Conference in Baguio City

International Workshop on Philippine and Singapore Mathematics

Hotel Supreme Convention Plaza,

Baguio City

January 28 – 30, 2013

Promoting Critical and Creative Thinking:

Singapore Mathematics

Yeap Ban Har

Marshall Cavendish Institute

Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

Introduction A Glimpse of Singapore Math

Assumption Englsih School, Singapore

What is Singapore Math? A Glimpse – Mathematics Classroom

Bina Bangsa School, Indonesia

What is Singapore Math? A Glimpse – Mathematics Textbooks

x2 x

1

x2 x

1

x2 + 4x + 1


x2 x

x2 + 4x + 1

= x2 + 4x + 1 + 3 – 3

= (x + 2)2 – 3


What is Singapore Math? A Glimpse – Mathematics Examinations

Weiyang started a savings plan by putting 2 coins in a money

box every day. Each coin was either a 20-cent or 50-cent coin.

His mother also put in a $1 coin in the box every 7 days. The

total value of the coins after 182 days was $133.90 .

(a) How many coins were there altogether?

(b) How many of the coins were 50-cent coins?

Reference: Singapore Examination and Assessment Board

What is Singapore Math? A Glimpse – Mathematics Examinations

Weiyang started a savings plan by putting 2 coins in a money

box every day. Each coin was either a 20-cent or 50-cent coin.

His mother also put in a $1 coin in the box every 7 days. The

total value of the coins after 182 days was $133.90 .

182 7 = 20 + 6 = 26

140 42

182 x 2 + 26 = 364 + 26 = 390

There were 390 coins altogether.

40 cents 70 cents $1

7 5 $133.90 – $26 = $107.90

182 101

Hint for Part (b)

What is Singapore Math? A Glimpse – Teacher Preparation

National Institute of Education, Singapore

Learning to teach 34 x 42.

What is Singapore Math? Thinking and Problem Solving

Nanyang Primary School, Singapore

Mathematics is “an excellent vehicle for

the development and improvement of a

person’s intellectual competence”.

Ministry of Education, Singapore (2006)

thinkingschools learningnation

Ministry of Education, Singapore (1991, 2000, 2006, 2012)

The twin goals of mathematics in the

basic education levels, K-10 are

Critical Thinking and Problem Solving.

Mathematical problem solving is

finding a way around a difficulty,

around an obstacle, and finding a

solution to a problem that is unknown.

Department of Education, The Philippines (2012)

Singapore Math The CPA Approach, The Spiral

Approach and Emphasis on Relational

Understanding Globe Academy, London

Singapore Math The CPA Approach


6

2 1

3

concrete

pictorial

abstract


3

2

2

1

3

1

3

2

2

1

3

1

1

1

Seely Place Elementary School, New York



5

4

4

3


5

4

4

3


5

4

4

3

5

1

1

3=

5

13=


5

4

4

3 =

1

1 5

1

1

3

Singapore Math Three-Part Lesson Structure

Extended Engagement

with One Task

Teach Less, Learn More

w w w . b a n h a r . b l o g s p o t . c o m











Singapore Math Three-Part Lesson Structure: Guided Practice


Singapore Math The Spiral Approach

Singapore Math The Spiral Approach

Singapore Math Anchor Task

Guided Practice

Independent Practice

J Bruner Enactive, Iconic, Symbolic

Representations

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.


A

B

C 20

116 x

x x

x

x + 2x + x + 20 = 116

4x = 116 – 20 = 96

x = 96 4 = …

King Solomon Academy, London

A number is of a second number.

The sum of the two numbers is 120. 5

3

J Bruner Spiral Curriculum

Greenville Elementary School, New York



The CPA Approach

C P A

Students were asked to

make three nests of 2

eggs and, later, 3 nests

of 7 eggs. They were

only given 20 ‘eggs’.


CPA Approach in Developing Conventional Language

3 nests 3 nests of 2 eggs 3 groups of 2 3 twos

Escuela de Guetamala, Chile

6

6

6

6

Allfarthing Primary School, London

Math in Focus

Da Qiao Primary School, Singapore


Z Dienes Play Structured Learning

Practice

Jenaplanschool Cleoplas, The Netherlands

x x x

x

x

x

x – 1

x + 1

x – 2

x + 2

L Vygotsky Interaction

Pathlight School, Singapore


Globe Academy, London

R Skemp Relational and Instrumental

Understanding

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1

J Piager Assimilation, Accommodation

Keys Grade School, Manila

H Gardner Multiple Intelligences

Keys Grade School, Manila


Observing patterns and

making generalizations

involves reflection.

Student Achievement Average Learners Performing

Well

Pathlight School, Singapore

Singapore Math allows

average learners perform at

a high level. The following

are some data from some

international research on

math achievement and

attitude.

East Coast Primary School, Singapore

Score 1960-1970s 1980s 1990s 2000s

500 Japan Hong Kong Japan Korea

Hong Kong Japan Korea

Singapore

Hong Kong Japan Korea

Singapore

400 Thailand The Philippines Singapore Thailand

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.

mathematics

gra

de f

our

ma

them

atics

Singapore

South Korea

Hong Kong

Taiwan

Japan

Northern Ireland

Belgium

Finland

England

Russia

International

43

39

37

34

30

24

10

12

18

13

4

78

80

80

74

70

59

50

49

49

47

28

94

97

96

93

93

86

89

85

78

82

69

99

100

99

99

99

96

99

98

93

97

90

606

605

602

591

585

562

549

545

542

542

500

adva

nced

hig

h

inte

rmedia

te

low

average

gra

de e

ight

ma

them

atics

South Korea

Singapore

Taiwan

Hong Kong

Japan

Russia

Israel

Finland

United States

England

International

47

48

49

34

27

14

12

4

7

8

3

77

78

73

71

61

47

40

30

30

32

17

93

92

88

89

87

78

68

73

68

65

46

99

99

96

97

97

95

87

96

92

88

75

613

611

609

586

570

539

516

514

509

507

500

adva

nced

hig

h

inte

rmedia

te

low

average

gra

de e

ight

ma

them

atics

Singapore

Malaysia

Thailand

Indonesia

International

48

2

2

0

3

78

12

8

2

17

92

36

26

15

46

99

65

55

43

75

611

440

427

386

500

adva

nced

high

inte

rmedia

te

low

ave

rage

gra

de e

ight

ma

them

atics

Singapore

Malaysia

Thailand

Indonesia

International

48

2

2

0

3

32

39

26

20

26

23

15

16

10

31

611

440

427

386

500

adva

nced

like m

ath

dislik

e m

ath

ave

rage

gra

de e

ight

ma

them

atics

Singapore

South Korea

Taiwan

Hong Kong

Japan

48

47

49

34

27

32

8

14

19

9

23

56

53

37

53

611

613

609

586

570

adva

nced

like m

ath

dislik

e m

ath

ave

rage

International 3 26 31 500

Singapore

International

82

52

pere

ntage

corr

ect

Singapore

International

52

27

pere

ntage

corr

ect

Singapore

International

45

23

pere

ntage

corr

ect

Singapore

International

60

25

pere

ntage

corr

ect

three keys to successful implementation

assessment

Reference: Department of Education State of New York

Reference: Department of Education State of Hawaii

assessment

../../../Desktop/tulips.pdf

teacher preparation

Teacher as a learner (professor as a

model)

Teacher as an observer of learning

(lesson study)

Teacher as reflective practitioner

(professional learning community)

Singapore teachers learn what they need to learn through an

approach that balances content and pedagogy.

teacher preparation

National Institute of Education

Singapore

The practice component is given emphasis – micro teaching,

practicum and lesson study.

teacher preparation

National Institute of Education

Singapore

There is an

emphasis on

teachers

solving the

problems

themselves

during the

course.

teacher preparation

Teachers learn from the

textbooks and teachers

guide.

teacher development

We learn from the Japanese method to help teachers

develop better skills in observing students. This is lesson

study.

teacher development

Princess Elizabeth Primary School

Singapore

TEDS-M Elementary Teachers

Content Knowledge TEDS-M Elementary Teachers

Pedagogical Content Knowledge

TEDS-M Findings

National Institute of Education, Singapore

Fuchun Primary School, Singapore



Keys Grade School, The Philippines

Kranji Secondary School, Singapore

leadership Mayor of Newark gave an inspirational message to

teachers attending professional development on

Singapore Math.

International Workshop on Philippine and Singapore Mathematics

Hotel Supreme Convention Plaza,

Baguio City

January 28 – 30, 2013

Promoting Critical and Creative Thinking:

K-12 Mathematics • What can I do as a teacher?

• What can my school do?

• What can the education schools do?

• What government support should be in place?

Slides are available at

www.banhar.blogspot.com