Developing Critical Thinking Through Singapore Math

raisingcritical thinkersthrough

singapore mathDr Yeap Ban Har

National Institute of EducationNanyang Technological University

Singapore

Slides are available for download.

May 2010

Keys Grade School, Manila, The Philippines

internationalperspectives onmathematics

teaching

Tanjong Pagar PCF Kindergarten Singapore

What counts as mathematical proficiency?

procedural fluency

conceptual reasoning


strategic competence

K E Y S1 2 3 45 6 7 89 10 11 12

3948 ?Keys Grade School, Manila, The Philippines

adaptive reasoning

17

710

17 – 3


productive disposition


What counts as mathematical proficiency?

their understandingin a variety of

complex situations

mathz4kidz Learning Centre, Penang, Malaysia

This whole shape

stands for 1.

Trends inMathematics& Science Studies

applyand knowledge

What does this stand

for?

Trends inMathematics& Science Study

explaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia

Math for Developing Intellectual Competence

Mathematics as a vehicle to develop and improve a person’s intellectual competence.

Princess Elizabeth Primary School, Singapore

education

Bina Bangsa School, Bandung, Indonesia

mathematics

Ministry of Education Singapore 2006

an excellent vehicle for the development and improvement of

a person’s intellectual competence

“

”

using to develop

mathematicschildren’s

intelligence


4 7

47

11

47 – 11 Edgewood Elementary School, New York, USA

Edge

woo

d El

emen

tary

Sch

ool,

New

Yor

k

Edgewood Elementary School, New York, USA

What is Singapore Math?Challenging Materials

Meiling and Raja started on a 36-km cycling trip at the same time. They cycled at the same speed for the first 12 km. For the remaining 24 km, Meiling cycled at a faster speed. She arrived at the finishing point 10 minutes before Raja who was 4 km behind her. Raja did not change his speed throughout the trip and he completed the trip at 11 10.

(a) At what time did the trip start?(b) What was Meiling’s average speed for the remaining 24 km of the trip in m/min?

(PSLE Grade 6)MeilingRaja

Raja: 10 min 4 km

Raja: 10 min 4 km

??? min 36 km

Raja: 90 min 36 km

11 10 hrs 10 10 hrs 09 40 hrsRaja, and hence Meiling, started the trip at 09 40.

Raja: First 12 km 30 min Raja: Last 24 km 60 min

Meiling: Last 24 km 50 min

Meiling: 24000 m 50 min

Meiling: 2400 m 5 minMeiling: 480 m 1 min

Meiling’s average speed was 480 m/min for the last part of the trip.

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?

(Teck Whye Primary School, Grade 6)

Album A

Album B

Album C

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?

(Teck Whye Primary School, Grade 6)

Album A

Album B

Album C

13 units 444 + 24 = 4681 unit 468 ÷ 13 = 36

468

390 78

7 units ?7 units 36 x 7 = 210 + 42 = 252There were 252 more stamps in Album C than Album A in the end.

210

5

1

8

3

High Student Achievement

Advanced

Intermediate

Low

High

1995

2003

2007

38 4138

70 7473

89 9291

96 9897

Grade 4

Catholic High School (Primary), Singapore

TIMSSTrends in International Maths and Science Studies

Advanced

Intermediate

Low

High

Swed

en

Med

ian

U S

A

3 105

24 4026

69 7767

93 9590

Grade 4

Elementary School in Japan


Japa

n

Sing

apor

e

4123

7461

9289

9898

Advanced

Intermediate

Low

High

Aver

age

Hon

g Ko

ng

Sing

apor

e

2 4031

15 7064

46 8885

75 9794

Grade 8

Telok Kurau Primary School


Kore

a

Taiw

an

4540

7171

8690

9598

Northlight School, Singapore

Advanced

Intermediate

Low

High

AVER

AGE

MAL

AYSI

A

SIN

GAP

ORE

TIMSS 2007

2 402

15 7018

46 8850

75 9782

Grade 8

Advanced

Intermediate

Low

High

Gra

de 4

41

74

92

98

Singapore

Catholic High School (Primary)


Gra

de 8

40

70

88

97

Advanced

Intermediate

Low

High

Gra

de 4

10

40

77

95

U S A



Gra

de 8

6

31

67

92

Advanced

Intermediate

Low

High

Gra

de 4

16

48

79

94

England



Gra

de 8

8

35

69

90

Advanced

Intermediate

Low

High

Gra

de 4

5

26

67

90

International



Gra

de 8

2

15

46

75

Using Mathematics to Develop Intelligent Behaviors

intelligent

what arebehaviors?

1000- 124

mathematics& intelligent

behaviors

1000- 124

199

1000- 124

999- 124 875

876

forlooking

connections

Bina Bangsa School, Bandung, Indonesia

ability

explainto

A Grade 6 US textbook written using the Singapore Pedagogy

mathematics& intelligent

behaviours

34

÷3 = 3 x 43

= 4

How to make sure the butterfly cannot fly

How do you get a butterfly?

First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.

When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.

If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.

The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.

If the butterfly is not left to struggle to come out of the cocoon, it will never fly.

We can learn an important lesson from the butterfly.

If we do not have struggles and challenges in our work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless.

Lim Siong Guan Head, Civil Service

5 cm

5 cm5 cm

11 cm

4 cm

Area = (11 + 5) ÷ 2 x 4

ability knowledge

to use

Key Success Factors

Princess Elizabeth Primary School, Singapore

Some of us come from

English-speaking

homes. Some of us don’t. I

speak Malay at home.

This is what help me learn mathematics well.…

Factors That Contribute to High Achievement Level in Mathematics

We like our teacher.Once, she was absent for two days. We missed her. She told

she had to learn new things to teach us better.

North Vista Primary School, Singapore

teacherquality

National Institute of Education, Singapore


x

professional developmentin-service

Keys Grade School. Manila, The Philippines

Hougang Primary School, Singapore

parentalexpectations

Seminar for Parents on Problem Solving

Last Saturday, Mum and Dad went to school – to learn the

model method so they can help me with schoolwork. But Mum

said she did not get it. In the end I had to teach her.

Teaching Every Child

singaporemath

Bruner’stheory

Photos: Princess Elizabeth Primary School, Singapore

We use concrete materials to learn mathematics.


singaporemath

emphasis onconcrete topictorial to abstract

representations

Catholic High School (Primary) Singapore

singaporemath

especially onthe model method

mathz4kidz Learning Center, Malaysia

Telok Kurau Primary School, Singapore

A lion weighs 135 kg. A cow weigh 87 kg more than the lion. An elephant weighs 139 more than the cow. How heavy is the elephant? (Primary 2)

bruner’s theoryconcrete


concreteexperiences


pictorialconcreteto

from


abstractpictorialto

from

All Kids Are Intelligent Series

symbols


concrete

A Public School in Chile

usingmaterials

Ateneo Grade School, Manila, The Philippines

Vygotsky’s Theory

Children Learn in Social

Situations

Fuch

un P

rimar

y Sc

hool

, Sin

gapo

re

interaction

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

singaporemath

thank you

[email protected]

www.askyeapbanhar.blogspot.com

www.math.nie.edu.sg/T3

www.mathz4kidz.com

[email protected]

http://www.askyeapbanhar.blogspot.com/

http://www.math.nie.edu.sg/T3

http://www.mathz4kidz.com/

Developing Critical Thinking Through Singapore Math

Education

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