introduction to the math for all professional development ... · to the math for all professional...
TRANSCRIPT
1
Introduction to the Math for All Professional Development
Program
W elcome to the Math for All professional development program. This book provides you with background information, materials, and
detailed instructions to guide you, as a facilitator, in the implementation of the Grade 3–5 Math for All workshop series. Since Math for All may be different from other professional development that you have provided or experienced yourself, this introduction will give you detailed information about the pur-poses, goals, content, and format of the professional development, so you will have a better sense of what to expect.
PURPOSE AND LEARNING GOALS
Math for All is a series of professional development workshops designed to enhance the preparation of general education and special education teachers to support all students, including those with disabilities, to achieve high-qual-ity, standards-based learning outcomes in mathematics. The workshop series introduces teachers to a process of collaborative lesson planning that is designed to support them in their efforts to make standards-based mathematics lessons accessible to students with different strengths and needs.1 This lesson planning process incorporates a neurodevelopmental theory of learning (see sidebar) to provide teachers with a framework for understanding the demands
1While the Math for All workshops focus primarily on improving learning outcomes for students with dis-abilities, the process for planning accessible lessons is suitable for any kind of student, including students who are receiving a response to intervention services, English language learners, gifted students, and general education students.
2 MATH FOR ALL FACILITATOR’S GUIDE (3–5)
of mathematical tasks and the strengths and needs that individual students bring to it. Key components of the lesson planning process include the following:
• Analyzing the goals of a math lesson and understanding how these goals relate to the mathematics that students studied prior to this lesson and that they will study in the future
• Analyzing the neurodevelopmental demands of the math lesson • Thinking about the neurodevelopmental strengths and needs of indi-
vidual students and how they will respond to the demands of the lesson • Selecting instructional strategies that address the strengths and needs of
individual students to make the lesson more accessible without chang-ing the mathematical goals
By engaging in this process of collaborative lesson planning in the context of videotaped case lessons and lessons that they carry out in their own classrooms, the professional development is designed to directly impact teachers’ knowledge and skills. Key learning outcomes for teachers include the following:
• Deepened understanding of and skill in analyz-ing the neurodevelopmental demands of math-ematical tasks
• Deepened understanding of and skill in assess-ing individual student’s neurodevelopmental strengths and needs
• Enhanced understanding of and skill in think-ing about the mathematics of specific lessons
• Deepened understanding of instructional strategies for teaching math and skill in selecting strategies to match individual students’ strengths and needs
Math for All also is designed to have a direct impact on teaching practices through classroom-based assign-ments that require teachers to observe individual stu-dents and to plan, implement, and reflect collaboratively on adaptations for specific mathematics lessons. Key outcomes for teaching practices include the following:
• Ongoing assessment of individual students • Use of instructional strategies, classroom struc-
tures, and materials that are responsive to indi-vidual students’ strengths and needs
• Pursuit of standards-based learning outcomes by all students, including those with disabilities
• Supportive teacher-student interactions • Increased collaboration among all the educators
who work with a child
The Neurodevelopmental Framework
Neurodevelopmental theory (e.g., Barringer, Pohlman, & Robinson, 2010; Levine, 2002; Pohlman, 2008) is based on the assumption that learning is not a one-dimensional pro-cess. Rather it involves eight different neuro-developmental systems or functions, which interact to enable students to acquire cer-tain knowledge and skills, or accomplish school tasks. The eight neurodevelopmental functions are as follows:
• Higher order thinking • Language • Spatial ordering • Sequential ordering • Memory • Attention • Psychosocial/social thinking • Motor coordination
Students must utilize these functions to varying degrees in order to succeed at dif-ferent learning activities, including math-ematical tasks. Each learner has a unique neurodevelopmental profile, a pattern of strengths and weaknesses in different neurodevelopmental functions. A learner’s profile can be more or less matched to the requirements or demands of different kinds of learning activities, which will influence his or her success at the task at hand. A learner’s neurodevelopmental
3INTRODUCTION
Math for All places a strong emphasis on the collabo-ration between general and special educators. Providing students with disabilities with access to significant mathe-matics content requires educators to draw on multiple bod-ies of knowledge, including knowledge of mathematics content and pedagogy, as well as knowledge of special education. Traditionally, these content areas have been part of separate disciplines (i.e., mathematics education, special education) and often reside in different people (e.g., classroom teachers and mathematics teacher lead-ers, or special education teachers and teacher leaders). Ideally, the Math for All workshops are co-facilitated by a math and a special education staff developer, so that they can build on each other’s expertise. Similarly, par-ticipants in the workshop series are intended to be teams of general and special education teachers who serve the same students at their schools. Where applicable, these teams also can include paraprofessionals or instruc-tional aides, math coaches, and instructional support specialists who work with the teachers.
CONTENT AND FORMAT
The Math for All program consists of video-case-based curriculum materials and learning activities that form the core of two workshop series for teachers who teach students in Grades K to5. One workshop series focuses on Grades K–2 and the other on Grades 3–5. Each work-shop series consists of five 6-hour sessions and is intended to be implemented over time during the school year, to make it possible for participants to apply what they have learned in their classrooms between workshop sessions. Each workshop series provides for 30 hours of class time (five 6-hour work-shops), plus 10 hours devoted to workshop-related assignments that partici-pants carry out in their classrooms. We also recommend spending at least 10 hours on follow-up meetings, for a total of 50 hours of professional develop-ment during the course of one school year.
The Math for All program has been carefully designed based on research related to learning and professional development. It has also been extensively piloted and field-tested with more than 600 teachers and 30 staff developers across the United States (see Appendix A for a summary of the research base). The mathematics content is aligned with the Common Core State Standards for Mathematics (CCSSO & NGA, 2010) and the Principles and Standards for School Mathematics of the National Council for Teachers of Mathematics (NCTM, 2000).
Each workshop session is organized around one particular case lesson. The case lessons vary in grade level (Grades 3, 4, or 5), the math content they
profile changes over time—each neurodevel-opmental function can grow in effectiveness, it can level off, or it can deteriorate. Many factors shape a learner’s profile, including genetic factors, family factors, cultural values, environmental influences, educa-tional experiences, physical health, peer influences, and emotional factors. Close observation and description of students’ strengths and weaknesses are necessary to understand their neurodevelopmental profiles.
To effectively support individual stu-dents, teachers should aim for manage-ment by profile. This means taking into consideration individual students’ strengths and weaknesses rather than focusing on isolated weak spots. Management by pro-file has multiple components. It involves demystification (helping students to under-stand their strengths and weaknesses), accommodations (building on students’ strengths to bypass their weaknesses), and interventions at the breakdown points (strengthening a student’s area of weak-ness). Teachers should take special care to bolster students’ strengths and affinities and to protect them from humiliation in an effort to nurture their sense of self-worth and efficacy.
4 MATH FOR ALL FACILITATOR’S GUIDE (3–5)
address, the strengths and needs that students who participate in the lesson have, and the kinds of adaptations the teachers use to increase the accessibil-ity of the lesson for their students. The case lessons were videotaped in general education classrooms that use standards-based math curricula (e.g., Every Day Mathematics and Investigations in Number, Data, and Space) and include students with disabilities. They capture typical practice in which teachers are successful in making math accessible to students with different strengths and needs, but the videotaped teachers also sometimes struggle to meet the needs of the broad range of students in their classrooms. The case lessons are not meant to serve as exemplary models that teachers should replicate. Instead, they are intended to be used as “objects to think with.” They give participants in the workshop a common reference for observing students, reflecting on practice, and thinking about how to solve problems that occur as part of everyday classroom practice.
The case lessons provide opportunities for teachers to apply the neurodevel-opmental framework that they are learning about as part of the Math for All workshops. The first workshop introduces teachers to the overall framework, while subsequent sessions focus on examining selected neurodevelopmental functions (language, memory, psychosocial functions, and higher order think-ing) in more detail. In conjunction with each workshop, teachers complete reading assignments that familiarize them with different aspects of the neuro-developmental framework (see workshop chapters for suggested reading assignments). And in each workshop, teachers have opportunities to discuss and apply their newly gained knowledge as they analyze the demands of math-ematical activities and the strengths and needs of individual students to help them select instructional strategies that make specific math lessons more acces-sible for these students. The workshops do not cover all of the eight neurodevel-opmental functions in detail. Instead, they introduce teachers to a process for using neurodevelopmental theory as an analytic lens in their lesson planning. Teachers are encouraged to continue their exploration of the neurodevelop-mental constructs not covered as they continue the process of collaborative lesson planning after the workshops end.
Each workshop addresses different math content. The case lessons, which are aligned with the content standards of the National Council for Teachers of Mathematics (NCTM, 2000) and the Common Core State Standards for Mathe-matics (CCSSO & NGA, 2010) address topics drawn from various strands of mathematics, including number and operations, data, geometry, and algebraic thinking. The Math for All workshops are not designed to provide teachers with new math knowledge, but rather help them deepen their understanding of the mathematical ideas with which they are most likely already familiar. In the workshops, teachers deeply engage in the math content of a variety of dif-ferent case lessons. They think deeply about the mathematical goals of these lessons and how the goals connect to other math concepts their students have studied and will study in the future. Participants examine how changes in materials and instructional strategies may impact these goals. The profes-sional development familiarizes teachers with a certain way of thinking about math content and offers them opportunities to make new connections between math concepts with which they are already familiar.
5INTRODUCTION
Each workshop highlights the experiences of a few focal students with and without disabilities. The focal children were chosen carefully by the case lesson teachers to reflect the range of students’ strengths and needs represented in their classrooms. The case teachers planned and adapted the videotaped lessons with the learning profiles of these focal students in mind. The focal students include children with a range of different kinds of disabilities (e.g., learning, speech and language, developmental, and behavioral disabilities). Several of the focal students are English language learners. The case lessons offer teachers the opportunity to explore the learning profiles of students with specific disabilities and those who are English language learners. Across the workshops, teachers will come to realize that even if students are diagnosed with the same disability or condition (e.g., a learning disability), their individual learning profiles can vary quite a bit. Teachers come to appreciate that diagnostic labels often are not very useful when it comes to instructional planning, and that there is a need for ongoing assessment to better understand individual students’ strengths and needs in relation to specific instructional activities.
All of the workshops illustrate adaptations that the case lesson teachers made to ensure that the lessons are more accessible to the full range of stu-dents in their classrooms. Adaptations refer to changes in a lesson, such as the use of materials or instructional strategies that are different from what is described in the curriculum guide, without changing the mathematical goals of the lesson. In some of the case lessons, the adaptations are relatively small (e.g., adding a handout or changing the way instructions are given), whereas in others the teachers redesigned the entire lesson (while still maintaining the mathematical goal of the original lesson). The workshops therefore offer teachers the opportunity to learn about the range of possible adaptations, to learn about specific instructional strategies that help to make math lessons more accessible, and to reflect on the decisions that the case lesson teachers made in their instructional planning.
As part of the workshops, teachers will spend a considerable amount of time analyzing and planning lessons following a carefully structured approach that includes identifying the mathematical goals of the lesson, analyzing the demands of the mathematical activities, thinking about individual students’ strengths and needs in relation to these demands, and planning adaptations that build on students’ strengths or address their needs without changing the mathematical goals of the lesson. By engaging in this process, teachers gain important insights into the nature of instructional differentiation. They will come to appreciate that making math lessons accessible to all students requires them to engage in an ongoing process of problem solving, decision making, and reflection, rather than simply applying instructional strategies “that work.” Often, there is no single approach that works for all students, and different students will need different types of support to reach the same goals. With repeated practice, teachers also will come to realize that there is no need to create individual lesson plans for each student in their classrooms. Instead, by focusing on a few focal students with different strengths and needs, and planning adaptations based on their neurodevelopmental profiles, teachers will find that their lessons become more accessible to many students in their classrooms.
6 MATH FOR ALL FACILITATOR’S GUIDE (3–5)
The instructional format of the workshops incorporates key components of constructivist pedagogy. These include deep inquiry into children’s thinking and behavior to provide the following:
• Guidance for responding differently to each learner in the classroom • The opportunity for reflection on classroom events to examine beliefs
and practices in relation to alternative approaches to particular situa-tions and in relation to theoretical ideas
• The opportunity for learning in groups where teachers can collabora-tively explore ideas, make plans, learn from analyzing what is and is not working, and revise plans
Each workshop includes the same essential elements and follows the same format but differs in content (the case lesson under consideration) from other workshops. Table 1 highlights the essential workshop elements, explains the rationale for each element, and details how these elements are implemented in each workshop. The recurring format is designed to make it easier for facilita-tors to implement the workshops and helps participants to better internalize the process for planning accessible lessons.
In each workshop session, learning activities are designed to deeply immerse participants in the mathematical activity of the case lesson, in ana-lyzing the learning demands of this activity using a neurodevelopmental framework, in observing a student engaged in the activity to assess the extent to which she or he meets the demands of the activity, and in analyzing teach-ing practices and instructional strategies that build on individual students’ strengths and address their weaknesses. After in-depth analysis of each case lesson in this fashion, participants connect what they have learned to their own classrooms. Working with the members of their team, they examine the mathematics of a lesson that they will be teaching between course sessions, analyze the demands of the core mathematics activity, discuss the strengths and weaknesses of one or more focal children from their classrooms in rela-tion to that activity, and then plan adaptations for the lesson to support stu-dent learning. Workshop assignments require participants to implement their lessons plans, to observe their focal students within that lesson, and to reflect on and revise the adapted lesson. Participants also have reading assignments to familiarize themselves with the neurodevelopmental frame-work. During follow-up meetings, participants continue the collaborative lesson planning process and reflect on adaptations that they have imple-mented previously.
IS MATH FOR ALL A GOOD FIT FOR YOUR SCHOOL OR DISTRICT?
We encourage the implementation of the Math for All program by as many schools and school districts as possible. However, Math for All is most likely to have a lasting impact on teachers and students in settings that share the core
Text resumes on page 13.
7
Tab
le 1
M
ath
for
All
Esse
nti
al W
orks
hop
Ele
men
ts
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
Situ
atin
g th
e W
ork
• To
be
expl
icit
abo
ut
the
lear
nin
g go
als
for
the
wor
ksh
op
and
expe
ctat
ion
s fo
r pa
rtic
ipan
ts•
To m
odel
goa
l-or
ien
ted
teac
hin
g an
d le
arn
ing
and
bein
g ex
plic
it a
bou
t ex
pect
atio
ns
• To
intr
odu
ce to
pics
ad
dres
sed
in th
e se
ssio
n
• M
ath
for
All
over
view
• Le
arn
ing
goal
s fo
r Se
ssio
n 1
• B
rief
ly s
um
mar
ize
wh
at w
as c
over
ed in
Se
ssio
n 1
.•
Lear
nin
g go
als
for
Sess
ion
2•
“Sto
ry W
ith
out a
n
E”
activ
ity
• B
rief
ly s
um
mar
ize
wh
at w
as c
over
ed in
Se
ssio
n 2
.•
Lear
nin
g go
als
for
Sess
ion
3•
Mem
ory
gam
e
• B
rief
ly s
um
mar
ize
wh
at w
as c
over
ed in
Se
ssio
n 3
.•
Lear
nin
g go
als
for
Sess
ion
4
• B
rief
ly s
um
mar
ize
wh
at w
as c
over
ed
in S
essi
on 4
.•
Lear
nin
g go
als
for
Sess
ion
5
Com
mun
ity
Bui
ldin
g •
To h
elp
part
icip
ants
to
get
to k
now
eac
h
oth
er a
nd
feel
co
mfo
rtab
le s
har
ing
thei
r ex
peri
ence
s an
d w
orki
ng
wit
h
each
oth
er•
To in
trod
uce
topi
cs
addr
esse
d in
the
wor
ksh
op in
an
in
tera
ctiv
e,
expe
rien
tial
man
ner
• B
ingo
act
ivit
y•
Ven
n d
iagr
am
activ
ity
• M
emor
izin
g n
ames
ac
tivit
y•
Mas
ter
desi
gn
activ
ity
• D
ivid
ing
shap
es
activ
ity
(Con
tinu
ed)
8
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
Dis
cuss
ion
of
Ass
ignm
ents
• To
con
nec
t w
orks
hop
con
ten
t to
teac
her
s’ o
wn
cl
assr
oom
s•
To p
rom
ote
lear
nin
g th
rou
gh r
efle
ctio
n•
To h
ave
part
icip
ants
sh
are
and
lear
n fr
om
each
oth
er (e
.g.,
abou
t th
e ra
nge
of
stu
den
ts th
at
part
icip
ants
hav
e qu
esti
ons
abou
t or
the
ran
ge o
f ar
eas
of
con
cern
am
ong
them
; ada
ptat
ion
s to
m
ath
less
ons
that
w
orke
d an
d di
d n
ot
wor
k)
• Pa
rtic
ipan
ts s
har
e de
scri
ptio
ns
of
stu
den
ts th
at th
ey
hav
e qu
esti
ons
abou
t.
• Pa
rtic
ipan
ts s
har
e ob
serv
atio
ns
of th
eir
foca
l stu
den
ts.
• Pa
rtic
ipan
ts s
har
e la
ngu
age
adap
tati
ons
for
thei
r m
ath
less
on a
nd
refle
ct o
n h
ow th
ey
wor
ked
for
thei
r st
ude
nts
.
• Pa
rtic
ipan
ts s
har
e m
emor
y ad
apta
tion
s fo
r th
eir
mat
h le
sson
an
d re
flect
on
how
th
ey w
orke
d fo
r th
eir
stu
den
ts.
• Pa
rtic
ipan
ts s
har
e ps
ych
osoc
ial
adap
tati
ons
for
thei
r m
ath
less
on
and
refle
ct o
n h
ow
they
wor
ked
for
thei
r st
ude
nts
.
Intr
oduc
tion
to
the
Cas
e Le
sson
• To
pro
vide
som
e co
nte
xt fo
r th
e vi
deo
clip
s an
d to
sit
uat
e th
e w
ork
• O
verv
iew
of
Cin
dy
Wan
g’s
thir
d-gr
ade
clas
s an
d th
e m
ath
of
the
“Arr
angi
ng
Ch
airs
” le
sson
• O
verv
iew
of
Cri
stia
n
Solo
rza’
s fo
urt
h-
grad
e cl
ass
and
the
mat
h o
f th
e “H
ow
Man
y R
aisi
ns
in a
B
ox?”
less
on
• O
verv
iew
of
Nat
alie
D
ean’
s an
d R
ebec
ca
Cab
an’s
thir
d-gr
ade
clas
s an
d th
e m
ath
of
the
“Div
idin
g a
Dol
lar”
less
on
• O
verv
iew
of
Dan
ita
Kn
igh
t’s a
nd
Mar
ia
Bot
to’s
thir
d-gr
ade
clas
s an
d th
e m
ath
of
the
“Sym
met
ry”
less
on
• O
verv
iew
of
Vilm
a C
aban
’s fi
fth
-gra
de
clas
s an
d th
e m
ath
of
the
“Mu
ltip
licat
ion
C
lust
ers”
less
on
Ana
lyzi
ng th
e D
eman
ds o
f th
e Ta
sk
• To
hav
e pa
rtic
ipan
ts
expe
rien
ce th
e m
ath
ac
tivit
y th
at th
ey
will
obs
erve
on
the
vide
o th
emse
lves
• Pa
rtic
ipan
ts e
xplo
re
the
dem
ands
of
the
“Arr
angi
ng
Ch
airs
” ta
sk.
• Pa
rtic
ipan
ts e
xplo
re
the
dem
ands
of
the
“How
Man
y R
aisi
ns
in a
Box
?” ta
sk.
• Pa
rtic
ipan
ts e
xplo
re
the
dem
ands
of
the
“Div
idin
g a
Dol
lar”
ta
sk.
• Pa
rtic
ipan
ts e
xplo
re
the
dem
ands
of
the
“Sym
met
ry”
task
.
• Pa
rtic
ipan
ts e
xplo
re
the
dem
ands
of
the
“Mu
ltip
licat
ion
C
lust
ers”
task
.
Tab
le 1
(C
onti
nued
)
9
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
• To
hel
p pa
rtic
ipan
ts
beco
me
mor
e aw
are
of th
e va
riou
s de
man
ds in
eac
h
task
• To
hav
e pa
rtic
ipan
ts
lear
n a
bou
t an
d ap
ply
the
neu
rode
velo
pmen
tal
fram
ewor
k
• In
trod
uct
ion
to
neu
rode
velo
pmen
tal
theo
ry•
Part
icip
ants
map
th
e de
man
ds o
f th
e “A
rran
gin
g C
hai
rs”
task
on
to th
e n
euro
deve
lopm
enta
l fr
amew
ork.
• D
iscu
ssio
n o
f la
ngu
age
fun
ctio
ns
• Pa
rtic
ipan
ts m
ap
the
lan
guag
e de
man
ds o
f th
e “H
ow M
any
Rai
sin
s in
a B
ox?”
task
on
to
the
neu
rode
velo
pmen
tal
fram
ewor
k.
• D
iscu
ssio
n o
f m
emor
y fu
nct
ion
s•
Part
icip
ants
map
the
mem
ory
dem
ands
of
the
“Div
idin
g a
Dol
lar”
task
on
to th
e n
euro
deve
lopm
enta
l fr
amew
ork.
• D
iscu
ssio
n o
f ps
ych
osoc
ial
fun
ctio
ns
• Pa
rtic
ipan
ts m
ap
the
psyc
hos
ocia
l de
man
ds o
f th
e “S
ymm
etry
” ta
sk
onto
the
neu
rode
velo
pmen
tal
fram
ewor
k.
• D
iscu
ssio
n o
f h
igh
er o
rder
th
inki
ng
fun
ctio
ns
• Pa
rtic
ipan
ts m
ap
the
high
er o
rder
th
inki
ng d
eman
ds
of th
e “M
ultip
licat
ion
Cl
uste
rs”
task
on
to th
e ne
urod
evel
opm
enta
l fr
amew
ork.
Obs
ervi
ng a
C
hild
• To
hav
e pa
rtic
ipan
ts
lear
n a
bou
t an
d pr
acti
ce o
bser
vati
on
as a
form
of
info
rmal
as
sess
men
t•
To h
ave
part
icip
ants
le
arn
abo
ut a
nd
appl
y th
e n
euro
deve
lopm
enta
l fr
amew
ork
• To
hel
p pa
rtic
ipan
ts
real
ize
that
all
stu
den
ts h
ave
stre
ngt
hs
and
wea
knes
ses
• Pa
rtic
ipan
ts v
iew
vi
deo
of Ja
shan
deep
w
orki
ng
on th
e “A
rran
gin
g C
hai
rs”
activ
ity.
• Pa
rtic
ipan
ts a
nal
yze
Jash
ende
ep’s
st
ren
gth
s an
d n
eeds
.
• Pa
rtic
ipan
ts v
iew
vi
deo
of A
riel
w
orki
ng
on th
e “H
ow M
any
Rai
sin
s in
a B
ox?”
act
ivit
y.•
Part
icip
ants
an
alyz
e A
riel
’s s
tren
gth
s an
d n
eeds
.
• Pa
rtic
ipan
ts v
iew
vi
deo
of L
uis
Car
los
wor
kin
g on
the
“Div
idin
g a
Dol
lar”
ac
tivit
y.•
Part
icip
ants
an
alyz
e Lu
is C
arlo
s’s
stre
ngt
hs
and
nee
ds.
• Pa
rtic
ipan
ts v
iew
vi
deo
of S
ham
ira
wor
kin
g on
the
“Sym
met
ry”
activ
ity.
• Pa
rtic
ipan
ts a
nal
yze
Sham
ira’
s st
ren
gth
s an
d n
eeds
.
• Pa
rtic
ipan
ts v
iew
vi
deo
of M
ich
ael
wor
kin
g on
the
“Mu
ltip
licat
ion
C
lust
ers”
act
ivit
y.•
Part
icip
ants
an
alyz
e M
ich
ael’s
str
engt
hs
and
nee
ds. (C
onti
nued
)
10
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
Iden
tify
ing
the
Mat
hem
atic
al
Goa
ls o
f th
e Le
sson
• To
hav
e pa
rtic
ipan
ts
deve
lop
skill
s in
id
enti
fyin
g th
e m
ath
emat
ical
goa
ls
of th
e le
sson
• To
en
sure
that
any
ad
apta
tion
s th
at
part
icip
ants
con
side
r su
ppor
t th
e m
ath
emat
ical
goa
ls
of th
e le
sson
, not
u
nde
rmin
e th
em
• Pa
rtic
ipan
ts r
ead
the
curr
icu
lum
gu
ide
for
the
“Arr
angi
ng
Ch
airs
” le
sson
an
d an
alyz
e go
als
in s
mal
l gr
oups
an
d sh
are
out.
• Fa
cilit
ator
s di
scu
ss
diffe
ren
ce b
etw
een
go
als
and
activ
itie
s.
• Pa
rtic
ipan
ts r
ead
the
curr
icu
lum
gu
ide
for
the
“How
M
any
Rai
sin
s in
a
Box
?” le
sson
an
d an
alyz
e go
als
in
smal
l gro
ups
an
d sh
are
out.
• Pa
rtic
ipan
ts r
ead
the
curr
icu
lum
gu
ide
for
the
“Div
idin
g a
Dol
lar”
less
on a
nd
anal
yze
goal
s in
sm
all g
rou
ps a
nd
shar
e ou
t.
• Pa
rtic
ipan
ts r
ead
the
curr
icu
lum
gu
ide
for
the
“Sym
met
ry”
less
on
and
anal
yze
goal
s in
sm
all g
rou
ps a
nd
shar
e ou
t.
• Pa
rtic
ipan
ts r
ead
the
curr
icu
lum
gu
ide
for
the
“Mu
ltip
licat
ion
C
lust
ers”
less
on a
nd
anal
yze
goal
s in
sm
all g
rou
ps a
nd
shar
e ou
t.
Teac
hing
P
ract
ices
• To
illu
stra
te h
ow
less
ons
can
be
adap
ted
to s
upp
ort
the
stre
ngt
hs
and
nee
ds o
f in
divi
dual
st
ude
nts
wh
ile
mai
nta
inin
g th
e in
tegr
ity
of th
e m
ath
emat
ical
goa
ls
of th
e le
sson
• To
sh
ow h
ow
diffe
ren
t tea
chin
g pr
acti
ces
can
su
ppor
t th
e va
riou
s
• Pa
rtic
ipan
ts r
evie
w
sam
ple
teac
hin
g pr
acti
ces.
• Fa
cilit
ator
s di
scu
ss
diffe
ren
ce b
etw
een
ad
apta
tion
an
d m
odifi
cati
on.
• Pa
rtic
ipan
ts v
iew
vi
deo
of C
indy
W
ang
teac
hin
g th
e “A
rran
gin
g C
hai
rs”
less
on a
nd
iden
tify
ad
apta
tion
s sh
e u
sed.
• Pa
rtic
ipan
ts r
evie
w
sam
ple
teac
hin
g pr
acti
ces
that
su
ppor
t lan
guag
e fu
nct
ion
s.•
Part
icip
ants
vie
w
vide
o of
Cri
stia
n
Solo
rza
teac
hin
g th
e “H
ow M
any
Rai
sin
s in
a B
ox?”
le
sson
an
d id
enti
fy
lan
guag
e ad
apta
tion
s h
e u
sed.
• Pa
rtic
ipan
ts r
evie
w
sam
ple
teac
hin
g pr
acti
ces
that
su
ppor
t mem
ory
fun
ctio
ns.
• Pa
rtic
ipan
ts v
iew
vi
deo
of R
ebec
ca
Cab
an a
nd
Nat
alie
D
ean
tea
chin
g th
e “D
ivid
ing
a D
olla
r”
less
on a
nd
iden
tify
m
emor
y ad
apta
tion
s th
ey
use
d.
• Pa
rtic
ipan
ts r
evie
w
sam
ple
teac
hin
g pr
actic
es th
at
supp
ort p
sych
osoc
ial
fun
ctio
ns.
• Pa
rtic
ipan
ts v
iew
vi
deo
of M
aria
Bot
to
and
Dan
ita
Kn
igh
t te
ach
ing
the
“Sym
met
ry”
less
on
and
iden
tify
ps
ych
osoc
ial
adap
tati
ons
they
u
sed.
• Pa
rtic
ipan
ts r
evie
w
sam
ple
teac
hin
g pr
acti
ces
that
su
ppor
t hig
her
or
der
thin
kin
g fu
nct
ion
s.•
Part
icip
ants
vie
w
vide
o of
Vilm
a Ca
ban
teac
hing
the
“Mul
tiplic
atio
n
Clus
ters
” le
sson
and
id
entif
y hi
gher
ord
er
thin
king
ada
ptat
ions
sh
e us
ed.
Tab
le 1
(C
onti
nued
)
11
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
n
euro
deve
lopm
enta
l fu
nct
ion
s•
To in
trod
uce
pa
rtic
ipan
ts to
a
vari
ety
of te
ach
ing
prac
tice
s an
d in
stru
ctio
nal
st
rate
gies
• Pa
rtic
ipan
ts li
nk
teac
hin
g pr
acti
ces
to
Jash
ande
ep’s
st
ren
gth
s an
d n
eeds
an
d th
e n
euro
deve
lopm
enta
l fr
amew
ork.
• Pa
rtic
ipan
ts
brai
nst
orm
ad
diti
onal
ada
ptio
ns
for
the
“Arr
angi
ng
Ch
airs
” le
sson
.
• Pa
rtic
ipan
ts li
nk
teac
hin
g pr
acti
ces
to
Ari
el’s
str
engt
hs
and
nee
ds in
lan
guag
e fu
nct
ion
s.•
Part
icip
ants
br
ain
stor
m
addi
tion
al
adap
tati
ons
to
supp
ort l
angu
age
fun
ctio
ns
in th
e “H
ow M
any
Rai
sin
s in
a B
ox?”
Les
son
.
• Pa
rtic
ipan
ts li
nk
teac
hin
g pr
acti
ces
to
Luis
Car
los’
s st
ren
gth
s an
d n
eeds
in
mem
ory
fun
ctio
ns.
• Pa
rtic
ipan
ts
brai
nst
orm
ad
diti
onal
ad
apta
tion
s to
su
ppor
t mem
ory
fun
ctio
ns
in th
e “D
ivid
ing
a D
olla
r”
less
on.
• Pa
rtic
ipan
ts li
nk
teac
hin
g pr
acti
ces
to S
ham
ira’
s st
ren
gth
s an
d n
eeds
in
psy
chos
ocia
l fu
nct
ion
s.•
Part
icip
ants
br
ain
stor
m
addi
tion
al
adap
tati
ons
to
supp
ort
psyc
hos
ocia
l fu
nct
ion
s in
the
“Sym
met
ry”
less
on.
• Pa
rtic
ipan
ts li
nk
teac
hin
g pr
acti
ces
to M
ich
ael’s
st
ren
gth
s an
d n
eeds
in
hig
her
ord
er
thin
kin
g fu
nct
ion
s.•
Part
icip
ants
br
ain
stor
m
addi
tion
al
adap
tati
ons
to
supp
ort h
igh
er
orde
r th
inki
ng
in
the
“Mu
ltip
licat
ion
C
lust
ers”
less
on.
Ref
lect
ion
on
the
Day
• To
rev
iew
pro
gres
s m
ade
tow
ard
lear
nin
g go
als
• To
su
mm
ariz
e an
d re
view
the
con
ten
t of
the
wor
ksh
op•
To m
odel
sel
f-as
sess
men
t of
goal
s ac
com
plis
hed
• Pa
rtic
ipan
ts r
espo
nd
to r
efle
ctio
n
ques
tion
s.
• Pa
rtic
ipan
ts r
espo
nd
to r
efle
ctio
n
ques
tion
s.
• Pa
rtic
ipan
ts r
espo
nd
to r
efle
ctio
n
ques
tion
s.
• Pa
rtic
ipan
ts r
espo
nd
to r
efle
ctio
n
ques
tion
s.
• Pa
rtic
ipan
ts
resp
ond
to
refle
ctio
n q
ues
tion
s.
(Con
tinu
ed)
12
Gen
eral
Fo
rmat
of
Wor
ksh
op
Sess
ion
s (E
ssen
tial
E
lem
ents
)R
atio
nal
e fo
r W
ork
shop
Ele
men
tW
ork
shop
Ses
sion
1W
ork
shop
Ses
sion
2W
ork
shop
Ses
sion
3W
ork
shop
Ses
sion
4W
ork
shop
Ses
sion
5
Col
labo
rativ
e Le
sson
P
lann
ing
• To
hav
e pa
rtic
ipan
ts
appl
y w
hat
they
le
arn
ed in
the
wor
ksh
op to
thei
r ow
n c
lass
room
an
d to
con
nec
t wor
ksh
op
con
ten
t to
teac
her
s’
prac
tice
• To
hav
e te
ache
rs
expe
rien
ce a
nd
deve
lop
skill
in
colla
bora
tive
less
on
plan
ning
(i.e
., to
hav
e te
ache
rs h
one
thei
r sk
ills
in w
orki
ng
toge
ther
to a
naly
ze
the
dem
ands
of
a m
athe
mat
ical
task
, ob
serv
e a
child
, an
alyz
e th
e m
athe
mat
ical
goa
ls
of m
ath
less
ons,
ad
apt l
esso
ns b
y se
lect
ing
teac
hing
pr
actic
es b
ased
on
st
uden
ts’ s
tren
gths
an
d ne
eds
whi
le
mai
ntai
ning
the
inte
grity
of
the
mat
hem
atic
al g
oals
)
• Te
ams
of
part
icip
ants
sel
ect a
fo
cal c
hild
an
d a
less
on th
ey w
ill
teac
h in
the
nex
t w
eek
or tw
o.•
Th
e te
ams
anal
yze
dem
ands
an
d go
als
of th
e le
sson
.•
Th
e te
ams
plan
for
an o
bser
vati
on o
f th
e se
lect
ed le
sson
.
• Te
ams
of
part
icip
ants
sel
ect a
le
sson
they
will
te
ach
in th
e n
ext
wee
k or
two.
• T
he
team
s ex
plor
e th
e la
ngu
age
dem
ands
of
the
less
on th
ey s
elec
ted.
• T
he
team
s di
scu
ss
the
stre
ngt
hs
and
nee
ds in
lan
guag
e fu
nct
ion
of
thei
r fo
cal s
tude
nt.
• B
uild
ing
on th
e st
ren
gth
s an
d n
eeds
of
thei
r fo
cal
stu
den
ts, t
he
team
s pl
an la
ngu
age
adap
tati
ons
for
the
sele
cted
less
on.
• Te
ams
of
part
icip
ants
sel
ect a
le
sson
they
will
te
ach
in th
e n
ext
wee
k or
two.
• T
he
team
s ex
plor
e th
e m
emor
y de
man
ds o
f th
e le
sson
they
sel
ecte
d.•
Th
e te
ams
disc
uss
th
e st
ren
gth
s an
d n
eeds
in m
emor
y fu
nct
ion
of
thei
r fo
cal s
tude
nt.
• B
uild
ing
on th
e st
ren
gth
s an
d n
eeds
of
thei
r fo
cal
stu
den
ts, t
he
team
s pl
an m
emor
y ad
apta
tion
s fo
r th
e se
lect
ed le
sson
.
• Te
ams
of
part
icip
ants
sel
ect a
le
sson
they
will
te
ach
in th
e n
ext
wee
k or
two.
• T
he
team
s ex
plor
e th
e ps
ych
osoc
ial
dem
ands
of
the
less
on th
ey s
elec
ted.
• T
he
team
s di
scu
ss
the
stre
ngt
hs
and
nee
ds in
ps
ych
osoc
ial
fun
ctio
n o
f th
eir
foca
l stu
den
t.•
Bu
ildin
g on
the
stre
ngt
hs
and
nee
ds
of th
eir
foca
l st
ude
nts
, th
e te
ams
plan
psy
chos
ocia
l ad
apta
tion
s fo
r th
e se
lect
ed le
sson
.
• Te
ams
of
part
icip
ants
sel
ect a
le
sson
they
will
te
ach
in th
e n
ext
wee
k or
two.
• T
he
team
s ex
plor
e th
e h
igh
er o
rder
th
inki
ng
dem
ands
of
the
less
on th
ey
sele
cted
.•
Th
e te
ams
disc
uss
th
e st
ren
gth
s an
d n
eeds
in h
igh
er
orde
r th
inki
ng
of
thei
r fo
cal s
tude
nt.
• B
uild
ing
on th
e st
ren
gth
s an
d n
eeds
of
thei
r fo
cal
stu
den
ts, t
he
team
s pl
an h
igh
er o
rder
th
inki
ng
adap
tati
ons
for
the
sele
cted
less
on.
Tab
le 1
(C
onti
nued
)
13INTRODUCTION
beliefs that underlie the program (see sidebar). Math for All will fit well into schools and school district that are:
• Committed to standards-based, constructivist teaching and learning of mathematics2;
• Dedicated to providing students with disabilities with a high-quality, standards-based math education;
• Supportive of the collaboration between general education and special education teachers; and
• Committed to ongoing professional development for teachers.
It is important that the program is supported and championed by district leaders and principals. All people involved (including administrators, staff developers, and teachers) need to have a good understanding of the time commitment that the professional development entails and be prepared to do the work required for participa-tion. Like other innovations, it may not be a good idea to implement this program during a time when other new initiatives are being introduced (e.g., a new curriculum) that require professional development as well.
MATERIALS FOR THE MATH FOR ALL WORKSHOPS
To implement the Math for All program, you will need the following key materials.
Facilitator’s Guide
This facilitator’s guide is designed to help staff developers plan the workshop sessions, to understand key content to be explored, to anticipate participant responses to the professional development, and to identify possible facilitation strategies and moves. It provides facilitators with an overview of the Math for All program and detailed information for the imple-mentation of each workshop session. The first two chapters introduce facilitators to the goals, purposes, content, and format of the Math for All program, as well as providing suggestions for how to prepare for its
2It is not necessary for schools and districts that want to implement the Math for All program to use the math curricula featured in the case lessons (Investigations in Number, Data, and Space; Everyday Math). We successfully implemented the program in settings that use other standards-based curricula (such as Scotts Foresman’s Math Trailblazer, Houghton Mifflin’s HSP Math, Impact Mathematics, Envisions, or Math Connects).
Core Beliefs Embedded in the Math for All Program
Mathematics. Mathematics is something you do. It is not a set of procedures that you learn. Mathematics is an art form. Solving a mathematical problem is a cre-ative act. Mathematics is useful in our everyday lives. But just as filling out forms is a use for writing, but not its primary use; such uses of math as figuring out the change at the grocery store and doing one’s taxes are not a primary uses of math-ematics. Our schools need to teach the mathematics that is useful in our society, but we must be careful not to lose the joy of doing mathematics for its own sake.
Learning Mathematics. One learns math by discovering the meaning and patterns inher-ent in it. One learns math by doing it. One learns math by discussing one’s thinking about it with others. One learns math by solv-ing problems. Some of these problems are found in the real world and some are not.
Teaching Mathematics. We can support student learning by providing students with problems that interest them and that they have enough background to solve. We can support the learning of math by removing
(Continued)
14 MATH FOR ALL FACILITATOR’S GUIDE (3–5)
implementation and sharing tips for facilitating the professional development.
Each workshop chapter includes a workshop over-view and a detailed implementation guide. The workshop overview presents a synopsis of the workshop, the learn-ing goals to be addressed, materials needed, suggestions for how to prepare for the workshop, synopses of the case lessons, the neurodevelopmental and mathematics con-tent to be covered, and a sample agenda. The implementa-tion guide includes detailed descriptions of each segment of the workshop, along with its rationale and suggested time frame. It also includes images of all PowerPoint slides for that session, along with annotations that elaborate on the content of the slides and provide suggestions for how to present the slides. Facilitator notes and possible answers are included also to highlight important facilitation moves and to help facilitators to anticipate participants’ responses to discussion questions. A completed accessible lesson planning chart is included at the end of each workshop chapter to give facilitators a sense of the work that par-ticipants might complete during the session.
The final chapter of the guide provides staff develop-ers with some suggestions for how to continue and sup-port collaborative lesson planning after the workshops end. Also included are a glossary that provides defini-tions for key terms used in the workshop session, and appendixes with information about the research base for Math for All, a sample letter to introduce workshop par-ticipants to the professional development, alternative warm-up activities, and a sample session feedback form.
DVD With PowerPoint Slides and Selected Handouts
The facilitator’s guide contains a DVD with Power-Point presentations for each workshop. The PowerPoint presentations highlight key content, instructions, dis-cussion questions, and embed video clips from the case lessons. The DVD also contains selected handouts for each workshop session that facilitators may need to adapt (e.g., agendas) or fill out during the workshop ses-sion (e.g., accessible lesson planning chart).
DVD With Video Files
The facilitator’s guide also contains a DVD with the video files only (the same video files that are embedded in
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the barriers that stand in the students’ way that may have nothing to do with the mathematics itself. We also can facilitate the learning of mathematics by providing students with supports that allow them to temporarily bypass what they do not know or by targeting for intensive work the math-ematical ideas and procedures that are difficult for them. We can support student learning by creating a culture of young mathematicians in which all ideas are respected and valued.
Mathematics for All. We share the beliefs expressed in the NCTM Equity Principle and the Common Core State Standards for Mathematics. When teachers under-stand the range of nonmathematical bar-riers that interfere with learning, most any child can access, appreciate, and use mathematical concepts as tools to solve life’s numerical and spatial challenges. We believe all children can become mathe-matically thinking citizens if their teachers are afforded the necessary supports to meet all students’ learning needs (NCTM, 2000). It is important that all students, including those with disabilities, are expected to meet high-quality learning outcomes in mathematics. Equity does not mean that every student will be treated the same. Rather it means supporting stu-dents to achieve high-level outcomes, and different students may need different kinds of support.
Professional Development. Teachers teach as they are taught. Professional develop-ment needs to be implemented in a way that reflects what we want teachers to do with children. It is most effective if it is practice-based and teachers have the opportunity to apply what they learn in their own classroom in a deep way.
Professional learning is enhanced if teachers have opportunities to collaborate. It requires a trusting, safe environment.
15INTRODUCTION
the PowerPoint presentations). You can use the DVD to install the files on the computers that participants will use to view videos in small groups.
Participant Book
The participant book contains all the handouts, worksheets, and curriculum materials that teachers need to complete the five workshops. It also provides participants with an overview of the Math for All program and individual workshop sessions. Appendixes contain templates that teachers can repro-duce and use in their ongoing lesson planning. You will need one book for each participant.
Participant Reading Materials
To familiarize themselves with the neurodevelopmental framework, par-ticipants complete reading assignments prior to each workshop session. We recommend that you use one of the following books:
Levine, M. (2002). A mind at a time. New York: Simon & Schuster.Pohlman, C. (2008). Revealing minds: Assessing to understand and support struggling
learners. San Francisco: Jossey-Bass.
You will need one book for each participant.Individual workshop sessions require additional materials, which are
detailed in the corresponding workshop chapters.
Learning about how to make instruction accessible to students with different strengths and needs is most effective if it is deeply embedded in subject matter con-tent and done collaboratively by general and special education teachers.