Experiencing Singapore Math a n i n s t i t u t e f o r a d m i n i s t r a t o r s

Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

S t L o u i s M i s s o u r i

Singapore

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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

General Overview of Singapore and its

Education System

General Overview of Singapore and its

Education System

Students 500 000

Teachers 30 000

Principals & Vice-Principals 900

Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools

The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.

Canossa Convent Primary School, Singapore

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.

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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.

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1992 Introduction of Problem-

Solving Curriculum

1997 Thinking Schools Learning Nation

1982 Introduction of Singapore mathematics

textbooks as they are known today. 2001 Introduction of textbooks published by

private publishers and approved by Ministry of Education.

2007 New editions of textbooks are

published with the introduction of the revised curriculum.

Mathematics is “an excellent

vehicle for the development and

improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

Page 1

2013 New editions of textbooks are

published with the revision of the curriculum.

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Page 4

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

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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

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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

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The brown sugar problem demonstrates the

importance of visualization.

110 g

290 g

Page 2

the same dish

Page 2

Not necessary to find

the mass that Bella

puts on the dish.

Professional Development in St. Louis, USA

110 g

290 g

Page 2

110 g

? ?

2 units = 290 g – 110 g = 180 g

1 units = 180 g 2 = 90 g

3 x 90 g = 270 g Bella puts 270 g sugar on the dish.

Professional Development in London, UK

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Bar model is introduced systematically and

provides a visual support in the learning of

algebra at the higher grade levels.

Escuela de Guetamala, Chile

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x + 2x = 12

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Students outside Singapore using the bar

model to solve word problems.

King Solomon Academy, London UK

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A number is of a second number.

The sum of the two numbers is 120. 5

3

Edgewood Elementary School, New York

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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.

In the learning of basic concepts such as

those in fractions, the emphasis is on

visualization, generalization and number

sense. There is also an emphasis on 21st

Century Competencies such as creativity,

critical thinking, communication, metacognition

and so on.

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Relational Understanding

R Skemp

Concrete Introduction J Bruner

Junyuan Secondary School, Singapore

what & how

Page 08

Page 13

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Page 5

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Share 3 fourths equally among 3.

3 fourths 3 = 1 fourth

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Share 3 fourths equally between 2.

3 fourths 2 = 6 eighths 2 = 3 eighths

Share 3 fourths equally among 4.

3 fourths 4 = 12 sixteenths 4 = 3 sixteenths

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3 fourths 4 = 12 sixteenths 4 = 3 sixteenths

3 fourths 4 = 1

4×

3

4

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The visual approach can be used in helping

remedial students in Grade 7 and beyond.

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1

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Globe Academy, London UK

Globe Academy, London UK

Long division and the learning of

multiplication facts emphasis that it is not

necessary to learn a procedural blindly and

it is not necessary to do rote memorization in

order to remember.

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Allfarthing Primary School, London

Teaching Multiplication Facts

Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Math in Focus

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Da Qiao Primary School, Singapore

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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.

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Primary Mathematics (Third Edition)

Visuals are used to teach

concepts – distributive

property of multiplication

– without using formal

terms.

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Primary Mathematics (Third Edition)

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