This is the one-day seminar for teachers from the school district.

1. Edgemont Union Free School District
Superintendent’s Professional
Development Day
January 2013

2. MAP101 Fundamentals of Singapore Math
Edgemont Union Free School District
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

3. Page 1

4. Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”.
1982 Ministry of Education Singapore 2006
Introduction of Singapore mathematics
textbooks as they are known today. 2001
Introduction of textbooks published by
1992 private publishers and approved by
Introduction of Problem- Ministry of Education.
Solving Curriculum 2007
New editions of textbooks are
1997 published with the introduction of the
Thinking Schools revised curriculum.
Learning Nation
2013
New editions of textbooks are
published with the revision of the
curriculum.
Page 1

5. Page 4

7. Singapore Math allows
average learners perform at
a high level. The following
are some data from some
international research on
math achievement and
attitude.

8. 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)

9. mathematics

10. ave adv high int low
Singapore 606 43 78 94 99
South Korea 605 39 80 97 100
Hong Kong 602 37 80 96 99
grade four mathematics
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
United States 541 13 47 81 96
International 500 4 28 69 90

11. 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

12. Let’s solve a typical word
problem from the Singapore
Page 2 classroom.

13. 110 g
290 g Page 2

14. 2 units = 290 g – 110 g = 180 g
1 units = 180 g  2 = 90 g
110 g
3 x 90 g = 270 g
Bella puts 270 g sugar on the dish.
? ?

15. Experiencing
Singapore Math
Professional Development in London, UK

17. the same dish
110 g
290 g Page 2

18. Not necessary to find
the mass that Bella
puts on the dish
Professional Development in St. Louis, USA
Page 2

19. The brown sugar problem
demonstrates the importance
of visualization.

20. Page 5

21. Share 3 fourths equally among 3.
3 fourths  3 = 1 fourth

22. Share 3 fourths equally between 2.
3 fourths  2
= 6 eighths  2 Share 3 fourths equally among 4.
= 3 eighths
3 fourths  4
= 12 sixteenths  4
= 3 sixteenths

24. 3 fourths  4 = 12 sixteenths  4 1 3
3 fourths  4 = ×4
4
= 3 sixteenths

26. 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.

27. Escuela de Guetamala, Chile

29. x + 2x = 12

30. Seely Place Elementary School, New York

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

32. 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’.

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

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

35. Seely Place Elementary School, New York

36. Seely Place Elementary School, New York

37. 3 4

4 5
Seely Place Elementary School, New York

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

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

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

41. 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
Seely Place Elementary School, New York

48. MAP101 Fundamentals of Singapore Math
incorporating differentiated instruction
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

49. Anchor Task  Guided Practice  Independent Practice
King Solomon Academy, London

50. Anchor Task  Guided Practice  Independent Practice
King Solomon Academy, London

51. Anchor Task  Guided Practice  Independent Practice
Globe Academy, London

52. Anchor Task  Guided Practice  Independent Practice
Globe Academy, London

53. Experiencing
Singapore Math

57.  Relational
Understanding
 R Skemp
what & how  Concrete
Introduction
 J Bruner
Junyuan Secondary School, Singapore
Page 08
Page 13

59. Differentiated Instruction

60. 30  3
21  3
51 = 50 + 1 King Solomon Academy, London
51 = 40 + 11
51 = 30 + 21
51 = 20 + 31
51 = 10 + 51

61. 60  3 = 20    = 
51  3 = Use digit tiles 0 to 9
54  3 = without repeating.
51  3 = 17
50  3 =
Write three story problems for 50  3 .
Write a note to Marc who is absent
today. Explain to him how to figure out
51  3 .

65. Singapore Math
Drill-and-Practice Through
Problem Solving

66. 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=.

67. 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

68. 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

69. 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