Motiverend rekenonderwijs met

hoge resultaten : de Singapore-aanpak

E D U C A T I O N S U M M I T

Slides are available at

www.banhar.blogspot.com

D e F a b r i q u e , U t r e c h t

Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.com

Mayflower Primary School, Singapore

High Achievement & Motivated Students: Effects & Principles of The

Singapore Approach

E D U C A T I O N S U M M I T

Slides are available at

www.banhar.blogspot.com

D e F a b r i q u e , U t r e c h t

Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.com

Mayflower Primary School, Singapore

Land 270 sq miles

700 sq km

People 5.3 million

GDP per capita 1965 USD500

2011 USD50 000 in current USD

Junyuan Secondary School, Singapore

introduction

High achievement was not a given. In 1960,

among 30 615 candidates who sat for the

first Primary School Leaving Examination,

45% of the candidates passed.

Keon Ming Public School, Singapore

Today, about the

same proportion

achieve the

highest grade in

each of the four

subjects tested.

Score 1960-1970s 1980s 1990s 2000s

500 Japan Japan

Korea

Hong Kong

Japan

Korea

Singapore

Hong Kong

Japan

Korea

Hong Kong

Singapore

400 Thailand Singapore

Thailand

The Philippines

Malaysia

Thailand

Malaysia

Thailand

300 Indonesia

The Philippines

Indonesia

The Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

All major international tests (literacy, science and mathematics) between 1964 and

2003 were placed on a common scale. Selected countries shown in the table.

See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary

School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey.

See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on

Higher-Order Thinking Skills. Paper presented at International Conference on School

Mathematics Textbooks Shanghai, China.

Primary Mathematics (Third Edition)

Primary Mathematics (Third Edition)

1992 Introduction of Problem-

Solving Curriculum

1997 Thinking Schools Learning Nation

1982 Piloting a New Approach to

Mathematics Teaching

Mathematics is “an excellent

vehicle for the development and

improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

Singapore

Taiwan

Japan

Hong Kong

Att

itu

de

Ac

hie

ve

me

nt

71 41

67 40

50 24

62 23

Gra

de

4

Kazakhstan

Russia

International

England

89 19

62 16

80 16

72 5

TIMSS 2007

Taiwan

Singapore

Hong Kong

S Korea

Att

itu

de

Ac

hie

ve

me

nt

37 45

33 40

60 40

47 31

Gra

de

8

Japan

England

International

Hungary

30 26

30 10

40 8

54 2

TIMSS 2007

Shanghai

Hong Kong

S Korea

Singapore

Me

an

600

562

555

546

15

ye

ar-

old

s

Taiwan

Liechtenstein

International

Finland

543

541

536

496

PISA 2009

Anchor Green Primary School, Singapore

an example

Let the piece of paper

represents a cake.

3 fourths 3 =

4

13

4

3

Let the piece of paper

represents a cake.

3 fourths 2 =

8

32

8

62

4

3

Let the piece of paper

represents a cake.

3 fourths 2 =

8

3

8

1

4

12

4

3

2 fourths 2 =

1 fourths 2 =

Let the piece of paper

represents a cake.

3 fourths 2 =

4

3

2

12

4

3

Let the piece of paper

represents a cake.

3 fourths 2 =

8

3

4

3

2

12

4

3

Let the piece of paper

represents a cake.

3 fourths 4 =

3 fourths 4 = 12 sixteenths 4

= 3 sixteenths

3 fourths 4 = 1

4×

3

4

Mayflower Primary School, Singapore

the singapore approach

Problem-Solving Approach

Concrete-Pictorial-Abstract Approach

x + 2x = 12

Exp

erie

nci

ng

Si

nga

po

re M

ath

Escuela de Guetamala, Chile

Victory Christian International School, The Philippines

Students in Chile and The Philippines

using the CPA Approach to learn

multiplication and fractions.

King Solomon Academy, London

Globe Academy, London

Students in Chile, England and The

Netherlands having lessons that

emphasized visualization.

The Netherlands

England

Chile

King Solomon Academy, London UK

A number is of a second number.

The sum of the two numbers is 120. 5

3

Edgewood Elementary School, New York

Box B contains twice as many

books as Box A. Box C

contains 20 more books than

Box A. Together, the three

boxes contains 116 books.

Globe Academy, London

Exp

erie

nci

ng

Si

nga

po

re M

ath

Problem-Solving Approach • The extended discussion challenges the advanced

learners to go beyond what they already know and to

think deeper, articulate better as well as to have

empathy for others.

• The extended discussion provides processing time for

struggling learners.

Concrete-Pictorial-Abstract Approach

• The CPA Approach is based on theory of representations

which explains how students learn abstract ideas

(Bruner).

• The CPA Approach engages students’ multiple

intelligences (Gardner).

• The CPA Approaches focuses on higher-order

competencies such as visualization.