE 6. 1 (cont inued)
Teacher-Led Discussion
T
Four
l i m b s ,
f inge r s ,
p a w s
M o v e m e n t :
c r a w l i n g
S w i m m i n g
Diet
&
Paws, c laws, three
s harp
c l a w s
V e r y
s l o w , s lowly
c l i m b s
u p a tree
l o o k i n g
a r o u n d
Student-Led Discussion
Gro up I Gro up 2
Very l o n g ,
especially
th e
claws of
the for
climbs,
th ree c laws
V e r y s l o w , s l o w l y c l i m b s
d o w n
the tree ,
exhausted,
l o o k i n g
a r o u n d
a s
soon
as
i t r e a c h e d
t he
b a n k ,
c l i m b e d
up the
t r ee ,
it
f i na l l y
fo u n d a new h o m e
Free s ty le
Gro up
4
H a n d s
an d
legs
ar e
very
l ong , nai l s are very
pointed
(sharp) , four l imbs are very
l o n g an d sma l l , claws ar e
very long and razor sharp
Puppy
style, frog style
(breast stroke), free style
O nly
eats leaves, l ike
th e
panda, it is pin
sihk (fussy
eater) , does no t ea t meat or
fish
Gro up 5
Eats on ly leaves, any k ind
of
leaves that it likes.
Note . T he fea tures in the s tuden t - led d i s c u s s i o n s tha t
w ere
n ot f o u n d in teache r - led
d i s c u s s i o n s
are given in i t a l i c s .
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6.
S E M A N T I C E N R I C H M E N T
OF T H E SPACE O F L E A R N I N G 1 57
L I N G U I S T I C
RESOURCES AN D
SEMANTIC
E N R I C H M E N T
In th is sect ion, we look at the w ay in w h i ch the same object of learning w as
construed semantically in very
different
ways in tw o classroom s because of
the
different l ingu ist ic resources avai lable
to the
teacher
and the
learners,
that is , one of the classes w as taught through the medium o f Chinese, w hich
w as the mother tongue for al l students (CM I), and the other through the me-
dium
of Eng lish, wh ich wa s a second language for all students (EM I).
The history lessons used as examples in this section further i l lustrate
w h a t w e mean by the
seman t ic d imens ion
of the learning space. (For the
background of
these lessons,
see
Tsui , Aldred, M arton, Kan ,
&
Runesson ,
2001.)
The
extracts
are f rom two
secondary Grade
2
(S2) (i.e., Grade
8)
c lass room s in w h i c h the sam e topic w as taught , and il lustra te the
difference
in the sem antic space opened up because of the different linguistic resources
avai lable to the s tudents .
H i s to r y L e s so n s : T h e M a r k e t in Early
Rural
C o m m u n i t i e s
In these tw o history lessons, the objec t of learning was the concept o f
m ar -
ket
in early rural com m unities in Hong Kong. The critical features that dis-
t ingu ish
this market (which perhaps t ranslates more accurately as "fair")
from
the market in modern societies, are the differen t func tions. In i ts his-
tor ical
contex t ,
th e
m arke t
was a
p lace w here people would come both
to
buy produce and to sell their ow n produce, or sometimes even to exchange
goods. The m arket w as also a p lace for social in teract ion, and w as loca ted
in a
particular place that
w as
accessible
to
man y villagers
and
clans. How -
ever, due to poor t ransportat ion markets w ere no t h eld every day but at r egu-
lar intervals.
The
fo l lowing
is an
excerpt
from
the EMI
lesson
in
w h ic h
th e
teacher
tried to elicit from the students the critical fe atures of the m arket in its his-
tor ical
con tex t .
6.8
[History Lesson/S2/EM I]
1
T : Do you think th e m arket at that time is the same as you[ V e ] go t n o w?
2
Ss: No.
3 T: How
[was
it]
d i f fe ren t?
4 Ss: [silent]
5 T:
H u h ?
6 Ss: [silent]
7 T: How [was it] different? Can you imagine? In the past,
market
[writing
8 the word "market" on the board]. Y ou[ Ve] got a m arket, there,
isn't
it?
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158
T S U I
9 Is it a market there? [Points to the market next to the school. ] Have you
10
been there?
11 S:
Yes.
12 T:
Yes.
But in the
past
we
call[ed]
it
heui. (Cantonese)
[ ̂ ]
[Writes
the
13 Chinese
character heui (Cantonese) [J^]
on the
blackboard.] Chan
14 heui.
(Cantonese) [ ̂ ̂ ] And then at hat time people going to
15 market, we call[ed] it chan heui.
16 Ss: [laughter]
17
T: [writes the words chan heui (Cantonese) [ ̂ 4sj|
]on
the blackboard]
18 And then what does it mean? At that time the people—you find out that
19 for the
market ...?
20 S: [silent]
21 T: The market opens every day? Is it? There? [Pointing at the market outside
22 the
window]
23 Ss: Yes.
24 T: But at that time the market [did] not open every day. They
w i ll
fix some
2 5 day, for example,
for
each month, [on the] fifteen[th] and thirtieth], they
2 6 will have [the] market. And then people go there, and then to sell...
w h a t
2 7
they produce.
For
example,
you
look
at
him,
he
go[es] there
to
sell
his
pigs
2 8 and cocks, and at the same time by making money he can buy something
29
that
he d id not
produce
by
himself. Understand?
So i t is
dif ferent
from
3 0 your market, isn't it? And at the same time, at
that
time the market has a
31
function. First
of
all,
it is
selling
and at
same
t ime you buy
something.
A nd
32
also
you f ind out
that,
in the
second paragraph, what
did he
say?
33 [referring to the diary of Tang Tai Man.]
34 Ss: [silent]
35 T:
What
did he
say?
36 Ss:
[silent]
37 T: What did he say?
38 Ss:
[silent]
39 T: Huh? [Nominate], what did he say in the second paragraph?
45 S: [reading from the second paragraph of the diary of Tang Tai Man]
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6. S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 59
46
"Today
I
also
met my f r iends
coming
f rom another village, we
47
chat[ted]."
48 T: Okay,
okay,
so what
did,
what
did he do in the
second paragraph?
49 S: [silent]
50 T:
What
is happening to
him?
51 S: He met his f r iends.
52 T: He met his
f r iends.
Okay, sit
down.
You
f ound
out
tha t then,
for the
5 3 market at that time, it also provides a chance for them to meet their
5 4
f r i ends . . . .
You
found
out
that
at
that
time [there
was]
no
transport,
you
5 5 can
only
?
56 S:
Walk.
57 T:
Walk.
Then sometimes it is
difficult
for you to find
your
friends, is it? So
58 the market provide[d] a place for them to
meet
their friends.... You think
59
about now,
is it
very easy
for you to see
your friends?
60 T: ... So you find out that here this is the function of the m arket [referring to
61 the
handou t ]
...
Here the t eacher w as t rying to br ing ou t the difference s be tween the mar -
ket in the past an d the m arket in the present, and its funct ions in early ru ral
c o m m u n i t i e s
in Hong Kong . S he started w ith a n open quest ion of how the
m arket in the old days w as different from the m arket nowadays (see l ine 3,
"How [was
it] different?").
W h e n
she failed to get an
answer ,
s he
na r rowed
down the question to specific features. First , she tried to draw on the stu-
dents ' m other tongue resources by invoking the exp ress ion chan heui ( Ca n -
tonese) [^^],
an
expression that
all
students were familiar with
as
evi-
denced by the l aughter . S he asked them to extrapolate one of the fea tures of
the m arket from
the
m eaning
of
this expression. (The word chan (Canton-
ese) [^ ] m e a ns to take the opportunity, and he word
heui
(Cantonese) [ ̂ ]
w as
used
by the
teacher
as an
equivalent
of the
market
in the
past . T herefore,
chan heui imp l ies tha t the market was not open every day, and t ha t w hen it
w as, people took the oppo rtunity to get what they wanted from the m arket .)
This
t e c h n i qu e
did n ot
m ee t w i th m uch succes s because unpack ing
a
Ch i -
nese expression in E ngl ish was far too difficult for the students. Failing to
get a response , the teacher s im ply pointed o u t tha t un l ike the m arke t nex t to
their school, m arkets in the old days were not open every day.
Af ter dea l ing wi th the first cr i t ical feature, the t eache r w en t on in the
same turn
to
provide
the
second critical feature
of the
m arket: U nl ike today,
peop le w e n t
to the
m arket
n o t
only
to
sel l their pro duc e
or to buy
som eth ing
they needed, but to do both at once. From lines 32 to 58, the teach er tried to
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160
T S U I
elicit
a
third critical fea ture
of the
m arket
f rom the
s tudents ,
by
ask ing them
to
look
at the second paragraph of the diary that she had been referr ing to
earlier. One of the s tudents , after s t ruggl ing w i th th e t each er ' s ins t ruc t ions ,
sim ply read
out the
second paragraph instead
of
inferring
from
th e
t ex t w hat
the th i rd cr i t ical feature wa s, as the t eacher h ad w a n t e d. A l th o u g h the stu-
dent w as able to provide an appropriate answer
after
several prompts from
the teache r (see l ine 51 ) , the conn ect ion be tw een w hat appeared in the t ex t
and the third cri t ical feature of the m arket ( i .e ., that the m arke t p rov ided a
place for people to meet thei r f r iends) had to be m ade by the teache r . The
connect ion between the funct ion of the ma r k e t fo r soc ia l in terac t ion and
poor t ransp ortat ion w as also made by the teache r .
W e
can see in the
ju s t c i ted excerpt that
th e
teach er tried
to
focus
the
s tu-
dents ' at tention on the cr i t ica l fea tures of the m a r ke t in old r u ra l c o m m u n i -
ties
by
varying
the
contex t s
of
pas t
and
p resen t . However , because
of the
s tudents ' l im i ted l in gu is t ic resources in En gl ish , the teache r h ad p rob lem s
engaging the s tudents in m ak ing s ense of the contex t s in w h ich t hese f ea -
tures were to be understood.
Let us compare this lesson wi th an excerpt below f rom a CMI lesson,
where the same concepts were being explicated.
6.9
[History Lesson/S2/CM I]
[The teacher asks the students to identify on the m ap place s that con-
tain the word
heui
(C antonese) [
̂ ]
[standing for "market."] The n he
con t inues to ask the s tudents the
funct ions
of a "market."]
1 T : Nex t I wan t to ask you , what are the funct ions o f a heui?
2 S :
[cheeki ly]
N o
use .
3 T :
W h a t? W h a t
are the funct ions
of
heui . H as
anybody heard
the
4 saying "Three, w ha t , make a
heui?"
5 Ss: Three w om en
6 T : Wha t does that m ean? N ow w e a re not discriminating against fe-
7 ma l e
students.
W e are not saying that female
students
are talkative. So
8 what is the function [of a
heui]?
In fact, how can three people m ake
9 a
heui? W h at
is the
characterist ic
of a
heui?
10
S:
V ery noisv.
11 T :
V ery noisy. M aybe
w e
should
not use
[ the w ord] noisy.
12
S:
Busy .
13 T : Busy A lot of fun . Other than this? W hat else?
14
S : Lots of th ings for sale.
15
T :
W h a t funct ion does
th e
m arket have?
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6 . S E M A N T I C E N R I C H M E N T O F T HE
S P A C E
O F
L E A R N I N G _
16 S: Transact ions .
17
Co nducting transactions, that's right. W hat kinds of things
for
us to
18 T: buy? In earlier
societies?
19 S: Jewelry.
20 T: Jewelry . A nything else?
21
22 T : That is, the market has the
function
of [conducting] transactions.
23 Where is it?
24 S: "Open air
n ightclub"
3
25
T :
"Open
air
nightclub
."That's
right . U sua lly
it is on a
piece
of
flat
2 6 land. W hereabouts? Is it near the village? Inside th e village ? N o.
27 Usual ly . . . c an you
imagine?
28 S: N e a r the vi l lage s .
29
T :
H m m ,
any
other suggestions?
30
S: Where there are lots of people.
31 T: W here there are lo ts of peo ple. An y other suggest ions?
32 S :
W here lo ts
of
people
can get to it.
33 T: W here lots of people can get to it. Is it a
place
only where people
34
w i th the surname "Tang" can go?
35
S: No.
36 T: The place is a piece of flat land where u sually other villagers can get
37 to as w ell . That is where th e m arket was loca ted. A lso, in the old
3
8 days, there w ere no buses, no subw ay, so it w asn 't so conven ient.
39 So w ou ld there be a m arket every day? W ould people go to
40 the
m arket every day?
41 S: No.
42 T: That seldom happen ed. U sua lly there was a
fixed
t im e, usual ly
43
several t im es a m on th, or once a w eek. B esides being a place
44 for co nd uc ting transactions, w hat other function did it have?
45
Jus t
n o w w e
said that three w om en m ake
a
m arket,
very
busy,
46
[people] cha t t ing
to
each other . W hat funct ion
[of the
m arket]
47 can you
deduce
from this? A h,
"You come from
the
nearby
48 vil lage , how is so and so?"
49 S: So cial interaction activit ies.
50 T : W hat kind of funct ion did it have?
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1 6 2 TSUI
51 S : Social
interaction activities.
52
T: That's right. Yo u are
correct.
It
actually
had a
kind
of
interactive
5
3
function,
the
interaction between villages, am ong people
from
54 differen t clans.
W e
can see from this excerpt that in the CMI c lassroom, the lea rn ing
space in wh ich the features of the market w as understood w as jo in t ly con s t i-
tuted by the
teacher
and the students. I t was
also
semant ical ly m uch richer
than that const i tuted in the E M I c lassroom.
Firstly,
by a l luding to the C hinese co l loquia l expression, "Three w o m e n
make
a
m arket,"
the
teacher
w as
im m ediate ly able
to g et the
students
to as-
sociate
th e expression
wi th
"very noisy" and "busy"
(l ines
10 and
12).
W hen he asked the s tudents w here the market w ou ld no rm ally be located,
they used the ana logy "open-air n igh tclu b" (l ine 24). (The
"open
a ir n igh t -
club" was a large , w el l-kno w n, open-air nig ht m arket in Hong Kong , that
besides
having
a
variety
of
things
for
sale, also
had
entertainment shows,
fortune-telling,
and
haw ker stalls. People w ent there
no t
j u s t
to buy and
sell
things, but
also
to
have
a
good t im e.)
The
teacher p icked
up on the
s tuden t 's
analogy (l ine 25) and further developed the topic by involv ing s tudents in
exploring the locat ions of markets . Again draw ing on s tudents ' kn ow ledge
of the expression, "three
women m ake
a
m arket,"
th e
teach er solicited
from
the students that another cri t ical feature of the m arket was its funct ion for
social
interaction (l ine 49).
Here we can see that the rich l ing uistic resources of the m other tongu e en-
abled
th e
teacher
and the
students
to
collaboratively construe
a rich
picture
of
the
m arket w ith
a
n u m b e r
of
seman t ic features:
for
exam ple , noisy, busy, joy -
ous; w ith lots of activities going on; buying and sell ing; people from
different
villages and
clans meeting
up and
making
friends;
people performing
and
watching entertainment shows. Going
to the
m arket
(chan heui) was a
social
event that
took
place at regu lar intervals rather than every day because of the
lack o f transp ortation. W e can also see that the s tudents ' understanding of the
market
w as
m uch m ore sophist ica ted
due to the use of
their m other tongu e.
For example, the concept of
social interact ion
is m uch m ore sophistica ted
than jus t
"meeting
friends" and
"entertainment,"
and the concept of t ransac-
tion is mu ch m ore sophisticated than "buying and sell ing."
The
fo l lowing tab le sum m arizes
the
semant ic features
of the
m a rk et
in
the two lessons (see Table 6.2).
C O N C L U S I O N
In
this chapter, w e have looked at another very important aspect of the
learning space, that
is , the wa y in
w hich
the
object
of
learning
(in the sense
of the l ived object of learning) is construed by the learners when they are
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6 . S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F
L E A R N I N G
1 6 3
TABLE 6.2
Features
of the
M a r ket
in C M I a n d E M I
Lessons
EM I
Lesson
Funct ions o f marke t
•
S e l l i ng as
w e l l
a s
b u y i n g
• M e e t in g f r iends ( b e c a u s e o f poor
t r anspor t a t ion)
Opening
N o t open
da i ly
( n o r ea sons
g iven)
Funct ions o f marke t
•
Tran sac t ions ( f ood and o t h e r
t h i ngs )
• Soc ia l in teract ion be tween v i l lage s and c l ans .
Imagery
" T h re e w o m e n m a k e
a
m a r k e t"
( to
d ed uce
func t ions )—noisy ,
busy ,
a lot of
activit ies,
j o y o u s
socia l in teract ion .
Analogy
"Open a ir
n ig h t c l u b"— bu y in g
and
se l l i ng , f ood ,
en t e r t a i n m en t show s , hav ing a good tim e .
Locat ion
Access ib le to peop le from
d i f fe rent
clans and
vi l l ages .
Opening
N ot open
da i ly ;
poor t r anspor t a t ion , no t
e n o u g h
goods and p rod uce for sa le .
able to bring in their ow n experiences, their ow n culture, their fo rm er learn-
ing,
fo lk lore ,
and so
for th .
W e
referred
to
this aspect
o f the
learning sp ace
as
th e
sem antic
dim ension
of the
space
o f learning, a nd
proposed that this
s e-
mant i c
dimens ion
is
elas t ic, that
is ,
that
it can be
enriched
or
impoverished.
W e
i l lus t rated
how the
teacher enriched
th e
semant ic dimension
of the
space of learning by help ing learners to perceive the interre lat ionsh ip of as-
pec ts of the pheno m enon that were hi therto perceived as unrelated. B y in-
t roducing
n ew
semant ic dom ains
or
d ifferen t levels
of
knowledge
in
w h ich
the
phenomenon
can be
con st rued,
the
teacher enriched
the
learning space
semantical ly. W e have also illustrated how the learners themselves en-
r iched the learning space sem ant ical ly by br inging their ow n experiences to
bear o n the object of learning, and how they can thus col laborat ively con-
struct and ass ign new m eanings to the object of learning. Th e w ay in w hich
the
semant ic dimension of the learning space is enriched and thus helps
learners exp erience
the
object
of
learning
in a
certain
w ay in
each lesson
is
an instan tiat ion that wil l eventually lead to the en larging o f the sem antic po-
tential in w hich the object of learning is being construed. Finally, by com-
paring
the
di f ferences
in
semant ic
richness of
const rual
of the
object
of
l ea r n ing—in
c lasses w here learners have the necessary l ingu is t ic resources
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164 T S U I
(mother tongue
medium), and
classes
in which they do not (second lan-
guage
medium)—we have illustrated the way in which language plays a
central
role
in the semantic enrichment of the space of learning.
E N D N O T E S
'The writ ten texts produced by the s tuden ts were in M odern S tandard Chinese .
The translations of the texts presented here are semantic translations but the syn-
tact ic s t ructures of the texts have been re ta in ed as far as poss ib le .
2
In
th is volume, characters and words spoken in C a n t o n e s e a re t ranscr ibed in
the Yale system, w h ich is
used
by some Can tonese-learning m ater ia ls produced by
the Ya le U nivers i ty , and by The U nivers i ty o f Hong K ong in it s C an ton ese-En g-
lish,
English-Cantonese
dic t iona r ies . (N ote that diacr i t ics that are used to indic ate
Cantonese
tones have been
left
out . These diacri t ics are very
di ff icul t ,
if at all pos-
s ible , to produce us ing Word, and some research repor ts us ing the Yale sy s t em
simply
do not
include
the
diacr i t ics .)
3
"Open
a ir nightclub" is the name given to a large , wel l-known, open-air n ight
m a rke t in Hong Kong . It does no t ex i s t anym ore in its o r i g ina l f o rm .
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T h e S h a r e d S p a c e o f e a r n i n g
A m y B . M .
T s u i
M ar to n an d B o o th ( 1997) ex p o u n ded th e qu a l i t a t ive ly
d i f ferent
w a y s i n
w h i c h
lea rn ing c a n b e exper ienced : T h e learner m a y f o cu s l a rg e ly on the
situation in
w h i ch
the
p h e n o m e n o n
is
e m b e d de d ,
or on the
phenomenon
as
it
is revea led in the s i tuat io n ( see p . 83) . The y o bserved tha t the asp ec ts of
the
p h e n o m e n o n
and the
re l a t i o n sh ip s be tw een th em th a t
a re
d iscerned
a n d
he ld in aw ar en es s s imu l t an eo u s ly de t e r min e th e w ay th e p h en o men o n i s
ex p e r i en ced
by the
in d iv idua l . Therefo re
th e
s am e p h e n o m e n o n
m a y b e e x -
p e r i en ced in qu a l i t a t ive ly d i f ferent w ay s by in d iv idu a l s becau se th e a sp ec t s
and the r e la t ions h ips tha t they d iscern m ay be di f fe rent , and w hat i s he ld in
a w a r e n e s s s i m u l t a n e o u s l y
m a y
a lso
b e
di f fe rent . Wh en th i s h ap p en s ,
th e
l ived o b jec t o f lea rn ing w i l l be
d i f ferent
from the enac ted ob je c t o f
l e a r n i n g .
To b r in g abo u t s uc c e s s f u l lea rn ing , it i s necessary tha t the teac her and the
learner share
a
l a rg e co mm o n g r o u n d
in
r e la t ion
to the
o b j ec t
o f
l e a r n i n g .
T h e
task befo re
th e
teache r , therefo re ,
is
th reefo ld . F i r s t ,
th e
t each e r
s h o u l d
en su r e th a t
the
co n d i t i o n s
a re
there
for the
lea rner
to be
ab le
to
d iscern
an d
s i m u l t a n e o u s l y ho ld in awa reness the c r i t i ca l aspec ts o f the ob jec t o f lea rn -
i n g , and the r e la t ionsh ips be tween these aspec ts . Secondly , th e t e a c h e r
sh o u l d
b e
aware
of the
lea rner ' s exper ience
of the
o b j e c t
o f
l ea r n in g ( s ee
a lso Ale xan dersso n , 1994), and be v ig i lan t o f s igna ls from learner s
i nd i c a t -
ing a
lack
o f
co m m o n g r o u n d . Th i r dly ,
th e
t each e r sh o u ld
t ry to
w i de n
th e
s h a r e d c o m m o n g r o u n d .
These
th r ee ta sk s can n o t
b e
ach ieved in dep en d-
e n t l y
o f each o ther ; they a re in te r twined .
W hat does a l l th i s m ean to the p rac t i tioner , and how
r
i s th i s th reefo ld t a sk
r ea l ized
in
c lass room discourse? Befo re
w e
p roceed
to
address th i s que s-
t ion , w e
n eed
to
h ave so me u n de r s t an d in g
o f
w h a t
is
in vo lved w h en
t wo o r
m o r e p eo p le
a re
en g ag ed
in a
d iscourse
o f
some sor t .
1 6 5
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166
T S U I
D I S C O U R S E A N D C O M M O N G R O U N D
When
two or
more people engage
in a
discourse
o f
some sort , they bring
w ith them a set of assum ptions that they bel ieve are shared between them .
There
are cer tain assumptions that per tain to communicat ion in general .
For exam ple, tha t these people speak the same langua ge, that they a re aware
of and observe s im i lar convent ions regarding discourse rules , tha t ne i ther
of them have speech and/or hearing im pairm ents, and so on. These assum p-
tions pertain to the channel o f com m unica t ion and not to a specific ut ter-
ance under discussion.
There a re
a l so assu m pt ions tha t
are
more specif ic
to
the com m unicat ive s i tuat ion. For exam ple, w hen w e talk to a co l league , we
assume that they have shared knowledge about people
and
events
in the
workplace that a re relevant to the day- to-day op erat ion, the l ines of respon-
s ib i li ty , and so on. However, e xac t ly how m uc h kno w ledge we share is not
known unt i l
w e
actu al ly enter in to
a
di scourse .
Le t us
take
the
fol lowing
piece
o f
conversa t ion—which
is
fabricated
bu t
w h i ch typ ica l ly occurs—
between two col leagues , A and B, for exam ple:
7.1
1
A: So the
meeting's been changed
to
Friday?
2 B : W hat m eet ing?
3 A: The departmental meet ing.
4 B : Oh, I
thought
i t w as
canceled.
5 A : A pparent ly not .
6 B: I don ' t know. A sk R ebecca. S he would know.
7 A: OK. Thanks.
When A asked B
w hether
the m eeting had
been
changed to Friday (line
1 ), A had cer tain assum ptions . A assumed that , f irs t, B knew w ha t m eet ing
A wa s
referring
to ;
second,
B
knew that
the
date
of the
m ee t ing
had
been
changed; third, i t was l ikely that B would be able to provide the answer.
However, A c ould not be abso lutely sure that these assum ptions were shared
unti l
B
responded.
B 's
response (l ine
2)
indica ted that
A 's
assump tion
w as
not shared, and
that
B did not
know w hich sp ecific m eeting
A w a s
referring
to. Bruner (1987) pointed out that reference typically "plays upon the
shared presupp osit ions and the shared con texts of speakers" (p. 87). A 's ref -
erence to the meet ing involved mapping A 's
subjective
sphere onto B's .
Upon hearing B's question, "What meeting?" ( l ine 2) , A real ized that th is
f irst assum ption wa s in
fact
not shared by B. A then im m ediately clarified
th e referent, that is, "the
meeting,"
by explici tly identifyin g it as "the depart-
menta l
meeting"
(line 3). B's response to A's clarif icat ion ( l ine 4 ) showed
that A's second assumption that the meet ing had been changed was not
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7.
T H E S H A R E D S P A C E O F L E A R N I N G 1 67
shared, an d A 's subsequent response showed that B 's assumption that it had
been canceled
w as no t
shared
either
(line
5).
Finally,
B 's response
showed
that A's
first
assumption ( that B might know the answer) was not shared
( l ine
6) . B directed A to another col league, R ebecca. B 's assumption w as
that A
knew
w ho
Rebecca w as ,
and
that there
w as a reason for
directing
the
question
to
Rebecca .
This
assum ption
w as
indeed shared,
an d A
thanked
B
fo r the redirection ( l ine 7).
A t the end of the
exchange ,
the
comm on ground be tween
A and B had
widened .
There w as more shared knowledge between them now than be-
fore. An y kind of discourse is a process of w idening the comm on ground be-
tween part ic ipants ,
and
this
is one of the
m ajor m ot iva t ions
fo r
people
to
talk
to
each other. Discourse is therefore a
process
in which m eanings are nego-
t iated and disam biguated, as w el l as a process in w hich comm on grounds
are
e s tabl ished
and
w idened (see Tsui , 1994).
CLASSROOM
D ISCOURSE
AN D E S T A B L I S H I N G
C O M M O N G RO U N D
In classroom discourse, there are also cer tain shared assum ptions betw een
the
t eacher
and the
students.
For
exam ple, there
are
shared assum ptions that
students
should
fol low the
teacher ' s ins t ruct ion, that they should answer
que stions wh en c alled on to do so, and so on. These pertain to the general
classroom protocols that
differ from
cul ture
to
cu l ture; cul ture
in the
sense
of ethnic cul ture
as
w e l l
as
social class culture .
For
example,
in
m any A s ian
classroom s, the protocol requires that s tudents s tand up when they answ er
the
teache r ' s quest ions because
the
t eacher
is a
f igure
o f
authori ty.
In
class-
rooms where middle-class cul ture predominates , working-class chi ldren
are ser iously disadvantaged because they do not share the same assump-
t ions as
m iddle-class chi ldren. Classroom social izat ion
a nd
a ccu l tu ra t ion
are
im portant aspects
o f
classroom learning,
but in
th i s vo lum e,
we a re not
par t icular ly concerned wi th the shared common ground in this respect . W e
are
more concerned wi th
the
aspects
of
comm on ground tha t
are
pert inent
to
the
object
of
learning.
There are also assum ptions that the teacher an d the learners hold that are
specific to the
ob jec t
of
learning.
It is not
u n c o mmo n
for the
teacher
to be
w orkin g on certain assum ptions that are not shared by the students, or vice
versa .
W hen this happen s , the abi l ity of the teacher to negot iate and w iden
the
comm on ground be tween h imsel f
an d the
students
is
cri t ical
to
effective
learning.
Let us
take
as an
example some data
from a
pr im ary Grade
4
(P4) Eng l ish
lesson on "The W eekly Plan." (For the backgroun d of this lesson a nd other
asp ects of this lesson, see Lo & Ko, 2002.). Let us cal l this class, C lass A.
The intende d object of learning in this lesson is the use of the sim ple present
tense to indicate hab itual act ion. Th e teacher, Teacher A , presented a diary
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168 T S U I
of Mickey Mouse tha t shows tha t he does
d i f ferent
act ivi t ies on different
days of the week . H e also does some of the act ivi t ies fo r m ore than one day.
After
get t ing the s tudents to focu s on "How
of ten
does he do (ac tivity)?," the
teacher wanted to
focus
on the tense used.
7.2 [English Lesson/P4A/Weekly Plan]
30 T: . . . he
goes
to the
l ib ra ry only one ,
one
t im e ,
O K ? O n e
t im e ,
31 OK? So we say once a week . Bu t why [do] w e add "-es" at
32
the end of the word "go?" [Teacher po int in g at the "-es"
33 ending on the bo ard.] Can you tell m e? [S s pu t up their
34
han ds.] Yes?
35
S 8: B e c a u s e he, she, it.
36 T:
Yes,
h e.
she,
it. but
w h a t
is
l inked
to the
tense?
T he
verb
...
37 the form of the verb? Sam uel?
38 S9: Present tense.
39 T: Present tense . W hat kin d of present tense? Sim ple—
40 Ss: Sim ple present tense .
41 T : W hy [do we use] "simple present tense?" W h y? W h y do
42 you think it is about simple present tense? B ecause it is
43 abou t _?
44 S1 0: [sit t ing in her seat] He do af ter school .
45 T: [po inting at S1 0] Yes?
46 S10: B ecause it is about ... he do
af ter
school .
47 T:
Yeah ,
it is
abou t
the
th ings ,
OK, he ,
M i ck e y M o u s e ,
he
48 M ickey M ouse, do [does] the thin gs af ter school . W e are
49 te l l ing people about h is hab i t . OK ?
From the studen t 's response in line 35 in the aforem ention ed excerpt, we
can see that w hat came to the fore of this studen t 's aw areness on hearing the
question, "Why [do]
we add
'-es'
at the end of the
word 'go'?"
i s
"subject-
verb agreement."
It is a
pe rfectly appropriate response
to the teacher's
ques-
tion. How ever, i t w as not w hat the teacher w as loo king for. This is evidenced
by the teacher accepting the answer bu t continu ing w ith the disjunct ive
"but,"
which is typical o f disagreement . T he answer
that
the teacher was looking fo r
w as "simple present tense" (see line 40). In fact it is both the third person sin-
gular
and the
simple present tense that necessitate
th e
inflection
of the
verb
"go." If the subject were the first or second person, there w ou ld have been n o
need
for the
inflection even
if the
verb w ere
in the
simple present tense.
A s the
discourse un folds, w e can see that the teacher was ena cting a script in w hi ch
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THE SHARED
SPACE
OF LEARNING 69
th e
teache r 's focal aw areness
w as
very m uch
on the use o f the
sim ple present
tense in describing h abitual action (see line 49), and not subject-verb agree-
m ent . The
latter, however,
w as
very much
in the
student's focal awareness
when
they answered the question. The teacher, being unaw are of how the stu-
dents were experiencing the object of learning, dismissed valuable contribu-
t ions from the
students
as
irrelevant.
L et us consider another example taken from the physics lesson on the
reed relay repo rted in chapters 1 and 5, and se e the difference tha t w as m a de
by
a teacher who shared a large comm on ground w i th the s tudents . In the
lesson
on the
reed relay, after
the
s tudents conducted
the
second experime nt
( in w hich the teacher asked the s tudents to connect a m otor to both the s im-
p le
ci rcu i t [w i thout
a
reed relay ]
and the
com plicated ci rcui t [w i th
a
reed
r e -
lay]) ,
the
teacher explained
the
different outcomes observed
in the
s imple
circui ts in the two experiments .
1
First, she explained why the m o to r did not
rotate in the
s im ple c i rcu i t w i thout
a
reed relay. Then
she
w e n t
on to
expla in
wh y the LED l it up in th is c i rcu i t .
L et us examine the fol low ing extract:
7.3
[Phys ics Lesson/S2/CM I]
1
T :
. . . W h y
is it
that
it
[the LE D] works
in
this circuit? [po inting
at
2 the s im ple ci rcu i t w i th the LED] W hy was i t so w el l-behaved?
3
W hy did i t
[LED] l ight
up?
[nominate]
4 S :
Because
the
resistance that
th e
LD Rneeds,
no , the
current
that it
5
needs
is
smaller than [that needed]
by the
m otor.
6 T: Sav that once again , you are nght. I unders tand you .
7
S : LDR needs
8
T : Wh i c h is the L D R ?
This
one?
9 S :
Because
the
electric that
L E D
needs compared
...
10 T:
Elect r ic w hat?
11 S : Electric curren t is smal ler compared wi th the motor .
12
T : That's right. S o if I press i t [the push b utton sw itch] here, there
13 w i l l be enoug h current to make this LE D glow. OK? N o w , w e
14 found that
if w e
don 't
u se the
reed relay
[in the
circuit w i th
a
15
m otor], then there
are
problems because some circuits m ust
use a
1 6 reed relay
to
operate.
L e t me
give
you an
example
.. .
In
this excerpt , the teacher asked an open "w hy-quest ion" that required
the
s tudents
to
explain
why the
s imple ci rcui t connected wi th
an LED
w orked (see Fig. 2a in chap. 5). Th e stude nt w as trying to construe the ex pe-
r ience gained from the experiments and present it to the teacher . She was
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170 TSUI
trying to relate the
reason
fo r the device lighting u p with th e size of the cur-
rent
that
was
needed
by the two devices
(the motor
and the
LED).
In
line
4,
we can see the
student struggling with this because although
she was
aware
of the
fact that
the
size
of the
electric
current needed
by the
motor
was
bigger
than that needed
by the
device that
l i t up
(LED),
she had
erroneously labeled
the LED as LDR, and had misrepresented electric current as resistance (see
lines
4 and 7). It is
clear that
the
student
had
some problems
in
construing
what she had experienced in the experiment through a m ean ingfu l l ingu is t ic
representation. The teacher, instead of
d i smiss ing
the student's contribution
as wrong, understood that the student w as formulating he r thoughts as she
went along. S he assured the student that she understood what she was trying
to say and
encouraged
he r to
represent
her
construal
of the
experience once
again.
As
soon
as the
teacher pointed
at the
diagrams
on the
board, where
the labels fo r the devices were given, the student realized tha t what she had
thought was an LDR was in fact an LED, and she corrected herself. The
teacher
further
helped the student to represent he r construal in more precise
terms by getting her to revise "electric" to "electric current. In contrast to
the previous classroom excerpt, (7.2), th e common ground shared by the
teacher
and the students was much larger. As a result, the student was able to
construe
h er
experience
in a mean in g f u l w ay and to
make
a va lu ab le
contri-
bution
to the
discussion.
STRUCTURE OF W RENESS
AND THE
SH RED SPACE
OF
LEARNING
T o
further elucidate
the
notion
of the
shared space
o f
learning,
let us
con-
sider
the notion o f structure o f awareness that w as discussed in chapter 1 .
W e
argued that
awareness
is the
totality
o f
experience,
and
th a t
characteris-
tically only
a
limited number
of
things come
to the fore of our
awareness
and the rest recedes to the ground. Marton and Booth (1997) referred to this
structure as figure-ground. However, what comes to the fore of
one's
awareness varies. When the teacher and the learners, fo r various reasons,
are working on d i f ferent assumptions, their structure of awareness m a y b e
dif ferent .
What is figura l to the teacher m a y b e ground to the learners, a nd
vice versa; equally, what
is f igura l to
some learners
m a y b e
ground
to
oth-
ers. When this mismatch occurs,
we say
that
the
space
o f
learning
is not
shared, or only partly shared.
L et us
compare data
from
Class
A
(the English lesson
on
The Weekly
Plan"
cited before) a nd another primary Grade 4 lesson on the same topic,
with exactly the same intended object of learning. Let us call the latter, Class
B. In
Class
A, the
teacher
put up o n the
board
the
diary
o f
Mickey Mouse
that
says
what he
does
from Sunday to Saturday. Above the schedule is the
question, What does
he do
after school? (see Table 7.1)
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7. T H E
S H A R E D
SPACE O F L E A R N I N G 1 71
T A B L E
7 .1
English Lesson/Weekly Plan/Primary Grade 4/Class A
White Board Description
Mickey Mouse s Picture Wh at Does H e D o After School?
Su n d ay
M o n d a y
Tuesday
W e d n e s d a y
T h u r s d a y
F r i d ay
S a t u r da y
Library
P i an o Lesson
B a ske t b a l l
S w i m m i n g
Baske tba l l
S w i m m i n g
Baske tba l l
T he fo l lowing is an
excerpt
from
Class
A, f rom the
point
in the
lesson
wh en the teacher directed th e students' attention t o Mickey Mouse's diary
on the
board.
7.4
[English lesson/P4/Weekly Plan/Class A ]
12 T: ... So let us
look
at his
[Mickey Mouse's] diary,
O K?
What does
13
he do after
school?
OK.
[Teacher
points at the
diary
on the
14
board.] This
is the
thing that
he
does
af ter
school.
O K ,
what
15 does he do af ter school? [Teacher puts a strip o f paper with
16
question What does
he do
after
school?
on the
board.]
C an
1 7 you tell m e, What does he do after school? Anybody?
18
[Students raise their hands]. Yes.
19
S2: He
goes
to the
library
on
Sunday.
20
T : Yes, h e goes to the library on ?
21 S :
Sunday
22 T : Sunday. Yes, after school. OK? He says he goes to the library
23 after school.
"After school."
OK, how about... What
else?
How
24 about others?
25
[Students raise their hands.
The
teacher looks
at one of the
26
students signaling
to her to
answer
the
question.]
27
S3 : He has a piano lesson on Monday.
28 T:
Yes.
We
sav—we
don't say "on Monday" first. OK? The
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172
T S U I
29 quest ion is "What does he do af ter school?" So he says that he
30
has a piano lesson af ter ? School .
31 Ss+T: S ch oo l
32 T: OK. Do you
unders tand?
33
Ss: Yes.
34 T: Yes, OK . How about th e other th ings? W hat does he do a f t e r
35 school? W hat else? [Stu dents raise their ha nds .]
36 S4: He
p lay basketba l l af ter school .
37 T:
Yeah ,
he
says
he
p l ay s baske tba l l
af ter ...
38 Ss+T: S ch oo l.
39 T : "Plays,"
[stressing
the "s"
sound ]
O K ?
Remember "p lays ,"
40 OK? W hat e lse? O n e mor e th ing . Sa m ue l?
41 S5 : He . . . he p lay s basketba l l on . . .
af ter
. . . ?
42 Ss+T: S ch oo l.
Here we see tha t when the s tudents were asked to descr ibe Mickey
M ou se 's d iary , they provided the act iv i ty and the day of the wee k (see l ines
1 9 and
27) . However , what
the
t eacher wan ted
to
e l ic i t
from the
s t u d e n t s
was wh a t M ickey M ouse does
af ter
school (see the teacher 's correct ion of
the
s tudents ' answers
in
l ines
22 to 23, and
l ines
28 to
30).
I t wa s
on ly
af ter
the
teacher m ade
it
c lear
to the
s tudents tha t they sho uld
not say the day of
the week ( l ine 28), tha t the s tude nts produced w ha t the teac her con sidered to
be the correct answ er ( l ine 36) .
W h a t
w as
h a p p e n i n g
in
th i s p iece
o f
d i scou r se?
H o w
m u c h c o m m o n
gr ound
w as
shared be tween
th e
t eacher
and the
s t u d e n t s? W h e n
th e
s tu -
d en t s p r od uced
th e "correct"
r esponse ,
in
w h a t
w a y w a s t h e
c o m m o n
gr ound w id ened ? Was th i s common g r ound pe r t inen t t o t he ob j ec t o f
l ea r n ing of the l e s son?
To unders tand the m ism atch be tween the s tudents ' answe rs and w hat the
teacher wanted to sol ici t
from
them , we need to see the i tem s on the w hi te
board as an integral par t of the s i tuat ion in w hic h the phen om ena of hab i tua l
act ion and
f req uenc y
are
em bed d ed.
On the w
r
hite
board were
the
fo l lowing
i tem s : M ickey Mouse ' s p i c tu r e ,
th e
d ia ry s t a t i ng w ha t M icke y M ouse
did
each
day of the
w e e k ,
an d the
ques t ion "W hat does
he do
af ter
school?"
T o-
gether they con s t i tu te a p iece of tex t tha t says tha t M icke y M ouse does some
act iv i t ies
tha t vary accord ing to the day of the w eek . The q ue s t ion "W hat
does
he do af ter
school?" provides
the
con tex t
f or
in t e r p r e t ing
the
ac t iv i ti e s
as ou ts ide school hours . T he aspects o f M icke y ' s d iary tha t were d iscerned
by the
s tudents ,
a nd
were
focal in
the i r aw areness , were
the
asp ects th at var-
ied:
ac t iv it ies
and
d ays
of the
w e e k
(as can be
seen
from
S2 's
and
S3 's
re-
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174
T S U I
T A B L E 7 .2
Engl i sh Lesson/Weekly Plan/Primary G rade 4/Class B
Cind y T i m m y
Weekly
Days
of the
w e e k
S unda y
M o n d a y
Tuesday
Wednesday
T hur sda y
Friday
Satu rday
Plan
T h i n g s to do
Play t ab le t enn i s
Go to the l ibrary
Ha ve a
p i an o
lesson
Have
a d an c in g
lesson
Go to the library
Ha ve a
com pute r l e s son
Play
t ab le
t e nn i s
Have
a c ompu te r lesson
The i tem s on the w hi te board a l so co ns t i tu te a p iece of tex t . This tex t says
tha t
Cindy does some ac t iv i t ies each day of the week . The presence of
Tim m y m eans tha t there are two people involved in th i s p iece of tex t . The
variants
in
th i s p iece
o f
tex t
are the day o f the week and the activity-. T he
weekly p lan be longs to Cindy . T immy does no t have a weekly p lan . The
teacher had se t up a d ia logue be tween C ind y and T imm y wher eby T imm y
asks,
"What
do you do on (day of the week)'+ s'?" and C ind y answ er s , "I
(verb + ac t iv i ty ) on (day of the w e e k ) '+ s'." For e x a m p le :
T i m m y : W h a t do you do on Wednesdays?
C indy: I go to the l ibrary on W ednesdays.
B oth var ian ts, day of the w eek and ac t iv ity , w ere focu sed on s im ul ta-
neous ly by the s tudents and the teacher, and bo th w ere evalua ted by the
t eacher when she wen t t h r ough C ind y ' s week ly p l an w i th the s tud en t s .
W h a t
w as
invar iant
was the
quest ion
from
T im m y ,
and the
l in gu is t ic s truc-
ture of the
answers
from Cindy that provided the scaf fo ld ing for the stu-
dents . The teach er also drew the s tudents ' a t ten t ion to the plu ral form o f the
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7. T HE S H A R E D S P A C E O F L E A R N I N G 1 75
days
of the
week
to
signify recurrence, which
is an
im portant feature
of ha-
bitual act ion.
After the teacher had gone through all the days o f the week and the cor-
responding act ivi ties ,
th e
teache r asked
th e
s tudents
to
sum m arize C indy ' s
schedule fo r T imm y and sol ici ted from the s tudents descr ipt ions o f f r e -
quency,
such as "you go to the library tw ice a week," "you play table tennis
three tim es a
week,"
and so on. A s these s t ructures
were
solici ted, the fre -
quency o f occurrence cam e to the fore o f the s tude nts ' awareness , an d the
day o f the
week receded into
the
ground. What
the
s tude nts held
in
thei r
awareness s im ul taneo us ly were the ac t iv ity and the f requency . Th is is evi-
denced by the fact that when the s tuden ts w ere asked to come u p w i th thei r
ow n
weekly
plans
and to
conduct
a
dialogue
asking
each
other
about their
week ly p l ans
and how
of ten they conducted
th e
act ivit ies, they
did not
have
prob lems .
In
Class
B, the
c ondi t ions o btained
for
discerning
the
c ri t ical aspects
of
habi tual action, w hich were nam ely
the
activity itself
and the
f requency
o f
occu rrence or recurrence. T he w ay that the teacher set up the s i tuat ion in
w h i c h the
ha bi tual act ion
w as
embedded enabled
th e
students
to
experience
the object
in the w ay
that
th e
teacher in tended.
The
structure
of
aw areness
of
the teacher and of the students converged, unlike in Class A, where the
teacher ' s
and the
s tudents '
foci o f
awareness
differed. W e
could
s ay
tha t
in
Class
B
there
was a
w ider shared space
o f
learning tha n
in
Class
A, and
that
the learning outcome—as evidenced by the s tudents ' oral performance of
the
t ask—showed tha t
the
teacher
in
Class
B w a s
more effective than
the
teache r in
Class
A in
designing
the
learning experience,
as far as the
t each-
ing of habi tua l act ion w as concerned.
N E G O T I A T I O N O F
M E A N I N G
A N D T H E SH ARED SPACE O F L EARNI NG
In the 7.1
conversat ion exam ple given
at the
very beginning
of
this chapter,
we saw
that par t ic ipants
A and B
w ere involved
in a
process
of
neg ot iating
the
referent for " the m eet ing" and widening the com m on ground that w as
shared between them .
In the
classroom excerpts (7.2)
and
(7.3),
we saw
that
w hen cer ta in assum pt ions were
n o t
shared betwe en
the
teacher
and the
stu-
dents , valuable con tr ibut ions
from
students could
b e
dismissed
or not
val-
ued. Beca use of the un equ al power relationship between the s tudents and
the teacher, s tuden ts w ere often unable to engage in the k ind o f nego t iation
of
m ean ing tha t
is
prevalent wh en
the
power relat ionship
is
sym m et rica l,
such as
w h a t
we saw in the
conversat ion between col leagues (7.1) .
It is
therefore impo r tan t
for the
teacher
to be
vigi lant
of
assum ptions that
are not
shared
w ith learners,
as
wel l
as to be
sensitive
to
signals
of the
lack
of
com-
m on ground, and to be a ble to respond to such s ignals by en gaging in a ne-
gotia t ion of m ean ing wi th the learners.
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1 76 T S U I
Let us take, for exa m ple, an excerpt f rom the lesson o n the s loth , w hic h
was discusse d in chapter 6. In this lesson, the teacher was r ev is ing w hat the
class
had
covered
in the
prev ious lesson , tha t
is, the
descr ipt ion
o f a
p a n d a ,
and w hat de ta i l s need to be covered w hen the s tude nts w r i te a descr ip t ion of
an
a n i m a l .
7.5 [Chinese Lesson/P3/The Slo th]
1 T :
[Ho ld ing
up a
t ex tbook showing
the
chap te r
on the
2
panda] OK, today, we w i ll do some wr i t ing . Our
3
wr i t ing
w i l l
follow
th e
chap te r
on the
p a n d a . . ..
I
w a n t
4 you to
tell
m e , w h e n w e w r it e abou t an a n i m a l , w h a t
5 do we need to include in the co ntents? ... Put up y o u r
6 han d s . W ha t d o we need to w r it e abou t
first?
7 [A s tuden t r a i ses h i s han d . ]
8 SI:
Body.
9 T: "Body" is
w h a t?
1 0 S I : Hu h? [M ean ing he d oes no t und er s t and the q ue s t ion ]
11 T: Bo dy.
1 2
S s:
B ody [Students
say
th i s
in
E n g l is h , from their seats . ]
1 3
T : B ody. W hat e l se? [W r ites "body" on the boa rd .]
14
S2: The brain , [meaning
"head"]
15
T : Yes , the head . W hat e l se? [W r ites "head" on the
16 board]
17
S3:
Four l im bs.
1 8
T :
Yes ,
four
l im bs . . . .
any
m ore? Yes .
19
S4: The
sk in ,
th e
color
of the
fur .
20 T: Color.
Yes.
[Writes "color" on the board]
21
S 5: Appear ance .
22 T : A ppearance . In fact , the word "appearance." wher e
23 should we put it? [Referr ing to location on the board]*
24 Ss: In
front .
25 T: In front of four
l imbs?
26 S5: In front of
four l imbs.
27 T: In
front?
In
fact.
I th in k . .. [pauses]
28
Ss: The h e a d .
29 S6:
Af t e r
the
head.
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178
TSUI
dents apparently understood
"appearance"
as m eaning jus t the facial appear-
ance
of the
animal.
This is
evidenced
by the fact
that they suggested that
th e
description
of
appearance should come before
the
description
of the
four
l imbs
in the
text,
and
after
the
description
of the
head.
Finally,
the
teacher
m ade explicit
th e
relationship between
"appearance" and the
specific fea tures
(see lines 30 to 32, and lines 30 to 40).
The
fact
that there are certain groun ds that are com m on, but that there are
also others that
are not
shared betwe en
th e
teacher
and the
students
is not u n-
usual in classroom discourse. There could be a num ber of reasons w hy this
happens, but frequently such divergent perceptions are caused by linguistic
means,
for
example,
by the
questions
the
teache r asks,
by the
pragm at ic
and
semantic presuppositions carried
by the
w ords used,
by the way the
teacher
responds
to the students' questions or responses, and so on. In this particular
excerpt, there w ere several cause s
for the
unshared ground. Firstly,
the initial
questions asked
by the
teacher, "W hat
do you
need
to
include
in the
content?
.. ." "What do you need to w rite about first?" (line 5 and line 6) were open to a
number
of
interpretation s.
It
wou ld have been approp riate
for
students
to
pro-
vide either
a
list
of
specific features
or the
superordinate
first. It is
clear
from
the data that the relat ionship between appearance, or "outw ard appearance"
to be
precise,
and the
other
features w as
very much
in the
teacher 's
focal
awareness, whereas it w as the specific features that were very m uch in the stu-
dents '
focal
awareness. S econdly, the unsha red ground wa s also caused by the
semantic ambiguity
of the
word "appearance"
in
Ch inese (yeuhng
m a a uh in
Cantonese) [ 4 f < . f f e ] can mean facial appearance or the entire outw ard appear-
ance.
T he
teacher
w as
using
th e
word
in the
sense
of
"outwa rd appearance,"
whereas
the
students were using
it in the
sense
of "facial
appearance."
W e can see, however, that the teacher w as able to respond very quickly to
signals
of
assump t ions
no t
being shared
by the
s tudents
by
abandoning
the
initial line
of
quest ioning
and
al lowing
the
students
to
list
the
specif ic
fea-
tures . The teacher w as also able to negot iate the m ean ing of the w ord "ap-
pearance," with
the
students
by
ask ing them where
the
word should
be
placed
on the
board,
and
guiding them
to see the
word
"appearance" as a
superordinate ( l ines 30 to 32). In th is way, th e t eacher w idened th e c o mmo n
ground shared between him self and the s tudents , so that even tual ly they
were
able to agree on a descriptive structure that form ed the scaffolding for
the
rest
of the
lesson.
In the
subsequent d i scuss ion am ong
the
s tudents
in
sm all groups, i t w as clear that the students had a good u nde rstan ding of "ap-
pearance"
as a
superordinate that subsum es specific phy s ica l fea tures .
COLLABORATIVE CO N STRUCTION O F M E A N I N G
A N D T H E SHARED SPACE O F
L E A R N I N G
In e lucidating the notion of the shared space of learning, we proposed that
there is another sense in w hich the space of learnin g is a shared space; that
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7. TH E S H A R E D SPACE O F L E A R N I N G 1 79
is, w hen the space of learning is jo in t ly con st i tu ted by the teacher and the
learners throug h
the
co l laborat ive const ruct ion
o f
m ean ing .
The jo in t co ns t ruc t ion of m eaning be tween ch i ldren and adul t s i s w el l
documen ted . Ha l l iday ' s work on ch i ld l anguage deve lopmen t p rov ides
am ple exam ples o f how a ch i ld , th rough in terac t ion w i th an adu l t , is able
to
con s t rue exper ience in to m eaning . Typ ica lly , the ch i ld ' s response to the
envi ronmen t
is
interpreted
by the
adu l t
as
i nd i ca t i ng communica t ive
in -
tent ions ,
and
responded
to
according ly .
In the
course
o f
responding
to the
chi ld , the a dul t con t r ibu tes to the co-cons t ruc t ion of the m ean ing in the
discourse
(see, e .g . , H al l iday , 1973, 1975, 1 993). W el ls (1 986) provided
the
fo l lowing
exam ple o f co -cons truc t ion o f mean ing be tween a pa ren t
and a
2-year-old
child.
7.6 [Wells, 1986, p. 46]
M ark (2 ;3) is s tanding by a cen tral hea t ing radiator and can
feel
the
heat coming from it. He initiates the conversation by
sharing
this inter-
est ing
in form at ion wi th
h is
m other.
M a rk : 'O t , M u m m y ?
M other: Hot? [checking] Yes, that ' s the radiator .
M ark : Been- burn?
M other : B urn? [checking]
M a r k : Y eh
Mother: Yes, you know
it'll
burn don't you?
In this piece of data, as W ells (1 999) observed, the child respon ded to the
cen tral hea ting radiator
by
mak ing
a
comm en t.
H is
mother checked that
she
had
co rrectly interpreted the ch ild's u t terance , and told him that the radiator
w as
the
source
of the
heat .
The mother's
correct interpretat ion
o f the
chi ld ' s
ut terance enabled him to extend the exchange and bring in the word "burn,"
w hich was in turn extended by the m other as "Yes, you know i t w i l l bum ,
don ' t
you?"
S ubsequent ly
in the
discourse (not shown here),
the
child
w as
able
to
take over
the
m eanings that w ere ini tia l ly co-constructed
and
apply
them to a novel s i tuat ion where he saw a bonfire in the garden and w as able
to say tha t i t w as hot and that it w ould burn as w el l.
Let
us consider how this happens in classroom learning. In the history
lesson that w e discussed in chapter 6 , the concept o f
clan
w as taught in the
context of ear ly rural com m uni t ies in Ho ng K ong. In th is context , a c lan is a
c o m m u n i t y
o f
people w i th
the
same surnam e
w ho
live togethe r
in one
area,
and are also somew hat related by blood. The fol lowing is an excerpt from a
Chinese medium classroom (CMI), where Chinese was the students'
m other tongu e, in which the teacher explored w i th the s tudents why clans
were formed
and for
wh at purpose .
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180
T SUI
7.7 [History Lesson/S2/CMI]
1
T: ... So,
people with
the
same surname stay together....
Why do
they
2 stay
together? Why do
they stay together? Why?
3 S: Convenient.
4 T: It's convenient. Would it be better
for
them to go their separate ways?
5
Would it be better for you to go your own way? Who says it's
6
convenient?
...
What
are the
advantages
of
living together?
7 S:
They
can
help each other.
8 T: Help each other. Yes, that's right.
Very
good.... What kind of things
9 do
they
need
to
help each other with?
I
want
to ask all of
you.
10 S: Farming.
11
T: Yes, farming, they need help from each other. You work on this part
12 [of the land] and I work on another part [of the land]. We help each
13 other. What else, apart from
farming?
14
S: Hunting.
15
T: Hunting, OK. But we know that it was an agricultural society already,
16 so there was not much hunting.
17 S: Raising animals.
18 T: Raising animals, that is, raising cattle and
sheep.
Yes. What
else?
19
What else?
20 S: Not to be bullied by others.
21 T: Not to be
bullied. Actually
this is
very important
To
protect each
other,
22 mutual protection, apart from farming together, living together.
2 3 Some students said looking for
food
together. There is also the function
24 of protecting each other. Why did they have to protect each
2 5 other? So that they would not be bullied, because they came to Hong
26 Kong from a
faraway
place and they did not know the place, right?
27 They did not know whether they would be disliked by other clans.
28 What if they were attacked by them? That's why they needed
mutual
29 protection. They had to be armed. In addition, there were blood ties as
3 0 well. Just now I told you that they had the same surname ... Another
31 function was to preserve the traditional l i f e style.
In this excerpt, the teacher posed a number of open questions. Each time
a student responded, the teacher took on the response and opened it up for
inquiry. For example, in line 2, the teacher asked why people with the same
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THE SHARED SPACE OF LEARNING
1 8 1
surname stayed together and one student responded that i t was for conve-
nience ( l ine
3). The teacher
took
on the
response
a nd
asked
w hy i t was con-
venient . When no
response
w as for thcoming, the teacher rephrased the
word
"convenient"
as
"the
advantages
of
living
together"
(line
6 ), and
asked
the students
to
list
the
advantages .
As w e can see,
th is im m ediately elic i ted
th e
response "help
each
other"
(line 7) from an other s tudent. A t the end of a
sequence of in teract ion around the topic , a sem ant ic netwo rk relat ing to the
formation o f clans w as collaboratively constructed by the studen ts and the
teacher: that is, mu tua l help ( fa rming) ; mutual protection (so as not to be
bul l ied by others; line 20 and line 21); bloo d t ies (bec au se they a l l had the
same
surnam e and therefore had the sam e ancestor; l ine 29 and l ine
30);
and
preservation of the tradit ional
l ifestyle
(line
31).
The col laborative const ruction of the sem ant ic netw ork during the inter-
active process is i l lustrated in
Fig. 7.1.
Figure
7.1 show s the way in w hich the teacher and the s tudents co-con-
structed the space o f learning by engag ing in a nego t iat ion of me aning . For
exam ple , the word
"convenient"
suggested by the s tudent w as too vague ,
and so the teache r clarified and elaborated the m ean ing of "convenient" by
rephras ing it as "the advantages of staying together." The
teacher's
interpre-
ta t ion
o f the
s tudent ' s in tended m ean ing helped
to
move
the
discuss ion for-
FI G. 7.1. Co llaborative construction of a
semant ic
ne twork of formation of c lan.
Note: Words
underlined
are
contributions from
th e
teacher
and
other contributions
are
from
students.
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182 T S U I
w ard, as can be seen from the imm ediately for thcom ing response from an-
other student. Had the teacher misinterpreted the s tudent ' s meaning, the
subsequent contributions from the s tudents w ou ld probably not have been
for thcoming
or they w ould have been
different
(see W ells , 1999). B y ask ing
the s tudents what the advantages o f s taying together were, the teacher
opened up a dimension of variat ion for exploring the benefi ts that people
gained
by
staying together. When
the
students
proffered "help
each other"
as an
ins tance
in the
dimension
of
advantages ,
th e
teacher took
on the re-
sponse and opened up a fur ther dim ension of variat ion f or ex plor ing th e di f -
ferent ways in which members of a clan needed to help each other . The
students suggested "farming," "hunting," "raising animals," a nd "not to be
bull ied by
others,"
as ins tances along this dimension. The teacher high-
l ighted the im portance of not be ing bu l l ied and rephrased it at a h ighe r
level
of abst ract ion by u s ing the phrase "m utual protect ion." Final ly , the teach er
contr ibuted tw o m ore reasons for the form at ion of clans : b lood t ies and pre-
serving tradit ional life s tyle . The interact ion between the teacher and the
s tudents was a process in w hich que st ions posed by the teacher opened up
dimens ions of variat ion that afforded opportuni t ies for s tudents to explore
the reasons for people to s tay together . These opp ortuni t ies w ere taken up
by the stude nts, and their con tributions w ere in turn us ed by the teac her to
open up further dimens ions fo r explorat ion. T he space of l earn ing opened
up was therefore a co l laborat ive effort be tween the t eacher and the l earners .
In
this sense, the space of learning was a shared space.
Embodied in the notion o f the jo in t con st i tu t ion of the space o f l earn ing is
also
the
col laborat ive c onst ruct ion
of
m ean ing am ong l ea rne rs . Th i s
is
par-
t icu lar ly evident w hen learners
are
engaged
in
g roup w ork .
For
example ,
in
chapter 6 , we saw how learners b rou ght the ir own know ledge of the w or ld ,
and
thei r previous experience,
to
bear
on the
ob jec t
o f
learn ing
as
they co l -
laboratively
constructed texts on the story of the sloth.
LIN G UISTIC
RESO URCES
A N D T H E
SHARED SPACE
O F
LEARNING
A s w e
have already pointed out , at tem pts m ade
by the
teacher
to
widen
the
shared space of learning may not always be successfu l . The cause of th i s
mismatch could
be
l inguist ic,
o r it
could
be due to the
fact that
the
structure
of the
learning experience brought about
different foci
o f
awareness .
In
classrooms
where the medium of instruction is not the students ' mother
tongue (i .e. , a l anguage in w h i c h the s tudents a re l ess com peten t ) , th e fail-
ure to widen the
shared space
of learning m a y be caused b y a lack of l ing uis-
tic
resources (p ar t icular ly
on the
par t
o f the
s tudents , a l thou gh som et im es
it
can also
be on the
part
of the
teacher).
Let us look at the fol lowing excerpt f rom an Engl ish medium lesson
(EMI; English
was not the
students' mother tongue)
on the
same history
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7.
T H E S H A R E D S P A C E O F L E A R N I N G 1 83
topic
as the CM I
lesson just ci ted (and
in
chap.
6), on the
early rural com m u-
nity. In this lesson, the teache r asked the students to compare the diaries that
they had writ ten befo re the lesson, w ith those w ritten by a father, Tang Tai
M a n ,
and his
son, Tang
S iu
M a n,
in the
days
o f the
rural com m uni t ies ( these
w ere g iven as han douts). T he teach er 's intention w as to bring out the
differ-
ent
l ifestyles
of people today and
people
in the past .
7.8 [History Lesson/S2/EMI]
The
teacher asked
the
students
to
w rite
a
diary prior
to
this lesson
and
then asked them to compare their diaries with the two diaries on the
hando ut by Tang Tai M an and his son, Tang Siu Ma n.
1
T: . .. OK ,
look
at the on e of
Tang
Siu
Man , Tang
S iu
M a n .
Is it
2 different from yours?
3 Ss: Yes.
4 T: How different? Can you tell me how different? Stephanie ,
5 give
me one
difference.
6 S: [speaking very softly] I have not the chicken .
7
8
T: Yes , then w hat else? W hy [does] the boy have chickens ,
9 duck s , and pigs? W hat did he do?
10
S: [silent]
11
T :
Wh a t
did he do? How
come
he has the
chickens ,
ducks , and
12 p ig s? W ha t did he do in his dai ly life?
13 S: [silent]
14
T:
Unders tand
m y
quest ion?
15
S : [speak ing very softly, inaudible]
16
T :
W h a t
is his
work, Stephanie? Angela,
can you
help?
...
In line 4, the teacher took on Stephan ie's response that her diary w as differ-
ent from Tan g's, an d tried to open it up for inquiry by
asking
her how they
were different. Stephanie tried
to
explain that
she did not
rear chickens.
T he
teacher took on S tephanie's response and ag ain tried to open it up for further
inquiry
b y
asking
her why
Tang
S iu M an had
chickens, ducks,
and
pigs .
The
teacher was
ho ping that Stephanie would point
out the
differences between
life
in
ear ly rural comm uni t ies
a nd
life
in
mo dern u rban societies. How ever,
Stephanie w as tong ue-tied, even after prom pting f rom the teach er tw ice ( l ine
10
and
l ine 11 ). Finally,
the
teacher
had to ask
another student
to
help out .
Throu ghou t the w hole lesson, there w ere a num ber of ins tances in w hich
no response w as for thcoming, even af ter the t eacher had repeated or re-
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184 T S U I
phrased the question. In other w ords, the teacher had considerable
difficul-
t ies trying to co-construct the space o f learn ing w ith the stu den ts due to the
students' lack
of
l ing uist ic resources.
A quant i ta t ive analysis was conducted on the two his tory lessons (one
EM I and one
C M I) that were discussed
in
this chapter
and in
chapte r
6 and
two other h i s tory lessons (aga in , one E M I and one C M I) teach ing the same
topic to see how
often
the teachers w ere able to m ake use of the s tu den ts ' an-
swers to open up the space for further inquiry, and facili tate the col labora -
tive
construct ion of m eanin g betw een teacher and s tudents . The f indings are
presented in Table 7.4.
W e can see from Table 7.1 tha t in the two EM I lessons, over half of the
students ' responses w ere s imp ly accepted or repeated by the teach ers w ith-
out
further
elaboration or c o m m e n t. T he s i tuat ion is a lmos t the m i rro r im -
age of the two CM I ( i .e . , m other ton gu e) lessons. It is not
difficult
to see tha t
in C M I c lassrooms, the teachers and the s tudents w ere engaged in
m a k i ng
sense of the object of learning col laborat ively. By contrast , in EMI
(nonm other tong ue) c lass room s, the interact ion w as ve ry much un id i rec-
tional an d the learners played a much more passive role.
C O N C L U S I O N
In
chapter 1 , we
proposed
the
notion
of the
space
o f
learning b eing charac-
terized by c lassroom interact ion in the
l ight
o f a
specif ic
ob jec t o f
lea rn ing .
A n d w e
pointed
out
that
th e
space
of
learning
is
cons ti tuted
by the
po ssibil i-
ties for lea rn ing brough t about b y w h a t i s takin g p lace in the c lassroom in
relation
to the
object
of
learning.
T he
po ssibilities
for
learning ( i .e . , w hat
w e have re fe r red to as the enac ted o bjec t of lea rn ing ) cannot be brou ght
about
by the
teacher alone,
or by the
learners themselves; they must
be
T A B L E 7 .4
Teachers
Responses
to Students Answers in E M I an d C M I Classrooms
Teachers 'Responses
to
Students '
Answers to Al l Teacher Quest ions
EMU EM
1 2
CMI 1 CM I 2
Rejection
Accept ing / repea t ing
s tudent ' s
answer
E xte nd ing s tudent ' s answer
No com ment /new q ues t ion
Tota l num ber
of
responses
0 1 ( 1 % ) 1 ( 1 % ) 1 (3%)
5 0( 6 9 .5 % ) 4 2 ( 5 9% ) 1 6 ( 1 7 % ) 1 2 ( 3 4 % )
1 6 ( 2 2 . 5% ) 1 4 ( 2 0 % ) 6 9 ( 7 3 % ) 2 2 ( 6 3 % )
6 ( 8 % ) 1 4 ( 2 0 % ) 9 ( 9 % ) 0
72 (10 0%) 71 (1 0 0 % )
95
( 1 0 0% ) 3 5 ( 1 0 0 % )
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7.
T H E
S H A R E D S P A C E
O F L E A R N I N G 1 85
joint ly consti tuted by both the teacher and the learners. In light of this, we
proposed, in this chapter, that the space of learning is a shared space.
The joint consti tut ion of the shared space of learning has very mu ch to do
with
the s t ructure of aw areness o f the par t ic ipants in a discou rse. If w hat co-
m es to the fore o f their awareness is
different,
participants talk a t cross pu r-
poses .
In a
classroom si tuat ion,
the
learners ' s tructure
of
aw areness
is
often
shaped
by the way in
wh ich
the
teacher organizes
the
learning experience,
and
the way in
w h ic h
he
presents
the
mater ials . Using data
f rom two
pri-
m ary Grade 4 lessons on "the w eekly
plan,"
we i l lustrated the way in w h i c h
the learners ' s t ructure of awareness was shaped by the mater ials that the
teache r put on the board, and the way in wh ich m ore
effective
learning w as
b rough t
abo ut w hen the teach er ' s s t ructure of aw areness accorded w i th that
of the s tudents .
T he
space
of
learning
is a
shared space
in the sense
that
the
interaction
between the teacher and the learners i s fel ici tous only when both part ies
share some common ground on which further interaction can be based. W e
have looked a t examples of c asua l conversat ion and classroom data to see
w h a t
happens w hen there is little or no com m on ground shared between par-
t ic ipants .
In the case of the con versation betw een tw o co l leagues (7 .1 ) , th e
interlocutors
had to
work very hard
to
w iden
the
comm on ground
in
order
to
advance the co nversat ion. In the ca se of the En gl ish lesson on the w ee kly
plan in prim ary G rade 4A, an appropriate con tribution by a student w as dis-
m issed by the t eacher because the lat ter failed to see the ra t ionale beh ind th e
s tudent ' s
answer , and hence an ex cel lent oppo rtuni ty fo r learning w as lost.
B y co nt ras t, th e c lass room data from the reed relay experim ent (7.3) and the
lesson
on the s loth (7.5) showed h ow po ss ib i l it ies fo r l earn ing were opened
up wh en the teacher was aware of the comm on ground shared be tween h im -
self o r herse l f and the learners . In these tw o exam ples, w e also saw how the
shared space
of
learning
w as
widened
by the
n egotiation
of
m eaning
be-
tween the t eacher and the learners in the lesson on the s lo th , and by the
teacher helping
the
learner
to
clarify
h is or her
thinking
and
lingu istic repre-
sentat ion
in the
lesson
on the
reed relay.
T he space o f learning is a shared space also in the sense tha t th e po ssibili-
t ies for l ea rn ing are jo in t ly const i tu ted by the t eacher and the learner. In the
Ch inese m edium h is to ry l esson ,
w e saw how the
teacher opened
up
possi-
bi l i t ies fo r learning by ask ing ques t ions on the basis of the s tudents ' re-
sponses (7.6) , and how, as a consequence of the teacher ' s quest ioning, a
semant ic ne twork
o f
"clan"
w as
co l laborat ively con st ructed
by the
t eache r
and the s tudents .
T he proposal that the space o f learning is a shared space join tly c ons ti tuted
by the teacher and the learners is an impo rtant on e from the perspec tive o f the
w ay
we describe teac hing and learning in relat ion to one another. Investiga-
t ions of teaching an d learning m ust take into considerat ion not only the possi-
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186 T S U I
bilities for learning being opened up by the teacher, but also which
possibilities are actually made use of by the learners.
E N D N O T E
'The s imple c i rcui t wi thout the reed re lay carries a very smal l current and is
therefore able to l ight up the LE D, w hich on ly requ i res a very sm al l current to l ight
up. The
complicated c i rcui t w i th
the
reed relay
can
carry
a
very large current once
the reed switch is c losed and can therefore cause the m o to r to rota te .
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I V
O n Improving Learning
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190 LO ET AL.
O ur
point
o f
departure
is
that teaching
i s— or
sho uld be—a ra t ional ac t iv -
ity. In planning a lesson or a un i t , the teacher must take into account the
characterist ics of the students (e.g. , age, general a bil i ty ) as w e l l as the phys -
ical conditions
of the
classroom (e.g . , c lass s ize, equip m ent ava i lable ) .
However, a ll these
concerns mus t
be
translated into actions that
can
help
achieve specific goals, that
is, the
exp l ic i t capab i l it i es tha t s tuden ts
are ex-
pected
to
develop.
W e
call these cap abi l i t ies
th e
ob jects of l e ar n i ng . Even
in
the
m ost open classroom , students ' learnin g should
not be
acc id en ta l
bu t
should
b e the
resul t
o f
conscious at tempts
on the
part
of the
teacher
to
br ing
about the intended learning ou tcomes. In other words, at tent ion must be
paid
to the
w a y s
in
w h i c h
the
objects
o f
learn ing
are
deal t w i th
a nd
enacted
in
the
classroom.
Seen in this l ight, curre nt debates (e.g. , concerns abo ut the relat ive m er i ts
of
teacher-centered
and
s tudent-centered instruct ion ) that focus
o n
genera l
aspects, and not on
ways
of
dealing w ith
the
specific c ontent
of
learning,
are
of l im ited value both in term s o f providing learning op por tun i t ies for teach-
ers and in imp roving s tudent learning. T he t each ing a r rangem en t s ( such as
whole-class teaching
vs.
g roup teach ing ,
and the use of IT in the
c l a s s room )
should be of concern only i f d iscusse d in rela t ion to the sp ecif ic s of wh at is
taught
and
learned.
This
l ine o f a rgum ent para l le l s what K i lpa t rick , S w afford . and Findel l
(2001) referred to in the con tex t of ma them at i c s ed uca t ion :
M u c h deba te cen te r s
on
fo r ms
and
a pp r oa c he s
to
t e a c h in g : "d i re c t
ins t ruc t ion"
v e r s u s
" inqui ry ," " teache r -cen te red" ve r sus " s tudent-cen te red ," " t r ad i t iona l" ve r sus " re -
form." These labe ls m ake
rhe to r i ca l d i s t i nc t i ons
t ha t
of ten
m i s s
th e
po in t r e ga r d ing
th e qua l i t y o f i n s t ruc t i on . Ou r review of the
r e se a r c h m a ke s
p l a i n t ha t t he e f f ec t iveness
of
ma themat ic s teach ing
a nd
lea rn ing
does no t
rest
on
s im ple labe ls . Ra the r ,
the
q u a l -
it y
o f ins t ruc t ion is a
func t ion
o f
t e a c he r s ' know le dge
and use of m a t he m a t i c a l
c on -
t en t , teache rs ' a t ten t io n
to an d h an d l i n g o f s tudent s , and
s t u d e n t s ' e n g a g e m e n t
in and
use of
m a them at ica l ta sks,
(p .
318)
Several recent theories regarding the profess ional developm ent o f t each-
ers also appear to have focused on the different w a y s o f deal ing wi th the ob-
j ec t
o f
learning
in the
c lass room. Bas ing the i r a rgument
on a
s tudy
o f
California elementary school
teachers o f
m athema tics , Cohen
and
Hil l
(2000) pointed out that teachers ' opportunities to learn are a key factor af-
fect ing
classroom practice,
and
that such oppor tuni t ies exis t only when
teachers
are
asked
to
respond deeply
to
what they
are
supposed
to
teach .
They fou nd that profess ional developme nt act iv i t ies tha t al low ed teachers
to
leam about
the
cu rr iculum
had a
much
greater
effect
on
altering teaching
practices than those that appeared to be either gene ric o r per ipheral to sub-
jec t m at ter (Cohen
&
H ill , 2000). They even sug gested that classroom prac -
tice w as m os t e f fec t ive ly enhanced by those t raining a ct iv i t ie s that gave
teachers c oncrete , top ic-spe cif ic learning op po r tuni t ies . Their data also
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8. T O W A R D
A
P E D A G O G Y
O F
L E A R N I N G
1 91
showed that
the
mathemat ics ach ievement
of
s tudents
in
schools where
teachers w ere provided with these learning o ppo rtunities
w as
considerably
high er than in those w ithou t such opportunit ies. They con cluded that inter-
vent ion s tudies must change what teachers do wi th the curr iculum in the
classroom
in
order
to
affect student learning. W hat matters, therefo re,
is the
enac ted objec t of learning, that is , how the obje ct of learning is ac tua lly
dealt
w i th
in the
classroom.
It is in this context that we introduce the idea of the "learning study." T he
learning study is based on the Japan ese style "lesson study," w hich w e feel
takes
the
object
o f
learning
as its
point
of
departure,
bu t
wh ich also incorpo-
rates
the
m ethodologica l concept
of the
des ign experiment
pu t
forward
by
A. L .
Brown (1992)
an d
Coll ins (1992).
W e
explain these ideas
in
turn
in the
fo l lowing sections.
LESSON
STUDY
Stigler and Hiebert (1999) introduced the idea of the lesson study (jugyou
kenkyuu) in
Japan
in
their book,
The Teaching Gap. T he
lesson study, they
argued ,
gives Japanese teachers a m odel of con t inuou s school-based pro-
fess ional developm ent , w hich the two researchers see as one of the main
reasons
fo r the
success
o f the
c lass room prac t ice re form s
in
post-w ar Japan
( and
the relat ively high achievem ent rates of Japanese s tudents in in terna-
t ional com parison studies). St igler and Hiebert (1999) explained the rat io-
nale of the
lesson study
as
fol low s:
T h e p r e m i s e
b e h i nd
l e s son
s t udy
i s s imple : I f you w a n t to improve teach ing , the
m o s t
e f fec t ive
p l a c e to do so is in the co ntex t of a c l a s s ro o m l e s s o n . If you s ta r t
w i t h
l e ssons ,
t h e p r o b l e m o f how to a pp ly r e sea r ch
f i nd ings
in the c l a s s ro o m d is a p p e a r s .
Th e im p ro v em e n t s a r e d ev i sed
w i t h i n
t h e c l a s s room in the f irst p l a c e . Th e ch a l l en g e
n o w
b e c o m e s
tha t o f
i de n t i f y i ng
the k inds o f
c h a n g e s
tha t
w i l l
i m p r o v e
s tuden t
l e a r n i n g
in the c l a s s r o o m a n d , o n c e th e c h a n g e s a re i de n t i f i e d , o f shar ing
t h i s k n o w l -
ed ge w i t h
o th e r t e ach e r s
w h o face s i m i l a r
p r o b l e m s ,
or
s h a r e
s i m i l a r
g o a l s ,
in the
c l a s s r o o m , ( p .
I l l )
In
a typ ical lesson study, a group o f teachers com e together and select a
topic to be dealt with during one or several "research
lessons"
(kenkyuu
jugyou}.
Members
of the
group draw
on
each other 's experiences,
and to-
ge ther
they d ecide on the intended objec ts of learning and work out a lesson
plan designed to achieve these goals . On e teacher w i l l then teach the lesson,
whi le everyone in the group o bserves. Th e lesson is then e valuated and the
plan
revised. Ano ther teache r w il l then teach the revised lesson w ith the oth-
ers observing, and a second round of evaluation and reflect ion wil l take
place. The research lesson is then docum ented so that the outcome can be
shared with other teachers. According
to
S t igler
a nd
Hiebert (1 999),
a
les-
son study
is
com posed
of
eight steps:
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192 LO ET AL.
•
Def in ing
the
problem
• Planning the lesson
• Teaching the lesson
• Evaluating the lesson and reflec t ing on i ts
effect
• Revis ing the lesson
•
Teaching
the revised lesson
•
Evalua t ing
and
re f lec t ing again
•
Sharing
the
results
D E S I G N
EXPERIMENTS
A s such,
the
goal
of the
research lesson
is not
jus t
to
produce
an
effective
lesson, but , through careful p l ann ing and eva lua t i on , to ensure tha t the
teachers involved come to real ize why and how the lesson w orks . A lesson
s tudy is of
course
not a
control led experim ent
i n
w h i c h
one
factor
is
a l low ed
to
vary whi le others
a re
kept constant .
O n e
w ou ld ac tua l l y ques t ion
th e
value and the p ossibil i ty of a co nt ro ll ed exper im ent in such com plex a nd
con found ing
envi ronments
as
those
o f
educat ional set t ings . However ,
as
A .L. Brown (1992)
and
Coll ins (1992) suggested,
it is
s t il l w or th con duct -
ing
design expe rimen ts
in
edu cat ion , espe c ia l ly
in
c lass room resea rch .
A l-
though w e cannot control a ll aspects of the environment , argue Brow n and
Coll ins , we can
still
g ain considerable ins igh ts in to the operat ion of the m a-
jo r
variables through systematic intervention
and
unbiased observations.
Conclus ions
c an still be
drawn,
b y
com par ing
the
resu l t s ob ta ined
from
d i f -
ferent conditions, although w e have to interpret those re sults and guard our-
selves against making general c laims based
on
l im i ted observations .
T he
benef i ts
o f design experiments are that w e w i ll be able to contribute to the-
ory
development ,
and
improve pract ice
at the
s ame t im e .
T H E L E A R N I N G STUDY
It
w as in the spirit of
Brown's
and C oll ins ' design ex perim ents tha t w e tried
to r e fo rm ula te th e Japane se lesson s tudy in the research tha t w e report in the
latter part
o f
this chapter. Marton (2001) defined
the
learning study
in the
fo l lowing w a y :
A l e a rn ing s tud y is a s y s t e m a t i c a t t e m p t to a c h i e v e an
educa t iona l ob jec t ive
and learn
from
tha t a t t empt .
It is a
d e s ign
e x p e r i m e n t
t ha t
may or may not be a
lesson
s tudy.
Such a s tudy is a l e a rn ing s tudy in two senses . F i r s t , it a i m s a t
b r ing ing l ea rn ing
a b o u t ,
o r more cor rec t ly , a t
m a k i n g
l earn ing p o s s i b le . T he
s tudent s
w i l l
t h u s
learn , hopefu l ly .
Second , those teachers involved try to learn
f rom
the
l i terature, from
each o the r , from
th e s tudents , and n ot leas t , f rom the s tudy i tself , (p . 1 )
Specifically, in our own research fo r this book, w e w an ted to learn the po-
tent ia l
va lue
of the
theory
o f
variat ion from these s tudies .
T he
lesson study
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8.
T O W A R D A P E D A G O G Y O F
L E A R N I N G
1 93
is an appropriate m odel as i t a l low s researchers and teachers to see how the
objects o f learning are de al t w i th in the classroom . T he learning s tudy dif-
fers
from
the Japanese lesson study model in that our research lessons are
based
on a
theoretical frame w ork
of
learning— nam ely,
phenomenography
( c f . Marton & B ooth, 1997), and variat ion theory— and w e w i sh to find ou t
how
w el l the theory has w orked. In th is w ay the learning s tudy is a learning
study not in tw o, but in three senses, as the researchers are supp osed to learn
from it as w e l l.
T he
cycle
of a
learning study comprises
the
fol lowing
steps:
1. Choos ing
and def in ing a specific se t of educat iona l
object ives . These
are the ca pab i l it ies or values to be developed during one or several
lessons .
2.
Finding
out the
extent
to
w hich
the
students have developed
the
capa-
bili t ies
o r
va lues targeted before
the
t each ing beg ins .
3.
De signing a lesson (or series of lessons) aim ed at develop ing these
capabi l i t ies
or
values .
The
p lanning work m us t t ake in to accou nt
the
exist ing
know ledge of the s tudents , the teache rs ' pr ior expe riences in
dealing with the objects of learning, and the research literature.
4.
Tea ching the lesson (or lessons) according to the plan .
5. Eva lua t i ng the lesson (or lessons) to see the extent to w h i c h the s tu-
dents have developed the targeted ca pa bi l i ties or va lues .
6 . D o c u me n t i n g
an d
d i s semina t i ng
th e
a im, p rocedures ,
an d
r e su l t s
obtained.
In
the nex t three sect ions , we desc r ibe three c yc les of a learning s tudy in
two separa te p ro jec t s . The f ir s t two cy cles w ere co ndu cted w i th in an ongo -
ing rese arch pro ject ent i t led "Cater ing fo r Ind iv idua l Di f f e rence s (B u i ld-
in g
on V ariation)," commissioned by the Educat ion Department of Hong
Kong S pecia l A dm inis tra t ive Region of the Peop le 's R epu bl ic o f C hina ,
w h i l e
the
thi rd cycle consis ted
of an
independent p ro jec t tha t employed
the
theory of var ia t ion in des ign ing c lass room lessons to he lp s tuden ts to
learn
e c o n o m i cs .
CATERING FO R I N D I V I D U A L D I F F E R E N C E S
B U I L D I N G O N
V A R IA TIO N )
The "Catering for Individual Differences (B ui lding on V ariation)" project
is a 3-year, ongoing research project undertaken by a team of researchers
from
the
F acul ty
of
Educat ion
at The
Universi ty
of
Hong Kong ,
and the
Hon g Kong Ins t i tu te
of
E ducat ion , w i th Pong
and Lo as
principa l investiga-
tors and M arton as consu l tant . As there are different w ays in w hich the t erm
ca ter ing for ind iv idua l
differences
can be interpreted, i t is there fore im por-
tant that
w e
explain
our
understanding
of the
term
and its
bearing
on the
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1 94 L O E T A L .
aims of the project . T he project members bel ieve that because different
people
are bom
w i th different abil i t ies, charac teristics,
and
orientations ,
in -
dividual differences are a natura l phenomenon and are not a problem in
themselves. Individual
d ifferences
only become a problem in the classroom
sett ing, when
a
teacher
ha s to
teach
a
large group
of
s tudents
th e
same con-
tent. Th us, the project aim s at helpin g teach ers to find wa ys to enab le all stu-
dents—in a typical mixed-abi l i ty c lassroom set t ing—to leam what is
intended by tak ing into accoun t the s tuden ts ' diverse exis t ing know ledge
and unders tandings .
T o achieve this, the p roject team bel ieves that it is necessary to start wi th a
carefully defined object o f lea rn ing—tha t is, the cap abi l i t ies that s tude nts
are expected to acq uire . For exam ple , i f w e w ish the s tudents to u nderstan d a
certa in phenom enon, it fol lows that in order to accomm oda te individual d i f -
ferences, the teacher m ust f irs t have a deep and thoro ugh un dersta ndin g of
the different po ssible ways in wh i c h th e s tudents m ight unde rstand this phe-
nomenon. Research findings in phenomenography have shown
that
al-
though s tudents
are
un ique individuals , there
are
a lways
a
l im i ted num ber
of qual i ta t ively different wa y s in w hich they unders tand a par t icula r phe-
nomenon (Marton & Booth, 1997). These different w ays of unders tanding
arise m ainly because
a
different
set of
cri t ical aspects
of the
p h e n o m e n o n
are
discerned.
How do teachers gain access to such kno w ledge of s tudents '
exis t ing
u n-
derstandings? The team believes that teachers can first listen to, and leam
f rom, their studen ts. They can also share their findings wi th o ther teachers
in the
same school. Within
the
project , experience sharing w ith other teach-
ers takes place in col laborat ive groups co m pris ing teachers who teach the
same
subject a t the
same
level in one school. In this way, ind ividual differ-
ences becom e
a
resource
for the
teacher ra ther than
a
co ns t ra in t .
Bearing
in
mind
the
various
understandings students
m ay
bring
to the
classroom, and having identified the c ri t ical aspects of the objects o f learn-
ing,
the
group
o f teachers
move
on to
develop
a
research lesson that meets
those ends.
In
developing a research
lesson,
three aspects of variation are made use of
w ithin the project :
V a ri a t i o n
in
Terms
of Students
U n d e r s t a n d i n g
of
W h a t
I s
T a ug ht
Students understand that w hich they are supposed to leam in a l imite d num -
ber of
different ways .
O ur
research shows that teachers
w ho pay
close atten-
t ion to such differen ces (or varia t ions) , and w ho can bui ld on s tuden ts ' prior
understanding
and
experiences,
are
better able
to
bring abo ut
mean ing fu l
learning for their students. Students also learn more
effectively
w hen they
are made aw are of the different w ays in w hich their c lassmates deal w ith or
understand
the
same object
of
lea rn ing.
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8.
T O W A R D
A P E D A G O G Y O F L E A R N I N G 1 95
Variation in
Teachers'
Ways of Dealing With Particular
Topics
As a
teac her gains expe r ience
over the
years ,
he or she
w i l l bu i ld
up a
good
work ing knowledge about the
dif ferent
ways in which s tudents dea l wi th
par t icu lar concepts
or
p h e n o m e n a ,
and
w i ll a lso develop wa ys
of
hand l ing
these
dif ferences .
Such knowledge i s ex t remely valuab le and should be
ident i f ied, sh arpened, sy stem atical ly ref lected upo n, and above al l , shared
wi th
o ther teachers .
Variation
as a
Teaching Method
In
previous chapters, we have shown that in any particular lesson there are al-
way s things that teachers vary w hile other things are kept unch ange d, and that
this
pattern of variation— w hat is varied and w hat rem ains un chang ed— is of
decisive
importance in determining how effective th e lesson will be. In the
"Catering for Individual Differences" project , teachers are encouraged and
provided w ith opportunities to
observe,
reflect, and
share ideas
about their own
lessons as w ell as the lessons of other teachers. T he aim of this is for the teach-
ers to find
optim al patterns
of
variation
for
dealing with
the
intended obje cts
of
learning in a
lesson,
a nd
thus develop m ore pow erful w ays
of
helping their stu-
dents to learn.
In the first yea r of the p ro jec t , tw o pr im ary schools and a team o f abou t 1 0
researchers were involved.
In
each school,
two
learning s tudy groups w ere
fo rmed, each com pr is ing
five
teachers .
T he
fo l lowing tab le sum m ar izes
the
backgr ound in fo r m at ion
of the
groups (see Table 8.1) .
W orkshops on the theore tica l f r am ew ork of the pro jec t were conduc ted
wi t h the teachers of each school before the learning s tudy. Fu ndin g was ob-
tained to allow an
extra teacher
to be
employed
in each school, so that each
of the 1 0
teac he rs involved
in the
s tudy gained
a
n u m b e r
o f
extra
free
pe r i-
ods , thu s enab l ing them to take part. The m ee t ings w ere
off icial ly
scheduled
at
suc h t im es that al l the teachers involved w ere free, and able to a t tend the
m e e t i n g .
T A B L E
8.1
Ba c k gro u n d In f o rma t io n o f t he Le a rn i n g S t u d y G ro u p s
D u r i n g t he F i rst Year of the Project
L e a r n i n g N u m b e r
o f
Teachers
School Study Gro up Leve l o f Study Subject Part icipat ing
A
A
B
B
1
2
3
4
Pr imary Grade 4
Pr imary
G r a d e 4
Pr ima r y
G r a d e 1
Pr imary Grade 4
Chinese L a n g u a g e
Mathema t i c s
Ma the ma t i c s
Mathema t i c s
5
5
5
5
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1 96 L O E T A L .
Ea ch o f the learning study group s consisted of at least one researcher, a se-
nior research assistant,
and all
teachers teach ing
the
same subject
at the
same
level in that school. They m et once every we ek for 1 hour to plan the research
lessons. The group m eetings w ere audiorecorded, and summ ary notes were
kept
of
each m eet ing. Each cycle
of the
learning study consisted
o f
about
10
meetings,
and the
whole process
w as
structured according
to the six
stages
described previously. Each research lesson w as taught , in r u m , by all of the
teachers
in the
group.
A t
least
tw o
lessons were videotaped,
and
then ana-
lyzed
and
discussed
in the
group.
A n
im proved version
of the
lesson
was
then
developed and w ritten up. The s tudents ' perform ance w as a l so m easured be-
fore
and after th e lesson. O n average, each group com pleted tw o research les-
sons
in the first
year. School-based
and
joint school seminars were a lso
scheduled during the year to facilitate th e sharing of experiences am ong the
four
groups
of
teachers.
Tw o of the
learning studies
are
described here.
W e
believe that these studies no t on ly illustrate th e concept of the learning s tudy
and the use o f variation theo ry, bu t also th e l inguis t ic con st i tu t ion of
the
space
of
l earn ing
(wh ich
is
dealt with
in
chap.
3 of
th is volum e) .
A PRIMARY GRAD E 4 MATHEMATICS LESSON
O N UNITS AN D U N I T I Z I N G
T he
fol lowing
is a
learning study that
w as
carried
out by a
team
o f five
teachers
w ho
taught m athemat ics
at the
primary Grade
4
level.
T he
entire
cycle (from the incuba tion of ideas, to reflection and eva luatio n) took a total
of
nine meetings, which were distributed over
a
period
of 3
m o n t h s.
The Learning Study Cycle
Choosing th e Object
of
Learning . The first step was to choose a topic .
T he teachers chose fractions, as they felt tha t fractions presented some o f
the
m o s t diff icul t concepts
for
school ch i ldren
at
this level.
T he
seco nd step
was to f ind out why the s tudents had diff icul ty lea rn ing fractions; in other
words ,
w h a t
i t was
a b o u t
fractions
tha t m igh t
be di ff icul t fo r
s tudents .
Understanding
W h a t
Is
i f f i c u l t
and Critical.
The
teachers reflected
on
their ow n experiences of teaching fractions in the past, and shared these experi-
ences
in the
team m eetings.
The
follow ing questions w ere co ntinually raised:
• W h a t is actually learned, when learning about fractions?
• W hy i s
learning fractions
difficult?
•
W h a t
is it
that
makes
learning
fractions
difficult?
• How can we conceptualize these difficulties?
The un iversity consultant also introduced the
teachers
to the relevant re-
search literature, in
particular
Lamon's
(1999)
book
about teaching
and
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8. T O W A R D A P E D A G O G Y O F
L E A R N I N G
197
learning fract ions . Lam on argued that learning fract ion s con st i tu tes
the ba-
sis for proportional reaso ning , and that the teaching of fract ions should have
a
pr imary
focus o n concep tual unders tanding
ra ther
than procedura l know l-
edge.
S he
also pointed
out
that
a
cr i tical aspect
of
fractions that s tudents f re-
quen t ly fail
to grasp w as units
an d uni t iz ing.
T he
team then reviewed
th e
students ' textbook
fo r
pedagogica l adv ic e .
To
their surprise, they fo un d that
the
textbook
not
only lacked
a
form al treat-
m e n t o f uni ts and uni t iz ing, bu t that its presentat ion o f f r ac t ions ac tua l ly
cou ld
have contr ibuted
to the
s tudents ' misunders tand ing .
T he
chap te r
o n
addit ion o f f ract ions , fo r
example , began w i th
the
fo l low ing d iag ram ( F ig .
8.1) ,
accom pan ied
by a
question that asked
for a
fract io nal notat ion
of the
shaded area:
F I G . 8 . 1 .
T he
d i a g r a m u se d
in the
c h a p t e r
on add i t i on o f
f rac t ions , from Mathemat-
ics (Primary 4 , Firs t Term)
(
1997),
p. 49.
C o p y r i g h t
©
1997
by
C a m b r id g e P u b l i s h e r s
Ltd. Re p r in t e d w i th pe r mis s ion .
Having iden t i f ied un i t s
and
un i t iz ing
a s a
problem area,
t he
teache rs then
not iced that s tudents could have made
tw o
per fec t ly leg i t im ate guesses
in
respon se to this que stion in the textb ook (i .e. , 14/8 or 1 4/16), dep en ding on
w hat they unders tood
as one
u nit . However,
the
textbook exp ected only
o ne
answer (i .e. , 14/8);
the
tac i t assump t ion
in the
textbook bein g that each ci r -
cle cons t i tu ted one un i t .
A t
this stage, the teachers
we re
convinced that they should
focus
on
t each ing
un i t s
and
uni t iz ing
and
make this
the
object
o f
learn ing
of the re-
search lesson. They were also eager to f ind out w hat p rio r know ledge the i r
s tudents would br ing
to
their study
o f
f r ac t ions .
Despite
the fact
that several aspects
o f
f r ac t ions
had
a l ready been taug ht
in
p r imary Grade 3, not all teachers were sure that the s tudents in t h e i r
c lasses unders tood
the
concepts wel l .
In
par t icular , they
fel t
tha t
the
s tu -
dents
needed to
understand
the
idea
o f equal
shares
in
fract ions ,
as
w e l l
as
being ab le to con duct a s imple compar ison of f r ac t ions , befo re they could
unders tand
the
idea
o f uni t .
Developing a Test. The
teachers then designed
a
test
for the
s tudents .
T he purpose was to co l lec t in format ion about th e s tude nts ' way s o f th ink ing
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198 LO ET AL.
about f ract ions , especially w i th regard to those aspects that w ere expected
to be
difficult. Furtherm ore,
the
test
w as to be
used
a s a
pretest
to
provide
th e
team w ith a basel ine against wh ich the learning outcom es of the research
lesson
(as
measured
by the
same tes t ) could
be
com pared.
T he
test consisted
of three main themes (exemplar questions
are
shown below):
1 . The
concept o f
equal shares in
fraction,
for
example ,
Ques t ion : What fract ion of the diagram is
shown by the shaded area?
2 . Th e c o n c e p t o f fraction
size
( r e s t r i c t e d to t he c o m p a r i s o n o f
f r a c t i o n s
w i t h e i th e r th e s a m e d e n o m i n a t o r o r t h e s a m e n u m e r a t o r , f o r
e x a m p l e ,
Question: Is
1/2
of a cake (greater than/smaller than/equal to)
of a cake?
3.
T he concept of a uni t being referred to by a f ract ion , for example .
Quest ion: When 4 1 / 2 cakes are equa l l y d iv ided am ong 3 people,
how m any cakes does each person ge t? (You m ay draw diagram s
to
find
the answer.)
The resu l ts of the pretes t con fi rmed some of the teach ers ' spe cula t ions ,
and showed that there w ere few er s tudents
who had
m as tered
the
concept
of
uni t in
f ra ct ions than those
w ho
unders tood
the
concept
of
eq ua l shares ,
o r
were capable
of
com paring simple frac t ion s (see T able 8.2).
Planning
the Research Lesson .
Inform ed by the pretes t resul ts, the
teachers began to plan the lesson. They agreed tha t there sho uld be som e re-
vision of equ al shares bu t decided that th is should be t a u g h t in a separa te les-
son prior to the research lesson. The research lesson shou ld beg in w i th
compar ing fract ions bu t
focus
ma in ly on un i t s and un i t i z ing . There were
several rounds of lively discussion . T he result w as a fairly detai led plan that
w as
careful ly
del iberated
and
ful ly
di scussed.
A . T h e Lesson O p e n e r — C o n t e x tu a l iz a ti on
The plann ed lesson began by es tabl ishing a relevan ce s tructure ( i .e ., le t -
ting
the
s tudents view frac t ions
from a
po in t
of
view that they could im m edi-
ately
experience
as
mean ingfu l ) .
T he
s tudents w ere
to
di scuss
the
fo l lowing
problem
in
small groups (see
box on p.
200):
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TABLE 8.2
The
Results
of the Pretest
Them e Question
Freq. o f Correct
Responses
Classes
A— E
(N
=
151)
E qua l
sh are s W h at
f ract ion
of the diagram is
s h o wn by the shaded area?
Shade
1/9 of a
square.
Shade
1/8 of a
c i r c l e .
Shade
1/3 of the eggs in the
basket .
69
87
16
87
C o m p a r i n g
1/2 of a
cake
is
(greater than
/
eq u a l
to /
smal le r
f ract ions
tha n) 1 /4 of the
same
cake
2/4 of a cake is (greater tha n / equa l to / smal le r
than)
1/2 of the
same cake.
2/5 of a kg is (g rea te r than / equa l to / smal le r
t h an ) 4/5 of a kg.
1 1 2 of an hou r is (greater than / equal to /
smaller than) 1/200
of an
hour.
U n i t s
and
Divide
2
cakes in to three equal parts .
How
U n i t i z i n g
ma ny cakes
are
there
in one
part?
W hen 4 '/2 cakes
are
divided among three
persons , how many cakes does each person
get?
W h a t
fract ion of
squares
is
shown
by
the
black squares?
W h a t
f ract ion
of the
to ta l number
of
objects
is
shown
by the
black
squares?
63
58
1 1 1
39
13
3
20
22
199
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8. T O W A R D
A
P E D A G O G Y
O F
L E A R N I N G
201
were
in 1 /6 of
their pac k.
In
this instance,
the
size
of the
pack varied w hi le
the
fract ion
rem ained the same. The teacher then posed the quest ion: W hy
are the resul ts different w h e n the fract ion is the s ame? T he s tudents ob-
served
how the
number
o f
candies changed w i th
the
changing un i t .
D . Waff le Cakes
In
the next s tage, the teacher gave each group a paper disc that repre-
sented a round
waf f le
cake . In thei r groups , the s tudents had to cut out 1 /6
of the cake . When they
f in ished,
they w e re given 2 discs , and 1 i/2 di scs in
tu rn , wi th
th e
same task
o f
cu t t i ng
out 1 /6 of the
am oun ts g iven . They then
had to comp are the am ount o f cakes o b ta ined, and see how the s ize o f the
uni t
m a t te r e d .
T h e
d i f fe rence
be tween th i s ac t iv i ty
and the
p rev ious
o n e
was to
al low s tude nts
to see
tha t
th e
concep t o f
uni t
em braces bo th cou n t -
able
an d
uncoun tab l e amoun t s .
E .
Back to the First
Question
A t the en d of the
lesson,
the
teacher then returned
to the two
ques t ions
abou t the
fund-rais ing event that were discussed
at the
beg inn ing
of the
les-
son. The s tudents w ere to w rite out thei r own answers to the qu est ions m ak -
ing
use of
w hat they
had
learned
in the
lesson.
Quest ions:
• W ho has donated the m os t?
• W ho w as the most generous?
Teach ing t h e Les s on and
Reflect ing
on the Resu l ts .
A ll f ive
teachers
t au g h t their own classe s with the same plan. They also tried to observe the ir
col leagues teaching
the
same lesson,
and
shared their observations
after-
ward w i th
a
view
to
m odi fy ing
and
improving
the
p lan . Al though there were
some s l ight var iations w hen each teacher im plem ented the lesson plan , th e
teachers
a ll
fol lowed
the
structure
and
sequence
of
act ivi t ies
in a fai thful
manner .
T he sam e tes t that w as used for the pretes t w as adminis tered to the s t u -
dents
a few
days
after the
lesson
had
been taug ht .
T he
assessment i tems
re-
lating
to the
notion
o f
un i t
are
shown
in
Table 8.3.
T he
difference be tween
th e
pretes t
an d
post tes t re sul ts indicates considerable learning gains
by the
students .
After
all of the
teachers
had
t augh t
the
lesson, they
met on a
n u mb e r
of
occasions to evaluate th e entire process. A l though the teachers felt that they
had
been overam bitious
and had
packed
too
m uch in form at ion in to
th e
dou-
ble lesson (totaling 80 min.), they
were
in general q uite satisfied w i th w ha t
they had achieved, and were pleased to learn about the students ' learning
outcom es. S uggest ions were m ade o n how to f ine- tune the lesson plan w i th
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TABLE 8.3
The
Dif ference B e twe e n
the P retest and
Posttest Results
Theme
Quest ion
Freq. of Correct
Responses
Classes
A-E
(N
=
151)
Pretest/Posttest
(% ga in
o r
loss)
Equal shares
Comparing
fractions
Un i ts and
Uni t iz ing
What fraction of the diagram is shown
by th e shaded area?
Shade
1/9 of a
square.
Shade 1/8 of a
ci rcle .
Shade
1/3 of the
eggs
in the
basket.
1 /2 of a cake is (greater tha n / equal to /
smaller than) 1/4 of the
same
cake.
2/4 of a cake is (greater tha n / equal to /
smaller than)
1/2 of the
same cake.
2/5 of a kg is
(greater tha n
/
equal
to /
smal le r
than) 4/5 of a kg.
1 /2
of an hou r is (greater than / equal to /
smaller than) 1/200 of an hour.
Divide 2 cakes into three equal parts. How
man y cakes are there in one par t?
W h e n
4 1 / 2
cakes
are
divided among three
persons, how
many cakes
does
each person
get?
W hat f raction of squares is shown by
the
black squares?
What fraction
of the
total number
o f
objects i s shown by the black squares?
45.7/68.9
*(+23.2%)
57.6/64.9
(+7.3%)
76 8/86 8
57.6/67.5
*(+9.9%)
41.7/50.3
*(+8.6%)
38.4/60.9
*(+22.5%)
73.5/81.5
(+8.0%)
25.8/45.0
8 7/4 7
(-4.0 )
2.0/44.7
*(+42.7%)
13.3/31 .3
14.7/32.0
*A significant change
in
percentage
is observed
w i t h / ?
<
0.05.
202
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8. T O W A R D
A
P E D A G O G Y
OF
L E A R N I N G
203
more consolidation work at differen t points in the lesson. T he posttest re-
sults show ed that al l the classes obtained sub stantial gain when com pared
with the pretest res ults (see Table 8.4). T he effectiveness of the lesson w as
thus
evident.
A
PRIMARY G RADE
4
C H I N E S E L E S S O N
O N
TEXT CO MPREH EN S I ON
This w as another learning study carried out in the first phase of the "Ca-
tering
for
Individual
Differences
(Bui ld ing
in
Variation)" project . Seven
m eet ings, one hour each, were used for the com plete cycle .
Stage 1: Choosing a
S peci f ic Object
of
Learning
After m uch de l ibera tion , the teache rs decided to choose chapter 10 of their
course book,
A
Pen cil End , as the m ain teaching con tent . This chapter was
chosen
for two
main reasons: First, according
to
their teaching schedule,
this
lesson
w as to be
tau gh t around la te N ovember,
and so the
t im ing wo uld
be about right. Second, the text contained some special features that the
teachers con sidered to be w orthw hile for the s tudents to learn. The text was
in th e form of a story w ritten by a boy who
felt
that a 2-inch long pen cil end
w as
too
short
to be
use ful ,
and so
threw
it
away.
He
threw
th e
pencil
end
away three t im es, and yet each t im e i t reappeared on his desk. Fina lly he re-
alized tha t i t w as his m other who had picked up the penc i l and put i t back on
his
desk, hoping that
he
would
u se it
again
and not be
w as tefu l .
The boy was
then ashamed of his ow n action and used the pencil to do his homework.
In subsequent m ee t ings , the teachers identified five w or thwhi le ob jec ts
of learning :
TA BL E 8.4
The
Average
Scores of Different Classes in the Pretests and Posttests
Cl a ss
A
Class B
Class C
Class
D
Class E
Whol e class
Pretes t :
Average Score
6.38
6.89
3.77
3.94
3.63
5.13
Posttest:
Average
Score
8.78
9.14
4.83
5.31
4.78
6.85
Both
Tests:
Total
Score
12
12
12
12
12
12
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204 LO ET AL .
1.
In the
text,
th e
same action (throwing away
the
penci l end) appeared
three t im es, yet the w ay in w hich the sen t ime nt of the boy w as conveye d in
each
case
w as
different.
T he
t eachers w ished
to
draw s tuden ts ' a t ten t ion
to
the way in
w h i ch
the
cho i ce
of the
ve rb s m a tched
the
ac t ions
and the
verbal
express ions ,
in
order
to
show esca la t ing
feel ings o f
d is l ike .
2. In the text , there were six words wi th the
"hand"
rad ica l [-f- ] or [ ^ ].
These
words can be considered to be in the s ame sem an t ic f ield as the word
n a h (Cantonese) [^ ] ( m e a n in g
"take"); al l the
w o r ds
a re
associa ted w i th
some act ion us ing the hand . Yet , each w ord has a s l ig ht ly
dif ferent
m e a n -
ing .
For e x a m p le , the w o r d taih ( Ca n t o n e s e ) [ -^ ] has the m e a n in g of
"carry , take ho ld of , or
l i f t i ng
s o m e t h i n g o u t " ; t h e w o r d
g im
( C a n t o n e s e)
[^ct]
has the
m e a n i n g
o f
"select
a nd
p ick up" ;
wing/\ihng
( C a n t o n e s e ) [ty]
has the m ean ing o f "throw"; laai (C an tonese ) [ 4& ] has the m ean ing o f
"puH";y/p (Cantonese) [4lc] has the m e a n in g o f "catch o r receive";
touh
(Cantonese) [}£) ] has the m e a n in g
offish
out ." In w r it ten l an gua ge , de-
pending on the con tex t, it wou ld be
more
ap propr ia te to use one of these
specif ic w ords ra ther than the w o r d
"take"
[ ̂ ] in order to convey m ore
p rec i s e mean ings a n d m a k e th e w r i tt en wo rk more e l eg an t . Y et in spoken
Ca n t o n e s e ,
it w o u l d b e p e r f ec t l y accep t ab l e , and in
fact
m o re n a t u r a l , to
use the
spoken form
of "take" [ ̂ ],
w h i c h
is l ing
(C an tonese ) [^] .
The
teachers w i shed to teach th e s tudents how to di s t ing uish th e me a n i n g a n d
usage
o f
each
o f
these w ords . Also, they w anted
the
s tudents
to
appreciate
tha t in w r i tt en l anguag e , the use of w ords h as to be mo re precise in order to
bring out the exact meaning to be conveyed.
3. T he text showed the different personal i t i es of the bo y and his m other.
The boy was
very imp at ien t
and
showed
h is
l ikes
and
dis l ikes ove rt ly .
The
mother w as more gen t le and sub t le . T h e t eachers sugges ted that the
mother's example could show
the
students
how to
relate
to
other
people,
such
as
their classmates.
4. In the
last paragraph ,
the
mother in troduced
the
idea
o f
conservation.
The
teachers w ished
to
cu lt ivate
in
their students
an
awareness
o f the
envi-
ronm ent and a posi tive at ti tude tow ard con servat ion.
5.
I t was the po l icy of the school that the Chinese panel head should
specify
the l earn ing ob jec t ives fo r each chapter at the b e g i n n i n g of the
school term. For th is chapter , a num ber of w ords and senten ce pat terns had
already been iden tif ied as teaching object ives , and these w ere to be assessed
in
th e exam ination .
On ly tw o periods h ad been ass igned for the t each ing o f th is chapter ,
and the t eachers fel t t ha t the re w ou ld no t be eno ug h tim e to cover eve ry -
th ing t ha t they w i shed
to
t eac h . They adm i t t ed t ha t they of ten
had to
rush
t h r o u g h t h i n g s super f ic ia l ly , an d tha t there w as l i t t le t i m e fo r i n -dep th
t r ea tme n t . As a r e su l t , m any s tuden t s w ere no t ab l e to l ea rn w e l l . Th i s
had a lways been the teachers' problem.
Af t e r
much di scuss ion , they
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8.
T O W A R D A P E DA G O G Y O F L E A R N I N G 205
agreed tha t
fo r the
research lesson, they w ou ld
try to
f o c u s
o n
f e we r
o b-
j ec t s
o f
lea rn ing,
and
dea l wi th each
on e in
grea te r depth . They dec ide d
no t
to
f o c u s
on the
affect ive aspec ts (objects
o f
le a rn ing num bers
3 an d 4)
a t
th i s poin t , because they
fel t
that these ideas should be
in f i l t r a ted
in
the i r l e ssons th ro ugh ou t th e year . O f the three remaining aspec ts , they
fel t tha t
th e
choice
o f
w h i ch
to
f o c u s
o n
shou ld depend
o n the
s t u d e n t s '
pr ior exper ience and knowledge . There fore , to he lp them make an in-
fo rmed decis ion, they decided to wai t unt i l they could obta in informa-
t ion about the s tudents
from
the pre tes t .
Stage
2:
F i n d i n g
Out the
E x t e n t
to
W h i c h
the S t u d e n t s
H a v e
Developed
th e
I n t e n d e d C a p a b i l i t i e s
A pretest w as administered to all five classes of 148 students. O n average,
over 85% of students in each class (m ore than 70% in the w eakest c lass) dem -
onstrated an un derstanding of the words and sentence patterns
specified
by
th e
panel head (object
of
learning number
5), and
were able
to use
these
words
to fill in
app ropriately
the
blanks
o f a
text. Therefore,
the
teachers
de-
cided
that
it
would
not be
necessary
to
focus
o n
these aspects
in the
lesson.
To
test
the
s tudents ' understanding
of the
w ords w i th
the
hand radica l ,
two que stions were set. In the first question , three sentence s w ere given . For
each sentence, three characters
o f
very sim ilar m eaning w ere provided
and
the s tudents had to choose the m ost appropria te o ne for the par t icula r con-
text.
In the
second question, students were required
to f ill in
seven blank s
to
com ple te a
text. Seven w ords w ith
the
hand radical were pro vided
and
s tu-
dents
had to
choose
the
m ost appropria te w ord
for
each b lank.
The
resul ts
of
the
test showed that students
had difficulties
dist inguishing words with
the
hand
rad ica l .
The
word that
w as
found
to be
m o s t
difficult
for the
s tudents
w as "fish out" [$0]. In the first que stion, on ly 10% of the stu dents cou ld use
th e
word "fish out" [$0] appropriately.
In the
second qu est ion, only
tw o
s tu-
dents in one class, Class 4C, got all the answ ers correc t . A ga in, the character
"fish out" [ $0 ] w as found to be the most difficult, as only 10% of the stu-
dents used it correctly. Other difficult words were "take" [
^ ]
(20% co r-
rect),
"carry"
[H] (30% correct), and
"pick
up" [^] (30% correct). Th us, it
becam e clear that w ords with th e h and radical needed to be given special a t-
tention,
especia l ly
the
words
"fish
out"
[
- J £ )
],
"take"
[ ̂ ], and
"carry"
[^ ].
Another question required
the
students
to put two
groups
of
w ords
in or-
der of the strength of feel ing expressed. The first group consisted of the
words
"excited"
[ - *
-f^], "pleased" [Ht -§-], and "happy" [ ' j Jf£].The second
group co nsisted of the wo rds
"angry"
[£_
i j ( 3 ,
"discontented" ffi / * £ ] and " fu-
rious" ['1^ ^J]. On ly abo ut 30% of studen ts w ere ab le to put the first group o f
words in the
correct
order, and about 60% of students were able to put the
second gro up o f wo rds in the correct order.
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2 06 L O E T A L .
To test w hether students w ere able
to
m atch
the
verbal expressions cor-
rectly with the feel ings o r sentiments expressed, they were asked to m a tch
three phrases with three verbal expressions.
For
example, students
had to
match the phrase, "M other said kind ly" with
"Don't
give up, you just have
to work harder next time." I t was found that about 60% of students could
ma tch
the
phrases with
the
verbal expressions correctly.
Th e resu lt of the pretest prom pted the teache rs to ma ke the decision to fo-
cus on the
first
tw o objects of learning:
• To be able to appreciate that the choice of verbs should m atch the actions,
and that the verbal expressions should effectively convey sentim ents.
• To be able to dis tingu ish the m ean ing and usage o f some w ords w i th
the hand radical , and to apprecia te that in writ ten lang uag e , the use of
words has to be precise.
Stage 3:
D e s i g n i n g
a
Lesson (Lessons)
A i m e d
to
D e v e l o p
th e
I n t e n d e d C a p a b i l i t i e s ( T h e I n t e n d e d
Objects of
L e a r n i n g )
Th e teachers shared their usua l m ethods of teach ing a text , w hic h typical ly
included going through
the
fo l lowing
five
stages:
1. B r ie f ly expla in ing
the
text
as a
w h o le
2. R eading the text a loud
3. E xp laining new characters and w ords
4.
Going through
the
questions
at the end of the
text
and
looking
at
each
paragraph in m ore deta i l
5. Teaching some of the sentence patterns and special l inguis t ic fea-
tures in the text .
T he
teachers
in
general
felt
that this routine, w hich they
had
been us ing
all
a long, w as som etim es boring, and that it failed to provide a structure that
helped
the
students
focus on the
objects
o f
learn ing. They hoped
that fo r the
research lesson , they could com e up w ith a better w ay of structuring the les-
son p lan in order to help the students focus on the objects o f lea rn ing by
means of suitable variations. I t was decided that tw o lessons w ould be used
fo r teaching—one for each object of lea rn ing. For the purpose of th i s chap-
t e r ,
only
the
lesson deal ing w ith
the
second objec t
o f
l e arn ing— w ords w i th
the hand radical— is described. Th e lessons of two c lasses (Class 4C and
Class 4H) were videotaped, and o nly data from these tw o c lasses are used
fo r
the analysis.
The Lesson Plan: Teaching
W o r d s W i t h
the Hand Radical . The l e s s o n
plan con tained the follow ing essential features, wh ich w ere aim ed at bring-
ing
ou t similari t ies a nd
differences,
contrasts, variation a nd invariance:
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8.
T O W A R D A
P E D A G O G Y
O F
L E A R N I N G
207
1 . Students shou ld find all the w ords showing act ion that had a s im ilar
meaning
to
"take,"
and
that used
the
hand radical . Then they sho uld
com m ent on the text
after
all
these words
had
been replaced w ith
the
word
"take."
2.
W ords w i th
th e
hand radica l should
b e
d iscu ssed toge ther ,
to
show
the i r s imi la r i t i e s and cont ras t the i r d i f fe rences , for example ,
"drop"
[- •]
and
"throw" [#}]; "pickup" [ j f c ] ; "pickup"
[^] and
"take"[$r].
3. V ariations shou ld be used to help students discern the m eanin g of the
words ,
for
exam ple , using exam ples
and
nonexam ples.
F or
each pair
of words, a sentence was to be used and i ts structure kept invari-
ant—only the word with the hand radical would be changed.
This
w as
intended
to
enable students
to
discern
the
subtle
difference in
m eanings of the
different
words.
Stage
4: Teaching the Research Lesson
( the E na cted
Object of
L e a r n in g )
The
Lesson
of
Class
4 C . The teacher first asked th e students to find all
the words w ith
the
same m eaning
as "take" [ ̂ ]. She
then pointed
out that it
w as
c o m m o n
for the
students
to
take
all
these w ords
as
synonymous ,
and
that they tende d to use only the word "take," instead of m aking use of these
different
words .
She
told them th at
if
they a lw ays
did
this, however,
the text
w o u l d
becom e very boring. S he used the m etaphor of their m other cooking
th e same dish for every m eal; even thou gh i t was good to eat at the begin-
ning,
it
w ould become bor ing after
a
w hi le .
T he
teach er then
focused on the
five
wo rds:
"receive"
[ ̂ ], "fish out" [ ̂ ) ], "take" [ ̂ ],
"carry"
[ ̂ %] , and
"pick up" [ % fc ]. These w ere writ ten on the board.
She attended to the w ords one at a time, always
com paring
each o ne w i th
the w ord
"take"
[ ̂ ]. She used a sentence in which the use of e i ther w ord
was poss ib le . The difference in m eaning of the two w ords was m ade more
prominent by put t ing them in the same context . By keeping the sentence
structure invariant and varying the wo rds, the
teacher
focused the students'
attention on th at w hich varied, that is, the difference in the m eaning con-
veyed by the tw o sentences becau se o f the
difference
in m eaning of the tw o
words . Fo r example , sh e dealt with the tw o w ords "take" [
̂
] an d "receive"
[ ̂ - ] in the
fol lowing
way.
The
teac her asked
the
students
to
com pare
the two
sentences:
He took the penci l from her hand.
He rece ived the penci l f rom h er hand.
She expla ined that w hen the word
"received"
[ ̂ ] was u sed in the second
sentence, there was an im plication that the one holding the pencil (sh e) was
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208 LO ET AL.
giving
it to the recipient
(him).
When the
word
"took" [ ̂ r ] was
used,
it had
a different imp l icat ion. The teacher added that the wo rd "took" in the first
sentence m ight
give
us the feeling that "he" was no t very p olite because he
took wi thout asking,
o r
w i thout be ing g iven
the
penci l
in the f irst
p l ace .
"Took" in the context o f the first sentence m eans that the ac tor is "he," and
"she" w as passive.
"Receive"
in the context of the second sentence means
that
the actor is
"she,"
and "he" is the pass ive recipien t .
T he teacher dea l t w i th the other words in a s imi l a r way .
The Lesson of Class
4H .
The
teacher
first
read
out
loud
a
piece
o f
text.
In
this
text , the word
"take"
was used m any t im es, som etim es inappropriately.
T he
teacher asked
the
students
i f
they noticed w hich w ord
w as
used most
of-
ten. Many students were able
to identify th e
word
"take."
Then
th e
teacher
asked, "What would y our teacher think if you wrote a composition with so
m a n y
"take's?"
M any students responded that the t eacher would n ot
like
it.
T he
teacher then asked
the
students
to find all the
words associated w i th
the
act ion
of the
hand. Nine words were found.
S he
then explained
the
meaning o f each w ord, role-played the act ion conveyed, and analyzed the
action of the han d. Fo r each pair of w ords, she also kept the sen tence struc-
ture invariant ,
b u t
changed
the
verb
and
asked
the
s tudents
to
c o m p a re
the
tw o
resu l t ing sen tences .
For
example , w i th
the
w o r ds
"drop" [ ̂ ] and
"throw"
[ /}],
she gave the fol lowing sentences :
•
Don ' t drop banana skins onto
the
floor.
•
Don ' t
throw
banana skins onto
the
floor.
She asked som e s tudents to com e out and act out how they "drop" some-
thing, and how
they "throw" som eth ing .
In the
subsequen t d i scuss ion ,
she
focused
on the
action
of the
hand
—
w hether
the
action
w as
large
or
sm al l,
the size of the swing , and the angle made by the arm. Then she said that o f
the tw o words that were used to fill in the blank in the same sentence struc-
ture, only
one of
them
w as
correc tly used
and
asked
the
students
to
ident i ty
the correct one.
S he
dea l t w i th
the
rest
of the
words
in
pai rs
and in a
s imi l a r way .
In
each
case, she focused on the physical movem ent of the ac t ion. For exam ple, she
stressed that with the wo rd
"carry"
[ H; ] , the arm should be held s t raight
down .
Final ly , the
teache r reread
the
text tha t
she had
read
ou t at the
b e g i n n i n g
of the lesson. This t ime, the s tudents suggested approp riate w ords to replace
the word "take" in each ins tanc e.
The En ac ted
Ob ject of
Learning .
W e see tha t bo th t eachers seemed to
have taug ht
in
very s im i lar w ay s. How ever, there
w as a
very im po r tan t d i f -
ference
in the i r ways o f dea l ing wi th th e ob jec t o f l ea rn ing . Wi th th e
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8. T O W A R D A P E D A G O G Y O F L E A R N I N G 209
t eacher
of C lass 4C, the focus w as on the subt le d ifference in m ean ings o f
the
di f ferent w ords. By keeping the sentence s t ructure invariant and vary -
ing
the wo rd used, she
helped
the s tuden ts to focus on the d i f fe rent mean -
ings
of the words . These m eanings w ere made expl ic i t by the ir re la t ion to
the l in gu ist ic con text , that is , the rest of the sen tences. Fo r exam ple the ac-
tor versus rec ip ient meaning—impl ic i t
in the
words "took" versus "re-
c e i v e , " r e s p e c t i v e l y — wa s m a d e e x p l i c i t
b y t h e
i n v a r i a n t s e n t e n c e
structure.
On the
other hand, despite
the
fact that
the teacher o f
Class
4H
also presented
tw o
wo rds
in the
same l ingu is t ic context ,
she
focused
on the
m eanin g of each word o n i ts ow n and the ac t ion of the hand conveyed by
each w ord. Th e teach er did not re la te the wo rd to the l ing uis t ic con text to
help
s tuden ts d iscern
the
d ifferences
in
mean ing . Th is me thod
o f
dea l ing
wi th
the mean ings o f w ords in a
decontextual ized m anner
c an create prob-
l e m s fo r
learners
o f
Ch inese ,
as one
charac te r
m ay
change
its
m e a n i n g
w hen u sed toge ther w i th another charac te r (or charac te rs ) to form a w ord
or a phrase . For exam ple , when the teacher fo cused on the mean ing of the
wo rd
"carry"
[ _ ] , sh e em phas ized tha t i t had the mean ing tha t the arm
should
b e
held straight do w n. This
is a
correct interpretation
if the
word
is
used
in the co ntex t of
"carrying
a br ie fcase /shop ping bag," bu t not correc t
wh e n it is used in the con tex t of
"car ry ing
a lantern," for example , in w h i ch
case
the arm
w ould p robab ly
be
ben t
a t the
e lbow.
Stage 5:
F i n d i n g
the Students
L e a r n i n g
Outcomes
Because
the obje ct of learning w as to help the students to discern the sub tle
differences in the m ean ing of the different w ords associa ted w ith the act ion
of the
hand ,
and to be
able
to use
them approp riately,
the
pos ttest also tested
such
a capab ility in the students. Judging from the enacted o bject of learn -
ing
of the tw o c lasses (and i f the way in w hich the teacher deal t w i th the ob-
j ec t
of
learning
is inf luent ia l ) , it
would
be
expected that
the
s tudents
o f
Class 4C should perform bet ter than those of Class 4H. This was indeed
borne out by the resul ts of the post test. The quest ions w ere the same in both
the pretest and the posttest. Table 8.5 shows the results of the quest ion
where s tudents were given seven words with the hand radical , and were
asked to fi ll in seven b lank s in a text with the approp riate w ords.
Th e resu lts of the post-test show ed that the students of Class 4C dem on -
strated
significant
imp rovem ent . In the pre test, on ly two students were able
to
choose
all
seven words correctly,
but in the
posttest,
1 7
students
got all
seven
w ords co rrect . Of the five w ords that the teach er attended to, al l stu-
dents in the
c lass w ere able
to fill in
three w ords correct ly: "receive"
[ ̂ ],
"fish out," [^)], an d "carry" [ ^ % ] .
S ignif icant
im provement w as a lso found
in Class 4H, however the improvement was not as great as in Class 4C.
About
1 0
students
go t all seven w ords
correct.
For the
w ord "fish out"
[
$0],
the re la tive improvem ent w as about 47% in Class 4H, w hereas the im prove-
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TABLE 8.5
Table to Compare the Results of the Pretest and the Posttest
Fil l ing
in the
Blanks
With th e
Appropriate
Wor ds
N u m b e r of S tuden t s C orrec t (Percentage)
St u den t
n u m b e r
Class 4C pretes t 33
Class 4C
posttest
33
Rela t ive improvement
4H
pretest
3 1
4H
pos t tes t
3 1
R el a t i ve
i m p r o v e m e n t
[1 ]
pick
u p
14
( 41%)
24
(73%)
54%*
7
(23%)
1 1
(35%)
51%*
[2 ]
#5
t h row
26
(74%)
27
(82%)
31 %
1 1
(35%)
18
(58%)
35%*
[3]
receive
24
(68%)
33
( 1 00%)
100%*
9
(29%)
22
( 71%)
59%*
[4]
pul l
27
(82%)
30
( 9 1 % )
50%
17
(55%)
24
(77%)
49%*
[5 ]
ft
fish ou t
9
(27%)
33
( 100%)
100%*
2
(6%)
16
(52%)
47%*
[6 ]
t ake
14
(42%)
32
(97%)
95%*
9
(29%)
18
(58%)
4 1 % *
[7]
carry
14
(42%)
33
(100%)
100%*
10
(32%)
18
(58%)
38%*
Key. Rela t ive i m p r o v e m e n t
=
i n e r e a s e
in % -
m a x i m u m p o s si b l e in c r e a se
in %.
* Words th at h ad been spec i f i ca l ly dea l t w i t h in the lesson by the t eacher .
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8. T O W A R D A P ED A G O G Y O F
L E A R N I N G
2t t
m e n t was 100% in C lass 4C. For the word
"carry"
[ t̂. ], the relative im-
provement
in
C lass
4H w as 38% and in
C lass
4C, i t w as
100%.
In the question that required students to choose the m ost appropriate
word
to be
used
in a
sentence,
i t was
also
found
tha t
the
students
in
both
classes made significant improvement
in the
understanding
of the
word
"fish out"
[ ̂ ]. In 4H, the
improvement
was
from
10% to 61% of
s tudents
getting
it
correct,
whereas in
Class
4C, the
im provement
was
again greater,
from
21% to
94%.
A s w e m ent ioned
earlier,
these tw o studies w ere some of the first studies
(carried ou t
w i th in
a
research project with developmental ambit ions)
that
w ere based on the part icular theory of learning described brief ly in chapter
1.
Both s tudies proved
to be
successfu l
in
te rms
of
gains
in
s tudent ou t-
comes. Furthermore , they showed
a
phenomenon tha t
w as
also
found in
later
s tudies: Al though the teachers had agreed on the intended object of
learning, the enacted object o f learning varied betw een the groups, and that
the
res ults (the l ived object
o f
learning) varied acco rdingly.
Since these s tudies w ere carr ied ou t , m any others have fo l low ed
(22 by
th e end of the second year of the project), m ostly w ith results that are very
m u c h in
l ine with
the
resul ts
of the two
studies described
in
th is chapter.
(Reports
on other
learning studies conduc ted
in
this project
can be found on
the Internet at this address: http:/ /cidv.hku .hk)
The two
studies
w e
have jus t looked
at
cam e
f rom a
project w ith
a
strong
emphas is
on the
enhancement
o f
teachers ' professional development .
In
this way, the a im s of the project were close to those o f the Japanese lesson
study
m ode l.
The aim of the
study described
in the
fo l low ing sect ion
w as
primari ly to test theoretical con jecture s, and thus this s tudy w as c loser to the
idea o f the design experiment .
A
SECONDARY
GRADE
4
E C O N O M I C S
LESSON
O N T H E
I N C I D E N C E
O F A
SALES
TA X
The a im of
this learning s tudy
w as
threefold:
to find a pow er fu l way for
teachers to help secondary Grade 4 students h andle a rather diff icult bu t im-
por tant economic con cept ;
to
evaluate
th e effectiveness o f a
learning s tudy
in
the
improvement
of
teaching
and
learning
(in comparison to the
lesson
s tudy
approach) ; and to test the tenet o f a specific theory o f learning
(i.e.,
the theory
of
variation— that learning
to
experience
som ething
in a
certain
w ay is
cont ingent
on the
pattern
o f
variation
in the
c ri t ical aspects
of the ob-
j ec t
of
learning).
The
investigation also promised
to
demonstrate that
a
learning
s tudy cou ld
be a
design experiment (B rown, 1992; C ol l ins , 1992)
and
serve primarily
as a
research tool .
T he ob jec t of learning for this study was the capa bili ty o f taking into ac-
count the no tion of the relative elastici ty of dem and and sup ply in determ in-
ing the
distribution
of a tax
burden between buyers
and
sellers result ing
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2 1 2 L O E T A L .
from the
introduction
of a
sales tax.
I t was
envisaged that
if
students could
develop
an
economic
perspective in understanding th e topic of the inci-
dence
of a
sales tax,
the different
w a y s
in
w hich they were able
to
under-
stand
the
econom ic phenom enon w ould increase.
Th e Economic
Topic
Used in the
S t u d y
The
economic topic used
in
this study
is
"the incidence
o f a
sales tax," taken
from the
Hong Kong economics curriculum
for
secondary Grades
4 and 5.
When
a
governm ent levies
a
sales
tax on
goods
and
services,
a
certain percent-
age
of the
cost
of our
purchase
as
consumers
is
paid
to the
government.
A t
pres-
ent, Hong Kong
does
not
have
a
general
sales
tax,
but a
limited number
of
commodities such
as
tobacco
and
liquor incur excise duty (i.e.,
a
particular
form
of
sales ta x).
The
Hong Kong government
is
cu rrently considering
a
gen-
eral sales tax,
and
this
has led to
heated discussions am ong
the
general pub lic.
M ost people believe that
if the
general sales
tax is
introduce d,
the
sellers
wil l
transfer
th e
entire
tax
burden
to the
buyers,
and
simply
raise the
price
of the
commodities
by the
amount
of
sales tax.
The
object
of
learning
for
this study
was the
capa bil i ty
o f
taking into
ac-
coun t the notion of the relat ive elast ici ty of dema nd a nd su pply in determin -
ing the distribution of a tax burden betw een buy ers an d sel lers tha t results
from the introduction of a sales tax . I t was envisaged that if students could
develop an economic perspective in thei r unde rs tanding of the topic of the
incidence
of a
sales tax ,
th e
different w a y s
in
which they were able
to
under-
stand
the
econom ic phenomenon w ould increase .
The view th at if a general sales tax is introduce d, the sellers wi l l transfer
the entire ta x burden to the buyers by raising th e price of the com m odities by
the
amoun t
of
sales tax,
is not fully
supported
by
econom ics . Econom ists
ar-
gue that instead of mak ing the buyers shoulder the
full
tax burden in every in-
stance,
th e
distribution
of the tax on a
part icular com m odity depends
on the
relative elasticity
of
demand
and
supply
of
that com m odity. A ccording
to the
law of demand and supply, whe n prices of a com m odity increase, th e quan tity
demanded falls, an d the qu antity supplied rises. Sellers are w il ling to supply
more
of a
com m odity w hen they
can
earn more
for
wh at they sell; buyers
are
less keen on purchasing a com m odity w hen they get less for their money. The
effect
on prices is therefore not a unifo rm price increase on all goods.
People need some
com m odities
more
than
others;
w ater
and
staple foods
are the classic exam ples. Even when the price o f these com m odities
nses,
the
quanti ty demanded wil l n ot drop sign ificantly. In other w ords, th e demand is
said
to be
inelastic,
or the
elasticity
of
demand
is low
( the quan ti ty dem anded
does
not
change
as
mu c h
as the
price).
For
other com m odities such
a s
luxury
cars an d jewelry, demand is highly
susceptible
to
price
change, and the quan-
t ity demanded changes m ore than
th e
change
in
price. Such dem and
is
said
to
be
elastic,
or the
elasticity
of
demand
is
said
to be
high.
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8.
T O W A R D
A
P E D A G O G Y
O F L E A R N I N G 21 3
Based
o n a
com m onsense understanding, sellers
of
com m odities with
in-
elastic
deman d w ill sim ply add the new ly introduce d sales tax to the current
prices,
and the
buyers w ill then
bear th e
entire
tax
burden. A ccording
to
eco-
nomic analysis, however, when determining the sharing of the tax burden,
th e
seller 's condition should also be taken into accou nt. For instance, for sta-
ple
foods (such
as
potatoes
o r rice),
people's demand tends
to be
inelastic,
but in the case of an especially good harvest , sellers have piles of unsold
stock
in
hand that they need
to
sell before
the
food spoils.
The
supply
is
more
or
less fixed over
th e
period
and so is not
very sensitive
to
price
changes .
In
such
a
case
of
oversupply,
the
supply
is
said
to be
very inelastic
and sellers m ay need to arrange to absorb part o f the sales tax in their p rice,
instead of passing i t on to the consum ers.
In general , the m ore elastic the dem and and the less elastic the supply, the
greater likelihood of the sales tax being absorbed in the price, and so the
sellers will share more of the tax burden than the buyers. Conversely, the
less elastic the dem and and the more elastic the supply, the greater the likeli-
hood of the w hole sales tax being added to the previous prices, in w hich case
the buyers w il l bear the w hole tax burden. How ever, in a s i tuat ion w hen both
the demand for and the supply of a commodity are elastic or inelastic, we
mu s t compare the elastici ty of demand and the elastici ty of supply. If the
elasticity
of
dem and
is greater
than
th e
elasticity
of
supply,
the buyers
have
the upper hand, and vice versa. In the case of staple foods, for exam ple, de-
m a n d
is
usually more inelastic than supply,
so the
buyers have
to
carry
a
greater part of the tax burden. O verall , the distribution of the tax burden b e-
tween buyers and sellers is a function of the relative elasticity of demand
and supply.
Des i g n
of the
S t u d y
Two groups, each with
five
economics teachers, part icipated in the main
study. On e of the groups fol low ed the Japanese lesson s tudy m odel . In this
group,
the teachers and a researcher
(who
did not
take
the lead)
discussed—
during three preparatory meetings, each of which lasted for around 2
hours—the ways in which the object of learning could best be handled.
Draw ing on their ow n experiences and the resul ts of a pi lot s tudy in w hich
students ' qu alitatively
different
understandings
of the
incidence
of a
sales
ta x
w ere assessed, the group developed a jo in t lesson plan for a series of
four lessons, w hich were then taugh t in five different classrooms.
The procedure was basical ly the same for the other group of teachers ,
with one ma jo r difference . In this group , the researcher actively participated
in the discussion, and introduced the theory of variation a s a tool for devel-
oping a lesson plan to the teachers. B oth the lesson p lan and the enacted ob-
jects
of
learning demonstrated teachers ' understanding
of the
theory
of
variat ion
as
applied
to the
part icular object
of
learning.
In the
fol lowing sec-
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214 LO ET AL.
tion, this grou p is refe rred to as "the learning study group," whereas the
first
group
is
referred
to as
"the lesson study
group." T he
lesson study group
served
as a
reference
to
reveal
the effect of the
instru ction al design based
o n
the
theory
of
variation.
Using
th e
data obtained
on
teaching
and
learning, both inter-
a nd
intra-
group
comparisons were
conducted in
order
to
explore
the relationship be-
tween
th e
enacted objects
o f
learning
and
student understanding. This
investigation therefore com prises
a
learning study
and a
lesson study, with
th e
primary em phasis being on the comparison between these tw o studies. A sec-
ondary emphasis
is on
com parisons between classes w ithin each study.
T en
teachers participated
in the
main study,
five in the
learning s tudy
group
a nd
five
in the
lesson s tudy group.
T he
teachers
in the two
groups
had
8
years
and 7.2 average
years
of teaching
experience,
respectively. Fu rther-
more ,
in
Hong Kong, secondary school s tudents
are
divided into
five
"bands,"
where Band
1
represents
the
high est level
of
academic a t ta inmen t
and B a n d 5 the lowest . Four of the five classes in the lesson s tudy group
comprised Band
1 and 2
s tudents ,
and one
c lass
was of
Band
3
students.
The
learning s tudy group included one B a n d 1 , two B a n d 2 and two B a n d 3
classes. Students in the lesson s tudy group were thus classif ied as hav ing
somewhat higher expected attainment.
There
were altogether
356
students
in the age
range
16 to 1 8
years
and
they
all
s tudied econom ics
a s a
school
subject .
A ll the
lessons were videotaped
and
subsequ ent ly ana lyzed
in
term s
o f
the enacted objects of learning. A f te r the series of lessons, all 356 students
w ere required to com plete a wri t ten task, and f ive s tudents from each c lass
were chosen random ly
for
interview s.
The
w ri tten tasks
and the
interview s
were
to
evaluate student understanding
of the
topic concerned.
Prior to the main s tudy, a pi lot s tudy w as carried ou t w i th tw o groups,
each co nsisting of two teachers and their stude nts, in order to try ou t the re-
search design and test the ins t ruments set for eva lua t ing student lea rn ing.
M ore im portan tly, this pilot study attemp ted to identify the qual i ta t ively dif-
ferent
w a y s
in
w hich s tudents m ade sense
o f the
distribution
of tax
burden,
so as to provide inp ut for the m ain s tudy. A t the en d of the p i lot s tudy, th e
participating students ' understanding
of the
topic
was
probed
by
asking
them to answer the fo l lowing quest ion in w ri ting:
In
a
r ecen t
Legis lat ive C o u n c i l
m e e t i n g ,
the
proposal
to
b r i n g
in a
sales
tax to
H o n g
Kong was rejected. A new spaper then conduc t ed i n te rv i ews w i t h m e m b e rs of the p u b -
li c t o
canvas s op in ion s
on the
t ax . M os t people opposed
it.
The y sa id
tha t
pr ices
w o u ld
increase by the a m o u n t of the t ax . Do you agree
that
p r ices w ou ld increase by the
a m o u n t
of the
t ax?
W h y o r w h y
n o t ?
Answers from 158
students participating
in the
pilot study
were
analyzed
in
a
phenom enographic
way in
order
to
reveal their conc ept ions regarding
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8. T O W A R D
A
P E D A G O G Y
O F L E A R N I N G 21 5
the incidence
of a
sales tax .
In
addition
to
answering
th e
written qu estion,
a
subsample of 16 students w as interview ed about their understand ing o f the
phenomenon. The analyses of the data from this interview facil i tated the
analysis
of the
written data.
Th e pilot study revealed six qualitatively different w ays of conceptualizing
th e incidence
of a
sales
tax
(Co nceptions
A
through
F on
Table 8.6),
a nd
these
were used
as the
basis
for the
main study.
A ll six
conceptions w ere
identifi-
able in both the written tasks and student interviews, and
represent
the varia-
t ion in the w ays in w hich the students experienced the phen om enon .
The set of categories of description described revea l the different under-
s tandings am ong s tudents of the incidence of a sales tax, m aking up the di f-
ferent
conceptions or
"ways
o f
seeing."
Corresponding to the
different
referential aspe cts, w hich represent
different
m ean ings
o f the
incidence
of a
sales tax, there are different structural aspects, representing what the stu-
den ts discerned and focused on. B y com paring the concept ions , the cr i t ical
features of the concept ions w ere iden tified, nam ely the features that dis tin-
guished them from one another.
During the preparatory meetings for the main study, teachers in both
groups drew
on the findings of the
pilot study (i .e.,
the
students ' quali ta-
tively
different ways of understanding tax incidence), and agreed that the
cr i tical aspect of an econom ic w ay o f unders tanding w as the relat ive elas t ic-
ity
of
demand
and
supply. They then started
to
plan
a
series
of
lessons
around this
concept.
As
regards
the intended object of learning, two com-
monal i t ies
a nd
three critical difference s between
the two
groups were iden-
t if ied.
In
terms
of
similari t ies, both groups tried
to
establish
a
contex t
for
learning this topic
by
employing current news about
the
int roduct ion
o f a
general sales tax in Hong Kong, as wel l as an exam ple of an authen t ic gaso-
l ine bil l . This b uilding
up of
context
is in
accordance w i th
the
principle
of
building up a relevance structure for students, as espoused by Marton and
Booth (1997).
Furthermore,
i t was found
that
all
teachers
had
made systemat ic
use of
variat ion; in a sense the intuit ive use of variat ion w as a key feature of all the
teaching in the study. Both groups introduced variat ion sequen t ia lly in the
dimension
of
elasticity
of
demand
and
supply.
T he
teachers
first
varied
the
elasticity
of dem and against the invariant elast ici ty of supply, and then var-
ied the elast ici ty of supply a gainst the invariant elast ici ty of dem and , in or-
der to
di rect s tude nts '
focal
awareness toward
the
effect
o f
such e last ici ty
on
th e
distribution of the tax burden.
However , there were three major differences between the two groups:
First , al l the teachers in the theory-inspired group sought to f ind out the
w a y s in
w h i ch
the
students understood
the
phenomenon
of the
incidence
o f
a sales tax, and use these as the basis for developing their lessons. In con -
trast, only
one
teacher
in the
comparison group at tempted
to do the
s ame .
Second,
a ll the
teachers
in the
theory-inspired group wa nted
to
in t roduce s i-
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TABLE
8.6
Categories
of
Description
for the Incidence of a Sales Tax
Leve l o f
Unders tanding Con ception Referen tial Aspect
Structural Aspect
O ne
O ne
O ne
Two
D
Tw o
Three
Tax is
ful ly
borne by
bu y e r s ,
and the tax
burden
is
related
to the
demand side
o f the
marke t .
Tax is fu l ly
borne
by
buyers,
and the tax
burden
is
related
to the
supply s ide of the
marke t .
Tax is
fu l ly
borne by
sellers, and the tax
burden
is
related
to
dimens ions o ther than
d em an d
and
supp ly .
Tax is
shared between
bu y e r s
and
sellers,
and
the tax burde n is re lated
Focused
on the demand
condi t ions of the market in
w h i c h
th e
goods
a re
s i tuated. Variat ion
is
brough t abou t
by one or
m o re of these factors , such
as the
n a tu re
of the goods.
Focused
on the
s u p p ly
conditions
of the
m arket
in
w h i c h
the
goods
a re
s i tua ted . V ar ia t ion
is
bro u g h t
abou t
by one or
more
of
these factors , such
as the m arke t power of the
sel lers .
Focused on the nonma rke t
mechan isms
of the
market
in
w h i c h
t he
goods
are
s i tuated.
Var ia t ion
is
b r ough t
abo u t
by aspects
o ther than marke t op era t ion ,
for ex am p le , g o v e rn m en t
i n t e rven t ion , and so on.
Focused
on the
e las t i c i ty
of
demand
of the
goods.
Varia t ion
i s b rou gh t abou t
to the dem and s ide of the by chan ges in dem and
marke t .
Tax is
shared
between
buyers
and
sel lers ,
and
the tax
bu rd en
is
related
to the
supply s ide
of the
m ark e t .
Tax is shared between
buyers
and
sellers,
and
the tax burde n is re lated
to
s imultaneous
interact ion
be tween the
demand and supply s ides
of the m ark e t .
condi t ions .
Focused
on the
elasticity
of
supp ly
of the goods.
Variat ion
is
brought about
by
changes
in
s u p p ly
condi t ions .
Focused
on the
re la t ive
elasticity
of
demand
and
supp l y
of the
goods.
Variat ion
is
brough t ab ou t
by
r e l a t i v e ch an g es
in
both
aspects.
2 1 6
AH
H
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8.
T O W A R D
A
P E D A G O G Y
O F
L E A R N I N G
21 7
mul taneous
variation in elasticity of demand and supply, a l though none of
th e teachers in the comparison group planned to do so. T hird, all the teach-
ers in the theory-inspired group
endeavored
to introduce the variations in a
contextual ized
m anner, and by using the same produ ct ( red w ine) in every
case. In contrast, none of the teachers in the co m parison group tried to pro-
vide a context for students wh en dealing w ith variation in the elasticity of
demand and
supply,
nor did
they
use the
sam e goods
as a
context
for
learn-
ing th roughou t th e lessons.
Res ul t s of the S t u d y
The key
findings
of this study can be categorized into three areas: nam ely,
the
enac ted objects
o f
learning, student learning,
and the
relat ionship
be-
tween the enacted objects o f learning and student learning.
The En ac t e d Objects
of
Learning
A ll the teachers, in both the learning study group and lesson study group,
focused
on the
object
of
learning that
had
been agreed
on ,
that
is, to
help
students
to
develop
the
capability
of
taking into consideration
the
relative
elast ici ty
of demand and supply when looking at the incidence of a sales
tax .
Th e teachers did not begin by thinking abo ut c lassroom organizat ion;
or the teaching arrangements to be used; whether there would be group
work or
ind ividual study;
or
w hether they w ould
use
in format ion technol-
ogy
o r
no t. Instea d, they paid great attention
to the w ay in
w hich they should
deal wi th the objec t o f learning in the lessons.
The two
commonali t ies between
the two
groups that were identified
in
the intended object o f learning (i.e., the bu i lding up of a relevance structure
for
students and the introduction of variation in elasticity of demand and
supply
in a
sequ ential m anner) w ere also found
in the
a ctual enactment
of
the intended object o f learning (i.e., the enacted object o f learning) . How -
ever,
of the three critica l
difference s
be tween the tw o groups tha t w ere iden-
t ified in the intended object of learning, only the
second
and third critical
differences were
found
in the enacted object of learning. The teachers in the
theory-inspired group introduced simultaneous variation and contextu-
alized variation whereas those in the comparison group did not . The first
critical
difference,
w h ich is the solicitation of studen ts' existing understand-
ing of phenomenon, was not found because the students in the theory-in-
spired grou p were inhibited by a num ber of things, including the presence o f
a
cam era, an observer, and the use of Eng lish as the m ediu m of instruction.
In the intragroup comparison regarding the building up of a relevance
structure for
students
( as
shown
in
Table 8.7), three teac hers
in the
learning
study
group (Teachers 1 ,2,
and 3) did not
follow
the
agreed lesson plan,
an d
did not employ the example of an authentic gasoline bill to illustrate how
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8.
T O W A R D
A P E D A G O G Y O F L E A R N I N G 21 9
sales tax appears in daily transactions. Although al l of the teachers at-
tem pted to reveal the studen ts '
different
w ays of unders tanding the dis t ribu-
tion of the tax burden between buyers and sellers (using th e exam ple of a
sales tax imposed on red wine), only three of them (Teachers 1, 3, and 4)
con duc ted a m inisurvey inviting students to express their view s. This part of
the lesson plan wa s not very
successful
in any of the classes bec au se o f the
reluctance of students to speak up generally in class.
However, al l teachers in the learning study group introduced simulta-
neo us variat ion
in
elasticity
o f
demand
and
supp ly (al thou gh Teacher
3 did
it m ore successfu l ly and wi th more s tudent con tr ibut ion than other teach-
ers). W ith regard
to the
contextualizat ion
and
consis tency
of
contexts ,
all
teachers in th is group organized their lessons us ing red w ine as the ex am ple
product . Three of the teach ers (T eachers 1 ,2, and 3) kep t this pro du ct invari-
ant throug hou t al l the lessons in order to m ake the s im ul taneou s variation in
elasticity
of dem and and supply eas ier to discern, w hereas Teacher 4 and
Teacher 5 did not u se it in the last lesson .
Table 8.8 show s that all teachers in the lesson s tudy group succe eded in
carrying out
w h a t
w as
stated
in the
lesson plan ,
and
tha t som e
o f
them in tro-
duced a ddit iona l tasks to enha nce the o riginal lesson plan . In order to bu ild
up a relevance s t ructure for the students to learn the top ic , Teacher 8 further
added
h i s own
personal experiences
of
sales
tax (from the
t im e when
he
lived in Can ada som e years before) , and brough t in a "giveaway" i tem from
a gasol ine s tat ion (a box of t i ssues) , which he showed together wi th the
w orkshee t on the gasoline bil l . Teacher 7 designed an ex tra w orkshe et in or-
der to he lp s tude nts to acqu ire the ski ll s to t ransform nu m erical data in to
graph format , and find out the tax burden be tween buyers and sel lers .
Final ly ,
w hen int roducing variat ion
in
elasticity
of
de ma n d
and
supply
s e-
quent ial ly , Teacher
9
further
included extrem e cases that were
no t
covered
in
the
lesson plan, such
a s
perfect ly elas tic dem and,
perfect ly
inelas t ic
de -
m a n d ,
perfect ly
elas t ic supply
and
pe rfect ly inelas t ic supply.
S t u d en t Learning
(The
Lived
Object
of Learning)
In
phenomenography ,
learn ing
is defined as a cha nge in the dynam ic s tate
of awareness
or the way of
experiencing (Pong
&
Marton, 2001) . Hen ce,
the present study describes student learning
in
accordance wi th s tudent
ways of experiencing the phenomenon or concept ions
identif ied,
rather
than merely count ing the percentage of s tudents who gave the correct
w ords or num bers as answers to quest ions set in a diagnost ic tes t . Studen ts
are said to have shown evidence of learning if they can successfu l ly display
advanced and pow erful concept ions of the phen om enon in quest ion.
A total of 356 students part icipated in the m ain study, in w hich Scho ol A
to School
E
belonged
to the
learning study group,
and
School
P to
School
T
belonge d to the lesson s tudy group. A l l s tudents were required to com plete a
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[3 TABLE 8.8
®
Comparison With in
the Lesson
Study
Gro u p
—
The
Enacted Objects
o f
Learning
Teacher 6
B ui l t
u p
re levance st ructure
Y es
Revealed varia t ion in the s tudents ' No
ways o f u n de rs t an d i n g
Int roduced varia t ion in the Yes
d i men s i o n s
o f
e l a s t i c i t y
o f
deman d
and
su p p l y
in a
sequent ia l manner
In t roduced varia t ion
in the
c r i t ica l
N o
aspect of re la t ive e last ic i ty o f
demand and su p p l y in a
s i mu l t an eo u s man n e r
Co n t ex t u a l i / a t i o n a nd consistency N o
of contexts
Teacher
7
Y es
N o
Y es
(Add-on:
an
ex t ra
worksheet
o n
g rap h i ca l
representa t ion
of tax
i n c i den ce )
N o
N o
Teacher 8 Teacher 9
Yes Yes
(Add-on :
personal
stories about sa les t ax
an d g i veaw ay s f ro m
g aso l i n e s t a t i o n )
N o N o
Yes Yes
(Add-on: discussion
on
ex t reme cases)
N o N o
N o
N o
Teacher
10
Y es
Part ia l ly effected
(Di d
no t
co n du c t
a
class
su rvey)
Y es
(A dd- o n :
an
ext ra
workshee t on
g rap h i ca l
representa t ion of tax
i n c i den ce )
N o
N o
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8. TOWARD A PEDAGOGY OF LEARNING 221
written task at the end of the series of lessons, and five students from each
class were chosen randomly
to
attend
an
interview
on the
same
day as the
last
lesson.
T he
data that were co llected
from
these
tw o
sources were an a-
lyzed, and the way s of experiencing that w ere iden tif ied w ere then catego-
rized
in
accordance wi th
the
outcome space (which
w as
described
in the
previous sect ion) .
T he
learning outcomes
( in
term s
of the
concept ions
de-
veloped by s tudents) are reported on a group basis , wi th a comparison m ade
between
the
learning study group
an d the
lesson study group,
as
we l l
as be-
tween classes w i thin each group.
T he
major qual i t a t ive difference
in the
unders tanding
of the tax
inci-
dence
lay in the
s tuden ts ' unders tanding
of the
s im ul taneous interaction
be-
tween the demand and supply s ide of the market ( i .e . , the s imul taneous
r e la t ionsh ip
betw een the elas t ic i ty of dem and and supply) . Abou t 73% of
th e learning study
group managed to show this
u nderstanding,
and
mani -
fested Concept ion
F ,
w hich took into accou nt
the
relat ive elast ici ty
of de-
m and and sup ply in determining the dis t ribution of the tax burden betw een
buyers and sel lers. In the lesson study g roup, ju st un der 30% of the studen ts
reac hed th is level of und erstan ding. The deta i ls are shown in Table 8.9.
A s
regards intragroup variat ion in the learning study group, there were
marked
d i f ferences in the
s tudents ' learning ou tcom e am ong
the
classes.
A s
w e
can see in
Table 8.10, School
C had the
bes t per formance w i th
the
w ri t-
ten
task, with 80.0%
of the
students expressing Conception
F in
thei r
an-
swers . S chool A ( 77.5%) fol low ed, and then School B (72.5%), School D
(66 .7%) , and
School
E
(60.7%).
T A B L E
8.9
Distribution of Conceptions for the Written Task
The Learning
Study Group
The Lesson
S tudy G roup
(181
students)
(175
students)
Group
Conception
A
B
C
D
E
F
Occurrence
9
4
8
25
4
131
Percentage
5.0%
2.2%
4.4%
13.8%
2.2%
72.4%
Occurrence
19
15
17
66
7
51
Percentage
10.9%
8.6%
9.7%
37.7%
4.0%
29.1%
Note. Chi - square
=
67.553
(df=
5;p< 0.001) .
N o
cel ls (0.0%)
have expected
coun ts
of
less than
5.
T he
m i n i m u m expected
count is
5 . 41 .
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2 2 2 L O E T A L .
TABLE 8 . 1 0
Distribution of Conceptions W i t h in th e
Learning
S t u d y G r ou p —
Th e
Written Task
School
A
Conception (40)
A 1
(2 .5%)
B 1
(2.5%)
C 1
(2.5%)
D 5
(12.5%)
E 1
(2.5%)
F 31
(77.5%)
B
(40)
2
(5.0%)
1
(2.5%)
1
(2.5%)
6
(15.0%)
1
(2.5%)
29
(72.5%)
C
(40)
2
(5.0%)
0
(0.0%)
2
(5 .0%)
4
(10.0%)
0
(0.0%)
32
(80.0%)
D
(33)
2
( 6 . 1 % )
1
(3.0%)
1
(3.0%)
6
(18 .2%)
1
(3.0%)
22
(66.7%)
E
(28)
2
( 7 . 1 % )
1
(3 .6%)
3
( 10 .7% )
4
(14.3%)
1
(3.6%)
17
(60.7%)
Total
N u m be r o f
Conceptions
9
(5 .0%)
4
(2 .2%)
8
(4 .4%)
25
(13 .8% )
4
(2 .2%)
1 31
(72.4%)
In the
lesson study group,
as
shown
in
Table 8 .11 ,
the
percen tage
o f
Con-
cept ion
F was
s imi lar am ong
the
classes, w ith School
T
recording
the
h i g h -
est
score (38.5%), followed
by
School
S
(35.3%), School
R
(33.3%), School
Q
(20.8%),
and
School
P
(20.0%).
T h e Rel a t i o ns h i p Between th e E na cted
Objects
of L e a r n i n g an d S t u d e n t L e a r n i n g
T he d ifferences in the enacted object of learning (as show n by the different
patterns
of
variat ion made avai lable
in the
classrooms), were
ref lected in
student learning in term s of the ways of experiencing that were m anifes ted
by students
after
the lessons . The aspects of the phe nom eno n
that
s tudents
discerned m irrored the pattern of var ia t ions, m ore
specifical ly,
the obje ct of
learning experienced
by the
students
in the
class.
A s
seen
in the
data
o n
stu-
dent learning, the s tudents in the learning s tud y group (w ho were presen ted
with this par t icular pat tern of var iat ion) , learned more effectively than
those
in the
lesson study group.
Furtherm ore, w ithin the learn ing study group, the d ifferences in s tudents '
performance also seemed
to
coincide wi th
the differences in the
pa t tern
of
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8. T O W A R D
A
P E D A G O G Y
O F
L E A R N I N G
223
T A B L E
8 . 1 1
Distr ibut ion
of Conceptions W ith in the
Lesson
S t u d y
G r o u p —
The
Written Task
School
P
Concept ion (25)
A
4
(16.0%)
B 3
(12 .0%)
C 1
(4.0%)
D 12
(48.0%)
E 0
(0.0%)
F 5
(20.0%)
Q
(53)
5
(9.4%)
3
(5 .7%)
3
(5.7%)
29
(54.7%)
2
(3.8%)
1 1
(20.8%)
R
(24)
4
(14 .3%)
3
( 12 .5% )
5
(20.8%)
3
(12.5%)
1
(4.2%)
8
(33.3%)
S
(34)
3
(8.8%)
2
(5.9%)
6
(17.6%)
8
(23.5%)
3
(8.8%)
12
(35.3%)
T
(39)
3
(7.7%)
4
(10.3%)
2
(5 .1%)
14
(35.9%)
1
(2.6%)
15
(38.5%)
Total
N u m b e r
o f
Concept ions
19
(10 .6%)
15
(8 .6%)
17
(9.7%)
66
(37.7%)
7
(4.0%)
51
(29 .1%)
variation m ade available in each classroom . For instance, Teacher 3 allow ed
more
flexibility
for students to introduce simultaneous variation in both
elasticity
of
demand
a nd
supply,
and at the
same time used
the
context
o f the
red
wine throughout
all the
lessons.
In
con trast,
Teacher
5 did not
allow
as
m u c h
flexibility
for students to introduce simultaneous variation, and did
not keep the product invariant for the last session. It w as co nseq uen tly found
that the students tau gh t by T eacher 3 achieved a better u nderstanding of the
topic than the s tudents taugh t by T eacher 5, a
finding
that m ight be attribut-
able
to the
pattern
of
variation made available
in the
lessons.
Reflec t ions
on the Study
From an analy sis of the teach ing in terms of the dim ensions of variation that
were opened up in the lessons—that is, those aspects that were varied si-
mul taneous ly and those aspects that remained invariant—the pattern of
variation critical
to the
developm ent
of an economic
un derstanding
of the
incidence o f a sales tax became apparent. T he teachers in the learning study
group handled the object of learning in a w ay that was pow erful in enhanc-
ing studen t learning. They did this by
focusing
o n the object of learning and
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224 LO ET AL.
opening up s imultaneous var ia t ion in its critical aspects—that is, they
opened up the
relative
elasticity of demand and supply in a contextual ized
manner , and deliberately kept the product (red wine) invariant so that stu-
dents could
experience
a change in the way that they were aw are of the phe -
nomenon
in
quest ion. This approach wi l l
be he lp fu l to
teachers dealing
with
the
same object
of
learning.
In this study, the theory of variation w as examined in relation to its
effi-
cacy
when used
to
design
an effective
learning environm ent . From
the
data
on the
teaching methods
and the
students' learning,
the
learning study
(which bu i lt
on the
theory
of
variat ion)
w as
found
to be
very
effective in en-
hancing learning
in the
econom ics classroom ,
in
term s
o f the
possibil i ty
fo r
teachers
to
identify
critical aspects related
to
different
w a y s
o f
unders tand-
ing and to design the learning si tuation arou nd these cri t ical aspects. T his
m ethod w as foun d to considerably enhance the s tudents ' unde rs tandin g of
the phen om enon in que stion, that is , the inciden ce of a sales tax. Th e study
thus supports the tenet of the theory o f variat ion, tha t lea rnin g to see som e-
thing
in a
certain
w ay is a funct ion o f
experiencing s im ul tane ou s variation
in critical aspects
of the
object
of
l earn ing .
Finally, the f indings of the study seem to suggest that the col laborat ion
between teachers
in a
learning s tudy prem ised
on a specific
theory
o f
learn-
ing
( in this case, the learning study group prem ised on the theory of varia-
tion), is more effective than teachers w ork ing together w i thou t an expl ic i t
theoretical grounding
(as in the
lesson study group).
A s w e
m ent ioned ear-
lier,
more than twice
as
many s tudents
f rom the
learning s tudy group
reached a good u nders tanding of the topic of the incidence of a sales tax as
students in classes of the lesson study group. Th is
further
supports the no-
tion that
the
learning study
w as more
effective than
th e
lesson study
in al-
lowing teachers to im prove their teach ing , and thereby h elp students to leam
more
efficiently.
C O N C L U D I N G REMARKS:
L EARNI NG FROM L EARNI NG S T UDI ES
In
th is chapter, w e presented three ex am ples of s tudies aimed at im provin g
learning from the po in t o f view of the theore t i ca l background brief ly intro-
duced
in
chapter
1, and the
descript ive em pirical studies presen ted
in
chap-
ters
2
through chapter
7 . Our
basic idea
fo r
fac i l i ta t ing
more
effective
learning is thus as fol low s: Take as the po in t o f depar ture w hat it is tha t the
students
are
expected
to
learn ( the object
o f
learning);
f ind out
w h a t m a k e s
the difference betw een the stude nts w ho have a good grasp, and those w ho
do not; construct a space of l earn ing tha t makes i t po ssible for all s tudents to
have a good grasp of wh at is to be learne d; and finally, an aly ze the relat io n-
ship
between the
space
of
learning
a nd
wha t happened
in the
classroom (the
enacted object of l earn ing) , and the w ay in w hic h th i s re la t ionsh ip affected
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8. T O W A R D A P E D A G O G Y O F L E A R N I N G 225
the learning outcom es ( i .e . , w hat th e s tudents have achieved). In our view, it
is th is procedure— w hich w as fol low ed by all the teachers in the three learn-
ing studies reported
in
th i s chap ter—that
led to the
success fu l learning out-
comes
as
evidenced
by the
study findings.
A ll
the
studies
in
this chapter
had
certain features
in
c o mmo n :
the
same
theoretical grounding and systematic evaluation, a focus on the object of
learning,
and
condit ions that enabled teachers
to
work collaboratively.
T he
first
study in this
chapter
was a clear dem onstration of how teachers
m ade u se of the theory of variat ion as a ped ago gical tool . However, we saw
that even
if the
teachers
had
previously agreed
on
wha t
to do in the
class-
room , when they carr ied
o ut the
actu al lesson, ea ch lesson
differed in a
n u m -
ber of important respects (as i s wel l demonstrated by the second s tudy
reported
in
this chapter).
T o the
extent that such
d i f ferences are
recogn ized,
they can be seen to accoun t for di f ferences in the learning outcomes ( the
l ived ob jec t
o f
learning) .
In the
second study,
the
better perform ance
o f the
studen ts in Clas s 4C over those in Class 4H in the po sttest can be at tributed
to the difference s in the enacted objects of learning in the respective lessons.
Learning to focus on the c ri t ical aspects o f the object o f learning through the
use
of an
appropriate pattern
of
variation
is not
easy,
and
does
n ot
come nat-
ural ly even
to
experienced teachers .
T he
th i rd s tudy quo ted
in
th is chapter
showed that teaching and learning w as m u c h more
effective
when the teach-
ers
were gu ided
by the
theory
of
variat ion.
B y creating the co nditions fo r teachers to work together a s a team using
an act ion research approach, we enable teachers to learn and develop to-
gether. In fact, the bene f i ts go
beyond this .
T he
three learning studies show
that the process of designing, co nduct ing, and evaluat ing research lessons
benef i t ted a ll three parties: the students, the teachers, and the researchers .
The students gained a better understanding of the object of learning, the
teachers learned
how to
handle
the
object
of
learning
in a
more
effective
way, and the researchers gamed further insight into the ways in wh ich the-
ory can be
translated into practice.
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Epilogue
There is a widely held bel ief today that knowledge is becoming increas-
ingly impor tan t
in the
l ives
of
individuals
and in the
lives
o f
nat ions .
I f
this
is t rue, wh at kind of conclusion can be drawn
from
the studies reported in
this
book
w i th regard to faci l i tat ing the developm ent of know ledge on indi-
vidual and c ollec t ive levels?
The quest ion of prom oting the growth of know ledge can, of course, be
addressed
from
p ol i tical , econom ic,
a nd
social points
o f
view .
Our
perspec-
tive,
however, is pedagogical; w e are concerned w ith teaching and learning.
Teaching is a human act ivi ty involving someone teaching something to
someone else . There
is
someone teaching
(a
teacher) , someone t augh t
(a
learner or learners) and something taught ( the content) . In grammatical
terms, th e learner is the dative (indirect o bject), an d the content is the accu-
sative (direct object).
T he failure to
focus
o n
both
of these tw o
objects
at the
same t im e has hau nted educat ion for centuries . Foc us has , in the ma in, been
on on e or the other, but rarely on both at the sam e t im e. In one instan ce, the
emphas i s
has
been
on the
teacher
an d the
learner;
in
another ins tance,
the
emphasis
has
been
on the
teacher
and the
content
Learner-focused e ducat ion, w here the
focus
is on the learner, and on the
w a y s
in
wh ich teach ing
is adjusted to the
learner 's nee ds,
h as
very m uc h co l -
ored the 20th century movement cal led "progressivism." T he m ajor ity of
university educationalists in the W est probably subscribe to this orientation.
Where the
focus
is on the content , that i s , on the knowledge to be
learned, we ca l l th i s the " t radi tional i st " approach to educa t ion . A cco rding
to this approach, the mos t im por tan t th ing is that the t eacher has a good
mastery of the
content;
he or she has to be
good
at
w h a t
her
students
are
supposed
to
become good
at . For the
t radi t ional is t approach,
it is of
pri-
mary impor tance tha t the s tudents a re exposed to cer tain k inds o f con t en t ;
227
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228 E P I L O G U E
w hat i s covered in t each ing i s v i t a l . Th e "back to bas ics" m ove m en ts be-
long to this school of thought .
In the politics of education, these tw o orientat ions—progressivist and
t radit ionalist— have replaced each other
in an
ever-recum ng cycle
o f
peda-
gogical fashio n. This w e bel ieve is a m a jo r obs tac l e to improv ing pedagog i -
cal pract ices . In fact, pedagog ica l p rac t i ces w i ll o n l y i mp r o ve w h e n equa l
considerat ion
is
given
to
both
the
learner
a nd the
c o n t e n t .
T he
reason
w hy
both or ientations m ust be considered together i s very s im ple: There can be
no learning without a learner, nor can there be any l earn ing w i thout some-
thing learned. W e therefore ha ve to foc us both on the learner and o n the co n-
tent
o f
learning
at the
s ame tim e .
Let us
look
a t the
qu e s t io n "W h a t
is to be
l earned?"
In the
p a s t ,
sy l l a -
buses w ere fo rm ula t ed
in
te rm s
o f
ca t ego r i e s
of
c o n t e n t .
T he
qu e s t i o n
o f
W h a t is to be learned? w as answered in t e rm s o f d i f ferent par ts o f ma t h e -
matics, history, English, philosophy, and so on (e .g . . f ract ions , second-
grade equat ions ,
th e
French Revolu t ion , Wor ld
W ar I I,
i r regular verbs .
Ch uang Tzu , e t c . ).
B u t
w h a t
is to be
l earned
i s
never s im p ly
a
case
o f
f rac-
t ions
o r
C h u a n g T zu ,
o r
a n y t h i n g
of the
l ik e . W h a t
is to be
l ea rned
is
c a p a -
b i li ti es , tha t i s , w ha t the s tude nts a re expec ted to becom e cap ab le o f do in g
( in the widest sense). F or example , be ing ab le to express quant i t i es in
terms o f rat ional num bers , an d carry o u t ar i thme t ic o pera t ions w i th ra t io-
na l
numbers;
o r
having
an
unde rs tanding
o f
Chuan g Tzu 's v i ew
of
h u m a n
exis tence ,
an d
be ing ab le
to see
c o n t em p o r ar y p h e n o m e n a
in l i g h t of his
concep t ion o f Tao i sm.
Such ca pab i l i t ies are w h a t w e re fer red to in th i s book as the o bjec ts o f
learning. The concept of an
objec t o f learn ing
inc lud es bo th the learner
and the con tent; it is def ined in terms of the con tent i t sel f ( referred to as the
direct object o f learn ing in chap . 1) and in term s of the learn er ' s way of
handl ing
the
c on ten t ( re fer red
to as the
ind irec t objec t
of
learn ing
in
c h a p .
1 ).
Thus , w e canno t ta l k abou t th e ob j ec t o f l e a r n in g w i t h o u t r e f e r ri n g to
th e learner an d the con t en t a t the s ame t i me . O u r p o i n t i s
tha t
th e p r i ma r y
focus o f educat ion should be on bo th the l earner and the co nten t , and no t
on one o f them alone. Fai lure to focus o n bo th w i l l resu l t in lopsided per-
spect ives .
N o t
p a y i n g a t t e n t i o n
to the
l earners ,
to how
t h e y ma k e
sense—or should make sense—
of the
c o n t e n t , r e s u l t s
in an
e m p h a s is
on
j u s t w ha t i s covered— or shou ld be covered— by t each e r s "who know the i r
sub jec t ," and no t how the con ten t is handled, o r shou ld be ha nd led.
Currently, however, content tends
to be
u nderp layed
in
W estern educa-
t ional thinking, result ing in the resurgence of tw o i l lus ion s, albeit in
differ-
ent forms . O ne i l lus ion is the old dream of f inding "the art of t each ing all
th ings to all men." This phrase first appeared in the
subti t le
of C o m e n iu s '
book The
G reat Didact ics in
1657, w hich
i s
seen
as the
first sys t em at ic
at-
tempt to develop a science of teach ing. B ut the dream that w e can teac h any -
thing to anyone, i f only w e can find the r ight m ethod, i s probably older tha n
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E P I L O G U E 229
that .
It is
s t i l l very m uch al ive today, a l tho ugh
the
m ethods people com e
up
wi th
differ, of course , f rom t im e to time. Cu rrent ly m any people a re ta lk in g
abou t cooperative learning, IT-supported forms of learning, project work,
problem-based learning, and so on as the
pa ths
to the perfec t art of
t each ing .
However , after reading this
book;
it should be quite c lear that there are
specif ic
con dit ions necessary fo r learning spe cif ic objects o f lea rn ing . T he
condit ions differ from one ob jec t o f learning to another , and we have to find
out in each par t icular case w ha t these con dit ions are .
Peer
learning , IT sup-
por t , project work,
and
problem-based learning
may be
a r r angements
fo r
learning
that have great po tent ia l , but no general approach to instruct ion can
ever ensure that th e spe cif ic con dit ions necessary fo r the lea rn ing of
spec i f ic
objects
o f learning are brou ght about . In order to do this , w e m ust take the
specif ic ob jec ts
o f
learning
as our
poin ts
o f
depar ture .
The o ther i l lus ion i s about "gener ic capabi l i t ie s . " The cur rent l ine of
r ea son ing
goes
som e th ing like the f o l l o w i n g : W e a re f ac ing an e x p o n e n -
t ia l growth of knowledge . Widespread use of IT and the In te rne t a round
the g lobe , m eans th a t bas ica l ly a l l of th is know ledge i s ava i lab le to every -
one . As we do no t know w ha t k ind o f know ledge our s tuden t s w i l l need
wh en they grow up , the bes t th in g w e can do i s to equip them w i th ca pa bi l i -
t ies
fo r
ob ta in ing know ledge ins tead
o f
e q u i p p i n g t h e m w i t h k n o w l e dg e .
Thus
the e m p h a s i s is on gener ic capabi l i t ie s , such a s learning to l e a rn ,
r ead ing to lea rn , lea rn ing s t ra tegies , th inking s t ra tegies , coopera t ive
sk i l l s , com m un ica t ive sk i l l s , flex ib i l i ty , c rea t iv ity , and so on . W h a t is of-
ten
f o rgo t t en is tha t knowledge is
fu n dam en ta l ly
w a y s of seeing the w o r ld .
Gener i c cap ab i l i t ie s
do
exist ,
but not as
ind iv id ua l t ra i ts ,
or as a
type
of in-
t e l l ec tua l
musc le tha t deve lops independent ly f rom knowledge
a nd
c o n -
t en t . Gene r ic capab i l i t i e s a re w a y s o f dea l ing wi th dif ferent top ic s ,
con ten t ,
knowledge ; they do not re fe r to what peop le have o r w ha t they
are ; they re fe r to w ays in w hich
peop le
ac t . Gener ic cap abi l i t ie s a re do-
m a i n
spec i f i c . T he
fact
tha t a
person p ossesses
the capab i l i ty o f, say, ha n-
d l ing words c rea t ive ly , does
n o t
necessa r i ly imply tha t
th e
pe r son
possesses the capabi l i ty of dea l ing wi th num bers , m usica l or l ing uis t ic
tones , or econom ic t ransac t ions in the same w ay. Gen er ic capa bi l i t ie s de-
velop th roug h hand l ing som e th ing spec i f ic :
th e
m othe r tongue , c a lcu lus ,
q ues t ions
abou t the ecolo gical survival of our planet , and so on.
There seems to be another widely held bel ief , par t icular ly am ong educ a-
t ional
pol icymak ers , tha t language
is the
object
o f
inquiry
o f
l inguis ts ,
and
p ay in g a t tent ion to lang uag e pedag ogica l ly is the responsibi l ity of l an g u ag e
teachers
only . Discuss ions about lang uage in the context o f educa t ion have
la rge ly
f ocused on i s sues o f ef fect iveness a nd
efficiency
in a t ta in ing lan-
guage prof ic ien cy. W e hear concerns expressed by the com m unity about the
dec l in ing langu age standards of
both
learners and teachers , and that som e-
th ing
m ust be done about the language prof ic iency of language teachers and
learners .
W e
seldom hear com pla in ts about
the
lack
o f
a t tent ion paid
to
I an-
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230
E P I L O G U E
guage by subject teachers, such as teachers of mathemat ics , science, and
history.
N or do we
hear discussions abo ut
the effects of the use of
l anguage
on the
learning
of m athemat ical concepts, scientific concepts, and h istorical
concepts, fo r exam ple. T he relationship between lang ua ge and learning has
been narrowly confi rmed
to
language learning.
The exposit ion of the importance of the role of langua ge in bringing abou t
learning
is not
som ething new. Several decades ago, especially
in the
1970s,
a
number
of
scholars
had
already drawn attention
to the
importance
of
lan-
guage in education, and had made a strong case for p aying at tent ion to lan-
guage across
the
curriculum (see, e.g., Barnes, 1976; Barnes, Britton,
&
R osen, 1969; B ritton, 1970). P articu larly inf luential
w as the
work
of
M ich ae l
Halliday, wh o
showed that w hen
a
c hi ld leams
a
l anguage ,
he or she is not
j u s t
engaged
in one
kind
o f
learning,
bu t is
learning
the
foundations
of
learning
it -
self: Learning
is a
process
of
making meaning ,
an d
l earn ing language
is
learn-
ing how to m ean (see, e.g., Ha lliday , 1973, 1975, 1978, 1 993). T here fore , it
w as
argued, every teacher
is a
language teacher .
At the
t im e, wh en
the
lan-
guage awareness movem ent
w as
l aunched
in the
U ni ted Kingdom , l anguage
in
education w as made a compulsory m odule in teacher education programs
(see Hawkins, 1984).
T he
"language across
the
cur r icu lum "
initiative,
w h i ch
is one o f the
most important moves
in
educat ion ,
w as
unfortunately
not
sus-
tained (see Hawkins, 1999).
Wha t
w e
have tried
to do in
this book
is to
re vital ize
the
discuss ion about
th e
role
of language in learning by showing th e critical role that language
plays in bringing abou t the necessary co ndit ions fo r l earn ing . O ne necessary
condit ion
for
bringing abou t learning
is
that students
are
able
to focus on the
object
of
learning
and
discern
i ts
c ri t ical features.
W e
have dem onstrated that
language
is
crucial
in
structuring studen ts ' aw areness
so
tha t they become
fo-
cally aware
o f the
critical fea tures
of the
object
of
learning,
in
bringing about
simu ltaneo us awareness, both sync hron ically
and diachromcal ly , and in
ma k -
ing important conceptual dist inctions. W e have dem onstrated tha t because
language m akes meaning,
the
ability
of the
students
and the
t eacher
to
neg ot i-
ate
meaning
and to
const ruct meaning col laborat ively through language
makes qualitative d ifferences in the sem antic dime nsion of the space of learn-
ing
that
is
being c onsti tuted. A nother necessary co ndit ion
for
b r ing ing about
learning
i s
that
th e
space
of
learning
is
shared
by the
s tudents
and the
teacher.
W e
have dem onstrated that language plays
a
cri t ical role
in
es tabl ishing
as
wel l
as in
widening
a
shared comm on ground. W hen
the
ground
on
w h i c h
a
specific
object
o f
learning
is
enacted,
is not
shared,
th e
qu al i ty
of
learning wil l
be
adversely affected.
W e
have shown
the difference
l anguage makes
by
com-
paring
the
classroom discourse
of
students learning through their mother
tongue w ith that
o f
students learning through
a
second
and
w eaker language.
When students
a re
learning through
a
languag e that they
can
barely
use to ex-
press
themselves, they are inevitably handicapped because they do not have
the necessary resources for mak ing mean ing . There is a com m only he ld b e-
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E P I L O G U E 231
lief, especially am ong edu cational policym akers, that learning throu gh a sec-
ond
language is no more than learning the technical vocabulary in that
language. This simplistic view shows
a
lack
of
u nderstanding
of the
role
of
language
in
learning.
W hat we have demonstrated in th is book is that there are spec if ic condi-
t ions that
are
necessary
for the
learning
of specific
objects
of
learning.
T he
w ay
in which these o bjects of learning are handled and the extent to w hich
the necessary condi t ions are brough t about through languag e in the class-
room are of decisive importance for what the students can possibly learn
(and w hat they actua l ly learn).
There are, no doubt, general condit ions necessary for learning, such as
l ight , space, exposure, feedbac k, and a min im um level o f activity am ong the
learners.
There
m ight also be necessary condi t ions of learning that are spe-
cific to different groups. Some learners m ay not be able to learn som ething
wi thou t
sensu ous ex perience , for instance, w hile others are able to learn the
same thing
by
sym bol ic m eans ;
fo r
some there
m ay be a
great difference
be-
tween actual ly seeing som ething and ju s t hear ing som ething descr ibed,
w hereas for others there m ay not be an y difference at all . B ut we are not talk-
ing
ab out necessary condi t ions
for all
kinds
o f
learning,
or
about necessary
condit ions for specif ic groups of learners, but about necessary condi t ions
for the
learning
o f
specific objects
of
learning . These con dit ion s have
to be
discovered for every specific object of learning. Teachers should be en-
gaged in f inding out w h a t the spec if ic condit ions a re in every specif ic case,
and
h ow they can be brought about.
When these
con ditions are discovered,
teaching w i ll become
a
much m ore pow er fu l
and
m uch m ore profess ional
enterprise .
In the
last chapter
of
this book,
w e
described some teachers engaging
in
such
an
en terprise. They cam e together w i th spec if ic objects
o f
learning
as
their
po in t o f departure. They did not start w ith questions about general ar-
rangements
and
general teaching methods,
bu t
asked questions about
the
specif ic objec ts of learning to be dea lt w ith during a lesson or during a se-
quence
of
lessons. They also asked questions about
the
nature
o f the
capa-
bilit ies
they wanted
to
develop
in
their stude nts,
the
necessary condi t ions
for
developing these capa bi l it ies , how those condi t ions cou ld be m et , and the
kind o f
ar rangements
and
metho ds that could
b e
used
to
create these co ndi-
t ions. These
teachers
did not
start w ith questions abo ut generic at tributes;
they
asked quest ions about
how
domain
spec if ic
g eneric at tributes co uld
be
embedded in the
specific
objects of learning.
W e
hope that
the
ex am ples described
in
th is book have succee ded
in il-
lus t rat ing
w ha t w e believe to be the three core elem ents necessary for dra-
mat ica l ly improving learning in schools. T he first e l emen t is a pr imary
focus
on the
objects
of
learning.
T he
second element
is a
collaborative
effort
am ong teachers in planning and enac t ing the o bjects of learning in the class-
r o o m, as we l l a s ref lect ions on the enactment that a re f i rmly focused on the
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232
E P I L O G U E
objects of learning. The third element is powerfu l theoretical tools that
guide this planning , enactm ent
and
ref lect ion:
a
theory
o f
learning
and a
the-
ory of the role o f languag e in learning. W e hope tha t th is book has dem on-
strated ho w
these
three elem ents together can m ake a
difference
in learning .
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Author Ind ex
Aldred, D. , 157
Alexandersson ,
M. , 165
B
B arnes, D. , 230
B e hr ,
M. , 72
Bere i t e r ,
C, 8
Ber l ine r , D. C., 8
Berry, M . , 1 13
Biggs , J. B., 62
Booth ,
S ., 8, 11 , 22, 89,
153, 165, 170, 193,
1 9 4 , 2 1 5
Bransford ,
Y. D., 8
Br i t t on , J., 26, 35, 230
B r o w n , A. L., 8, 191, 1 9 2 , 2 1 1
Brown, G. A. , 128
Bruner , J . , 166
Chros towsk i ,
S. J., 66
Cleverley ,
J., 60
C o ck in g ,
R. R., 8
Cohen , D. K., 190
Col l i ns , A . ,
191,
1 9 2 , 2 1 1
Cor tazz i ,
M . , 62
Gu s h i n g , K. S., 8
DeGroot , A. D., 7
Edmondson ,
R. , 128
Egan, D. E., 8
Ehr l i ch , K., 8
Findel l ,
B., 190
Car l s son ,
B., 23
Carpenter, . P., 14
C e s t a n , M . L., 32, 33, 34
Chan , S., 141
Chase , W . G., 8
Cheng, K. M., 61
C h i , M. T. H., 8
Chik , P . ,
1 3 , 43 , 91 ,
1 21
Garden , R. A., 66
Gardner, H. , 60
G laser, R ., 8
Gonzales, E. J . , 66
Gregory ,
K. D., 66
Gu, L., 56, 57, 58, 59, 60
G u r w i c h , A. , 19
239
H
E
F
G
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240
A U T H O R I N D E X
H
Hall iday,
M. A. K., 24, 25, 26, 27, 28,
139,
1 7 9 , 2 3 0
Harel ,
G., 72
H a w k i n s , E., 230
Hiebert,
J., 45, 66, 191
H i l l ,
H . C . ,
1 90
Ho, D. Y. F., 62
Hoare ,
P., 143
Hua ng ,
R., 62
J
J in ,
L. , 62
K
Kan, F., 157
Kilpat r ick, J . , 190
Ko, P. Y., 1 0 ,4 6 , 91 , 167
Kress,
G. , 117
K w a n , T . , 4 3 , 9 1
N g , P . P . , 43, 91 , 11 4
o
O ' C o n n o r ,
K. M ., 66
O gb or n , J . , 117
Paine , L . , 6 1 , 6 2
Pa ng , M. F., 91
P o n g , W . Y . , 2 1 9
Po st, T., 72
Pow, S., 121
Qian ,
M ., 46
R
Rosen, H. , 230
Ru nesson, U. , 67, 91, 1 21, 157
Lamon, S . J . , 196
Lee, S., 61
Lee, W. O., 62
Lesg old, A. S . , 8
Lesh, R . , 72
L e u n g ,
Y. M . J. , 60
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1 0 , 9 1 ,
1 67
L undgr e n , U. P., 128
Lybeck, L. , 153
M
M a l i n o w s k i , B . , 27
M a r t i n , M. O., 66
Mar t ins , I . , 117
Mar t insson , M. , 153
Marlon, F., 8, 11, 22, 89, 91, 114, 153, 157,
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M atthiessen, C., 24, 139
McGi l l i cuddy, K. , 117
Mil le r ,
G. A , , 9
M o k ,
I . A.
C . , 7 5 , 9 1 ,
1 21
Moser, I. M., 14
Mo x ley ,
S. E., 15, 16
M ul l i s ,
I. V. S., 66
N
N e u m a n ,
D., 7
Sabers ,
D. S., 8
Sal jo ,
R., 90
Sapir, E. , 27
Scardamalia , M . , 8
Schwar tz , B. I. , 8
Seybol t ,
P. J., 60
S i m o n ,
H. A., 8
Sm ith, T. A. , 66
Soloway,
E., 8
Stevenson,
H. W ., 66, 67
Stevenson ,
W . , 61
Stigler, J. W ., 45, 66, 67, 1 91
Svensson , L., 11, 58, 74
SwafFord,
J., 190
T su i ,
A. B. M. ,
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V u o l a b , K., 28
W
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Wistedt, 1., 153
Wong, S . Y, 121
R
Q
S
TT
V
L
P
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242
S U B J E C T
I N D E X
M
M a t h e m a t i c s
lessons, 32-34, 36-37, 62-63,
66-73,75-84,86,91-94,
140-141, 196-203
div i s ion , 74
div i s ion-quot i en t , 92-93
Phy sics lessons , 1 17-1 21, 128-136,
169-170
reed relay , 114-121
Presuppos i t ions , 1 1 7 , 166,
1 78