Singapore Math at Edgemont School District New York

Edgemont Union Free School District

Superintendent’s Professional

Development Day

January 2013

MAP101 Fundamentals of Singapore Math E d g e m o n t U n i o n F r e e S c h o o l D i s t r i c t

Yeap Ban Har

Marshall Cavendish Institute Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

Page 1

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.

Page 4

Singapore Math allows

average learners perform at

a high level. The following

are some data from some

international research on

math achievement and

attitude.

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

United States

International

43

39

37

34

30

24

10

12

18

13

13

4

78

80

80

74

70

59

50

49

49

47

47

28

94

97

96

93

93

86

89

85

78

82

81

69

99

100

99

99

99

96

99

98

93

97

96

90

606

605

602

591

585

562

549

545

542

542

541

500

adv high int low ave

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

Let’s solve a typical word

problem from the Singapore

classroom.

Page 2

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

Exp

erie

nci

ng

Si

nga

po

re M

ath

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

The brown sugar problem

demonstrates the importance

of visualization.

Page 5

Share 3 fourths equally among 3.

3 fourths 3 = 1 fourth

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

3 fourths 4 = 12 sixteenths 4 = 3 sixteenths

3 fourths 4 = 1

4×

3

4

Summary of Session 1

Problem solving and thinking as well as

holistic development of the child are the

twin key features of Singapore Math.

CPA Approach is used to achieve the

development of visualization and

provides an impetus for making

generalization.

Escuela de Guetamala, Chile

x + 2x = 12

Seely Place Elementary School, New York


Observing patterns and

making generalizations

involves reflection.

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’.

Greenville Elementary School, New York

CPA Approach in Developing Conventional Language

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

Using bar model to introduce solving

algebraic equations

Solve 7 – 3y = 1 .

7

3y 1




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


For students who already

know a procedure, they

should be able to explain the

procedure visually.

Ideally, the visuals are

employed to help students

develop both procedural and

conceptual understanding at

the same time

MAP101 Fundamentals of Singapore Math incorporating differentiated instruction

Yeap Ban Har Marshall Cavendish Institute

Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

King Solomon Academy, London

Anchor Task Guided Practice Independent Practice



Globe Academy, London


Globe Academy, London


Exp

erie

nci

ng

Si

nga

po

re M

ath

Relational Understanding

R Skemp

Concrete Introduction J Bruner

Junyuan Secondary School, Singapore

what & how

Page 08

Page 13

Differentiated Instruction

30 3 21 3 51 = 50 + 1 51 = 40 + 11 51 = 30 + 21 51 = 20 + 31 51 = 10 + 51


60 3 = 20 51 3 = 54 3 =

51 3 = 17 50 3 = Write three story problems for 50 3 .

= Use digit tiles 0 to 9 without repeating.

Write a note to Marc who is absent today. Explain to him how to figure out 51 3 .

Singapore Math

Drill-and-Practice Through

Problem Solving

Summary of Session 2

How we can provide challenge to

advanced learners is discussed in the

51 3. We can also provide

challenge to all students, as

demonstrated in the x=.

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