The document discusses Singapore's approach to mathematics education, with a focus on promoting critical and creative thinking. It provides examples of Singapore math lessons, textbooks, and assessments. It also discusses key aspects of Singapore math like the Concrete-Pictorial-Abstract approach, the spiral curriculum, and emphasis on relational understanding. The presentation highlights the importance of teacher preparation, development, and leadership to successful implementation of Singapore math.

1. 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
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

2. Introduction
A Glimpse of Singapore Math
Assumption Englsih School, Singapore

3. What is Singapore Math?
A Glimpse – Mathematics Classroom
Bina Bangsa School, Indonesia

4. What is Singapore Math?
A Glimpse – Mathematics Textbooks
x2 x
1

5. What is Singapore Math?
x2 + 4x + 1 A Glimpse – Mathematics Textbooks
x2 x
1

6. What is Singapore Math?
A Glimpse – Mathematics Textbooks
x2 x
x2 + 4x + 1
= x2 + 4x + 1 + 3 – 3
= (x + 2)2 – 3

7. 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

8. 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
182 x 2 + 26 = 364 + 26 = 390
140 42 There were 390 coins altogether.
Hint for Part (b)
40 cents 70 cents $1
$133.90 – $26 = $107.90
5 7 101 182

9. What is Singapore Math?
A Glimpse – Teacher Preparation
Learning to teach 34 x 42.
National Institute of Education, Singapore

10. What is Singapore Math?
Thinking and Problem Solving
Nanyang Primary School, Singapore

11. thinkingschools
learningnation
Mathematics is “an excellent vehicle for
the development and improvement of a
person’s intellectual competence”.
Ministry of Education, Singapore (2006)

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

15. 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)

18. Singapore Math
The CPA Approach, The Spiral
Approach and Emphasis on Relational
Understanding
Globe Academy, London

19. Singapore Math
The CPA Approach

20. Singapore Math
The CPA Approach
2 1

6 3

21. concrete
pictorial
abstract

22. Singapore Math
The CPA Approach
1 2 1
  
2 3 3
1 2 1 1
  
2 3 1 3

23. Seely Place Elementary School, New York

24. Seely Place Elementary School, New York

25. 3 4

4 5
Seely Place Elementary School, New York

26. Seely Place Elementary School, New York
3 4

4 5

27. Seely Place Elementary School, New York
3 4 3 1
 = 
4 5 1 5
1
= 3
5

28. Seely Place Elementary School, New York
1
3 4 3 1
 = 
14 5 1 5

29. 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

30. Singapore Math
Three-Part Lesson Structure

31. Singapore Math
Three-Part Lesson Structure

32. Singapore Math
Three-Part Lesson Structure

33. Singapore Math
Three-Part Lesson Structure

34. Singapore Math
Three-Part Lesson Structure

35. Singapore Math
Three-Part Lesson Structure

36. Singapore Math
Three-Part Lesson Structure

37. Singapore Math
Three-Part Lesson Structure

38. Singapore Math
Three-Part Lesson Structure

39. Singapore Math
Three-Part Lesson Structure

40. Singapore Math
Three-Part Lesson Structure: Guided Practice

41. Singapore Math
Three-Part Lesson Structure

42. Singapore Math
The Spiral Approach

43. Singapore Math
The Spiral Approach

44. Singapore Math
Anchor Task
Guided Practice
Independent Practice

47. J Bruner
Enactive, Iconic, Symbolic
Representations
Edgewood Elementary School, New York

48. 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.
Edgewood Elementary School, New York

49. x + 2x + x + 20 = 116
4x = 116 – 20 = 96
x = 96  4 = … B x x
A x
116
C x 20
Edgewood Elementary School, New York

50. 3
A number is of a second number.
5
The sum of the two numbers is 120.
King Solomon Academy, London

51. J Bruner
Spiral Curriculum
Greenville Elementary School, New York

52. Seely Place Elementary School, New York

53. 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’.

54. CPA Approach in Developing Conventional Language
3 nests  3 nests of 2 eggs  3 groups of 2  3 twos
Greenville Elementary School, New York

55. Escuela de Guetamala, Chile
6
6
6
6

61. Allfarthing Primary School, London

62. Math in Focus

68. Da Qiao Primary School, Singapore

69. Z Dienes
Play  Structured Learning
 Practice
Bina Bangsa School, Indonesia

70. x
x
x+1
x x x x+2
x–1
x x–2
Jenaplanschool Cleoplas, The Netherlands

71. L Vygotsky
Interaction
Pathlight School, Singapore
Bina Bangsa School, Indonesia

72. R Skemp
Relational and Instrumental
Understanding
Globe Academy, London

73. Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1

74. Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1

75. J Piager
Assimilation, Accommodation
Keys Grade School, Manila

77. H Gardner
Multiple Intelligences
Keys Grade School, Manila

78. Observing patterns and
making generalizations
involves reflection.
Seely Place Elementary School, New York

79. Student Achievement
Average Learners Performing
Well
Pathlight School, Singapore

80. 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

81. All major international tests (literacy, science and mathematics) between 1964 and
2003 were placed on a common scale. Selected countries shown in the table.
Score 1960-1970s 1980s 1990s 2000s
500 Japan Hong Kong Hong Kong Hong Kong
Japan Japan Japan
Korea Korea Korea
Singapore Singapore
400 Thailand The Philippines Malaysia Malaysia
Singapore Thailand Thailand
Thailand
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

82. mathematics

83. intermediate
advanced
high
low
average
Singapore 606 43 78 94 99
South Korea 605 39 80 97 100
grade four mathematics
Hong Kong 602 37 80 96 99
Taiwan 591 34 74 93 99
Japan 585 30 70 93 99
Northern Ireland 562 24 59 86 96
Belgium 549 10 50 89 99
Finland 545 12 49 85 98
England 542 18 49 78 93
Russia 542 13 47 82 97
International 500 4 28 69 90

84. intermediate
advanced
high
low
average
South Korea 613 47 77 93 99
Singapore 611 48 78 92 99
grade eight mathematics
Taiwan 609 49 73 88 96
Hong Kong 586 34 71 89 97
Japan 570 27 61 87 97
Russia 539 14 47 78 95
Israel 516 12 40 68 87
Finland 514 4 30 73 96
United States 509 7 30 68 92
England 507 8 32 65 88
International 500 3 17 46 75

85. intermediate
grade eight mathematics
advanced
average
high
low
Singapore 611 48 78 92 99
Malaysia 440 2 12 36 65
Thailand 427 2 8 26 55
Indonesia 386 0 2 15 43
International 500 3 17 46 75

86. grade eight mathematics
dislike math
advanced
like math
average
Singapore 611 48 32 23
Malaysia 440 2 39 15
Thailand 427 2 26 16
Indonesia 386 0 20 10
International 500 3 26 31

87. grade eight mathematics
dislike math
advanced
like math
average
Singapore 611 48 32 23
South Korea 613 47 8 56
Taiwan 609 49 14 53
Hong Kong 586 34 19 37
Japan 570 27 9 53
International 500 3 26 31

88. perentage
correct
Singapore 82
International 52

89. perentage
correct
Singapore 52
International 27

90. perentage
correct
Singapore 45
International 23

91. perentage
correct
Singapore 60
International 25

93. three
keys
to successful
implementation

94. Reference: Department of Education State of New York
assessment

95. assessment
Reference: Department of Education State of Hawaii

96.  Teacher as a learner (professor as a
model)
 Teacher as an observer of learning
(lesson study)
 Teacher as reflective practitioner
(professional learning community)
teacher preparation

97. teacher preparation
National Institute of Education
Singapore
Singapore teachers learn what they need to learn through an
approach that balances content and pedagogy.

98. teacher preparation
National Institute of Education
Singapore
The practice component is given emphasis – micro teaching,
practicum and lesson study.

99. teacher preparation
There is an
emphasis on
teachers
solving the
problems
themselves
during the
course.

100. teacher development
Teachers learn from the
textbooks and teachers
guide.

101. teacher development
We learn from the Japanese method to help teachers
develop better skills in observing students. This is lesson
study. Princess Elizabeth Primary School
Singapore

102. TEDS-M Findings
TEDS-M Elementary Teachers TEDS-M Elementary Teachers
Content Knowledge Pedagogical Content Knowledge

103. National Institute of Education, Singapore
Edgewood Elementary School, New York
Fuchun Primary School, Singapore

104. Bina Bangsa School, Indonesia
Keys Grade School, The Philippines
Kranji Secondary School, Singapore

105. leadership Mayor of Newark gave an inspirational message to
teachers attending professional development on
Singapore Math.

106. 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