20151013221017lecture 2_dr ain
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prob solving in mathsTRANSCRIPT
7/21/2019 20151013221017LECTURE 2_DR AIN
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KMP6123
PROBLEM SOLVING IN PRIMARYMATHEMATICS
(PENYELESAIAN MASALAH DI SEKOLAH RENDAH)
LECTURE 2
By:
Associate Prof. Dr. Nor’ain Mohd Tajudin
Universiti Pendidikan Sultan dris !UPS"# Tanjon$ Mali%# Perak
norain&fs%t.u'si.edu.%y
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,-UP DS/USSN!01 %inutes"
/reate a 'ro*le% and a non
'ro*le% 2uestions in everyday lifesituation .
/reate a 'ro*le% and a non
'ro*le% 2uestions in%athe%atics.
Discuss 3hy do you call the% a
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/lass discussion !(1 %inutes"
Observe belos!"#$"!o%s&'#es"!o%s
• H o $ ) I * o ! % * " o + $ s s " , ! s e - $ ) ! % $ " ! o % .
• H o / $ % 0 o # b r ! % * # + 1 r o ) " , e r ! v e r e - $ / " l 0 s ! - l ! " e r s o 1 $ " e r
, e % 0 o # , $ v e o % l 0 " o / o % " $ ! % e r s 2 $ 1 o # r 3 l ! " e r + $ ! l $ % 4 $ % ! % e 3 l ! " e r + $ ! l 2
! " , , ! / , " o ) e $ s # r e . 5
• 6 , $ " ! s " , e v $ l # e o 1 e ! * , " " ! ) e s 7 v e + l # s " e % .
6HICH ONE IS A
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Pro*le%s listed a*ove havet3o thin$s in co%%on:
• So4)hat is a 'ro*le%+
(. S'eci5c $oals to *e deter%ined6. No i%%ediate %eans to achievethe $oal 7 lack of resources orkno3led$e
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,reeno !(89" :
A 'ro*le% is a situation in 3hich you face a$iven situation ; <the $iven state= and you
3ant another situation ; <the $oal state= 7 *utthere is no o*vious 3ay of acco%'lishin$ your,A>.
?@a%'le: n learnin$ %athe%atics 7 no
kno3led$e on al$orith%# rules# facts# theore%#etc.
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Goal
Kr#l!8 9 R#4%!/8 (:;;<) Proble Solv!%* = ",ree/r!"er!$
Acceptance
Goal
Blockage
Goal
Exploration
Acceptance – An indication that individual accepts the
problem. This shows personal involvement which
may be due to internal motivation or external
motivation, or simply the desire to experience the
enjoyment of solving a problem.
Blockage – The individuals initial attempts to solve the
problem are fruitless. !is"her strategies simply do
not work.
#xploration – the individual is personally involved in
solving the problem which forces him"her to
explore new methods of attack.
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(B$/8 "o ",e +rev!o#s +roble)
Observe ",!s s!"#$"!o%s $*$!%
6,!/, o1 ",e $bove !s $ +roble.
• H o $ ) I * o ! % * " o + $ s s " , ! s e - $ ) ! % $ " ! o % .
• H o / $ % 0 o # b r ! % * # + 1 r o ) " , e r ! v e r e - $ / " l 0 s ! - l ! " e r s o 1 $ " e r
, e % 0 o # , $ v e o % l 0 " o / o % " $ ! % e r s 2 $ 1 o # r 3 l ! " e r + $ ! l $ % 4 $ % ! % e 3 l ! " e r + $ ! l 2
! " , , ! / , " o ) e $ s # r e . 5
• 6 , $ " ! s " , e v $ l # e o 1 e ! * , " " ! ) e s 7 v e + l # s " e % .
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Part 6
)hat is a%athe%atical'ro*le%+
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What is a mathematical problem?
1. Reyes (1984) – “a problem involves a situation in which a
person wants somethin an! !oes not "now imme!iately
what to !o it et it#.
$. $osamentier % &tepelman (198') – “hallenin i its
solution re*uires creativity+ insiht+ oriinal thin"in+ or
imaination#
,oo" at below statements-
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anto3ski !(899" 7 a 'ro*le% e@ists 3henstudents encounter a dicult%athe%atical 2uestion 3hich they are
una*le to ans3er 3ithin a short 'eriod ofti%e or una*le to solve it at that 'oint inti%e due to lack of infor%ation.
nce students have develo'ed
%athe%atically# 3hat see% to *e a'ro*le% 'reviously could turn out to *e
just another routine %athe%atics e@ercisetoday.
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>ester !(899" 'oints out that# a 'ro*le% e@ists3hen students 3ish to carry out a task *ut donot have the a''ro'riate al$orith%s to do so.
Perha's the students are not fa%iliar 3ith theal$orith%s or %ay *e they are una3are of theal$orith%s re2uired to %ana$e the task.
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rulik and -udnick !(81" 'oint outthat# a 'ro*le% consists of a
situation# 2uantitative in nature orother3ise# faced *y the students thatre2uire a solution *ut they do not
'ossess the necessary strate$y or aclear %ethods in order to solve it.
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Cro% a 'sycholo$ical 'oint of vie3:
A %athe%atics 'ro*le% consist of'heno%ena or a %athe%atical situation thattri$$ers a co$nitive conict in a students’%ine that tries to solve it.
The student 3ill not *e a*le to overco%e this
co$nitive conict 3ith just the action ando'erational sche%es that he or she 'ossess.
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Ge%er$ll0 $ $",e$"!/$l+roble !s 4e7%e4
A 'ro*le% is a task for 3hich:
(" The 'erson confrontin$ it 3ants orneeds to 5nd a solution.
6" The 'erson has no readily availa*le
'rocedure for 5ndin$ the solution.0" The 'erson %ust %ake an atte%'tto 5nd a solution.
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,rou' Discussion !(E %inutes"
/o%'are these three 'ro*le%s. )hich is%ore dicult to teach and 3hy+
F;(. E @ 6 G +F;6. (6 @ 0 H I G +.
F;0. Jason jo$s around a rectan$ular 5eld ofK1% lon$ and (K% 3ide. Lo3 %any
%eters does he jo$ in t3o rounds+
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,rou' Discussion !01
%inutes"
Lo3 to teach%athe%atical
'ro*le% solvin$+