Seminar on Mathematics Learning

Yeap Ban Har Marshall Cavendish Institute

Singapore

yeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

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 the

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)

Southeast Asian nations did not

do well … … in science,

mathematics

and literacy.

1992 Introduction of Problem-

Solving Curriculum

1997 Thinking Schools Learning Nation

1982 Introduction of Singapore mathematics

textbooks as they are known today.

Mathematics is “an excellent

vehicle for the development and

improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

We started off badly but we

have managed to help our

students in learning math.

Score 1960-1970s 1980s 1990s 2000s

500 Japan Japan Korea

Hong Kong

Japan Korea

Hong Kong Singapore

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)

By 1990’s, Singapore has

buckled the trend …

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.

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 Boston College

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 Boston College

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 OECD

Singapore Math focuses on

the use of visuals and initial

concrete experiences..

Archipel Basisschool Tweemaster-Kameleon, The Netherlands

Let the piece of paper

represents a cake.

3 fourths 3 =

4

13

4

3

Archipel Basisschool Tweemaster-Kameleon, The Netherlands

Archipel Basisschool Tweemaster-Kameleon, The Netherlands

28

62

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 =

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 2 =

8

3

8

1

4

12

4

3

2 fourths 2 =

1 fourths 2 =

Archipel Basisschool Tweemaster-Kameleon, The Netherlands

King Solomon Academy, London UK

A number (x) is of a second number (y).

The sum of the two numbers (x and y) is 120. 5

3

A number is of a second number.

The sum of the two numbers is 120. 5

3

8 units = 120

1 units = 120 8

1 units = 15

120

80 40

One of the numbers is 3 x 15 = 45.

The greater number is 5 x 15 = 75.

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.

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.

20 Box C

Box A

Box B

116

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.

x

x x

x 20 Box C

Box A

Box B

116

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.

20 Box C

Box A

Box B

116 – 20 = 116 – 16 – 4 = 96

4 units = 96

4 units = 80 + 16

1 units = 96 4 =

24

24 24

24

Box A ….

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.

x

x x

x 20 Box C

Box A

Box B

x + 20 + x + 2x = 116

4x + 20 = 116

4x = 116 – 20 = 96

x = 96 4 = 24

Box A …

Box B …

Box C …