20151013221017LECTURE 2_DR AIN

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

7/21/2019 20151013221017LECTURE 2_DR AIN


7/21/2019 20151013221017LECTURE 2_DR AIN


,-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

7/21/2019 20151013221017LECTURE 2_DR AIN


/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

7/21/2019 20151013221017LECTURE 2_DR AIN


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

7/21/2019 20151013221017LECTURE 2_DR AIN


,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.

7/21/2019 20151013221017LECTURE 2_DR AIN


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 % .

7/21/2019 20151013221017LECTURE 2_DR AIN


Part 6

)hat is a%athe%atical'ro*le%+

7/21/2019 20151013221017LECTURE 2_DR AIN


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-

7/21/2019 20151013221017LECTURE 2_DR AIN


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.

7/21/2019 20151013221017LECTURE 2_DR AIN


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.

7/21/2019 20151013221017LECTURE 2_DR AIN


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.

7/21/2019 20151013221017LECTURE 2_DR AIN


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$+

Documents

20151013221017LECTURE 2_DR AIN