This document provides an overview of Singapore's education system and the use of Singapore Math. It notes that Singapore has about 500,000 students, 30,000 teachers, and 173 primary schools. It highlights Singapore's high performance on international tests in literacy, science and math since the 1960s. The document discusses the introduction and evolution of Singapore Math textbooks from 1982 to the present. It emphasizes the focus of Singapore Math on relational understanding, conceptual development, number sense, and visualization skills. Examples from Singapore, US, UK, Chile and the Philippines illustrate how these concepts are taught.

1. MAP101 Fundamentals of Singapore Math
Maui, Hawaii
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

2. Singapore

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

4. General Overview of Singapore and its
Education System

5. General Overview of Singapore and its
Education System
 Students
 500 000
 Teachers
 30 000
 Principals & Vice-Principals
 900
 Schools
 173 Primary Schools (Primary 1 – 6)
 155 Secondary Schools (Secondary 1 – 4)
 13 Junior Colleges (JC 1 – 2) Canossa Convent Primary School, Singapore
 15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal education
system. The data excludes post-secondary education system which includes institutes
of technical education, polytechnics and universities.

6. High achievement was not a given. In 1960,
among 30 615 candidates who sat for the
first Primary School Leaving Examination,
45% of the candidates passed.
Today, about the
same proportion
achieve the
highest grade in
each of the four
subjects tested.
Keon Ming Public School, Singapore

7. 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 Japan Japan Japan
Korea Korea Korea
Hong Kong Singapore Hong Kong
Hong Kong Singapore
400 Thailand Singapore Malaysia Malaysia
Thailand Thailand Thailand
The Philippines
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

9. 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

10. Page 4

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

12. 110 g
290 g Page 2

13. 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.
? ?

14. Professional Development in London, UK

15. Escuela de Guetamala, Chile

16. x + 2x = 12

17. Fundamentals of Singapore Math
Initial Concrete Experiences & Building Conceptual Understanding
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

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

19. Page 5

22. 3 fourths  4 = 12 sixteenths  4 1 3
3 fourths  4 = ×4
4
= 3 sixteenths

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

24. 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

25. Fundamentals of Singapore Math
Emphasis on Number Sense & Visualization
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

29. Student in The Philippines doing long division using number bonds.

31. Students’ work from Maui, Hawaii

34. King Solomon Academy, London

35. King Solomon Academy, London

36. King Solomon Academy, London

37. Globe Academy, London

38. Globe Academy, London

39. Globe Academy, London

40. Teaching Multiplication Facts
Allfarthing Primary School, London

41. Primary Mathematics (Third Edition)
See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary
School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey.
See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on
Higher-Order Thinking Skills. Paper presented at International Conference on School
Mathematics Textbooks Shanghai, China.

42. Visuals are used to teach
concepts – distributive
property of multiplication
– without using formal
terms.
Primary Mathematics (Third Edition)

43. emphasis
visualization

44. Math in Focus

45. Math in Focus

46. Math in Focus

47. Math in Focus

48. Math in Focus

49. Da Qiao Primary School, Singapore

50. 3 units = 18
1 units = 18  3 = 6
6 x 8 = 48
There were 48 coins at first.
Page 15

53. If can learn
our students must
too.
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