This was attended by principals and lead teachers.

1. Singapore Math at Highline Public Schools
March 2013  Session 2 at ERAC
Yeap Ban Har
www.banhar.blogspot.com
The Merlion by Yeap Ken Min

2.  Land
 270 sq miles
 700 sq km
 People
 5.3 million
 GDP per capita
 1965 USD500
 2011 USD50 000
Junyuan Secondary School, Singapore in current USD

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

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

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

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

9. Singapore Math
The CPA Approach

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

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

12. concrete
pictorial
abstract

13. Seely Place Elementary School, New York

14. Seely Place Elementary School, New York

15. 3 4

4 5
Seely Place Elementary School, New York

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

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

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

19. 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

20. Singapore Math
Three-Part Lesson Structure

21. Singapore Math
Three-Part Lesson Structure

22. Singapore Math
Three-Part Lesson Structure

23. Singapore Math
Three-Part Lesson Structure

24. Singapore Math
Three-Part Lesson Structure

25. Singapore Math
Three-Part Lesson Structure

26. Singapore Math
Three-Part Lesson Structure

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

28. Singapore Math
Three-Part Lesson Structure

29. Singapore Math
The Spiral Approach

30. Singapore Math
The Spiral Approach

31. Singapore Math
Anchor Task
Guided Practice
Independent Practice

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

35. 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

36. 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

37. 3
A number is of a second number.
5
The sum of the two numbers is 120.
King Solomon Academy, London

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

39. Seely Place Elementary School, New York

40. 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’.

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

42. Escuela de Guetamala, Chile
6
6
6
6

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

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

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

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

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

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

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

52. H Gardner
Multiple Intelligences
Keys Grade School, Manila

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

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

55. 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

56. 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)

57. mathematics

58. 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

59. 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

60. 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

61. 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

62. 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

63. perentage
correct
Singapore 52
International 27

64. perentage
correct
Singapore 45
International 23

65. Singapore Math at Highline Public Schools
March 2013 
Yeap Ban Har
yeapbanhar@gmail.com
The Merlion by Yeap Ken Min