The document summarizes key aspects of Singapore's mathematics curriculum that has achieved high student performance and positive attitudes towards mathematics. It focuses on developing mathematical problem solving and thinking skills. The curriculum emphasizes concrete, pictorial, and abstract representations of concepts. Assessment is aligned with the curriculum and emphasizes higher-order thinking. As a result, over 40% of Singapore students demonstrate advanced understanding of mathematics compared to an international average of 5%. Students also have relatively high attitudes towards mathematics compared to other high-performing countries.

1. The Average Student on Top
The High School Renewal Committee
27 October 2010
Yeap Ban Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
Slides are available at www.banhar.com

2. vision and focus

3. Singapore mathematics curriculum
has its focus mathematical
problem solving and it is set
within an education system that
emphasizes thinking.

4. mathematical
problem solving

5. In Singapore, a
curriculum that focuses
on mathematical
problem solving was
introduced in 1992.
Mathematical
Problem
Solving
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
Reasoning,
communication &
connections
Thinking skills &
heuristics
Application & modelling
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinking
Self-regulation of learning
Beliefs
Interest
Appreciation
Confidence
Perseverance

6. thinking

7. The emphasis on thinking continues in the
late 1990s with the introduction of Thinking
School, Learning Nation philosophy to the
entire education system in 1997.
thinking schools
learning nation

8. strong
fundamentals

9. Princess Elizabeth Primary School, Singapore
2
4
6
3 5

10. Princess Elizabeth Primary School, Singapore

11. pedagogy

12. Pedagogy that focuses on
visuals, patterning and number
sense.

14. The CPA Approach – the progression
from concrete to pictures to abstract
symbols is recommended for concept
development. This is based on the work
of Jerome Bruner.
Fuchun Primary School, Singapore

15. For example, students learn the idea of
division by sharing 12 cookies among 4
persons as well as by putting 12 eggs in
groups of 4 before progressing to using
drawings to solve division problems. Later
they learn to use division sentence 12 ÷ 4 =
3. Princess Elizabeth Primary School, Singapore

16. For example, students learn to do
division of discrete quantities without
the need to write division sentence in
Grade 1.

18. The Spiral Approach – students get
to revisit core ideas as they deepen
their understanding of those ideas.
This is also one of Jerome Bruner’s
ideas.
Singapore Math in the Netherlands

19. In Grade 2, the revisit this idea and use
division sentences to represent the
situations. In Grade 3, the idea is
extended to include the idea of a
remainder. They also learn to regroup
before dividing for 2-digit and 3-digit
numbers.
Singapore Math in USA

20. In Grade 4, 4-digit numbers are used.
In Grade 5, division of continuous
quantities are dealt with where 13 ÷ 4 =
3.25 rather than 3 remainder 1.
Singapore
Math
in
The Philippines

21. assessment

22. Source
PSLE Mathematics Singapore Examination and Assessment Board

23. Source
Primary Three Examination Item from Henry Park Primary School,
Singapore
Angela, Bala, and Cheng Hao
have 872 marbles altogether.
Angela has 4 times as many
marbles as Bala. Cheng Hao has
50 more marbles than Bala. How
many marbles does Bala have?

24. Source
Primary Three Examination Item from Henry Park Primary School,
Singapore
Angela, Bala, and Cheng Hao
have 872 marbles altogether.
Angela has 4 times as many
marbles as Bala. Cheng Hao has
50 more marbles than Bala. How
many marbles does Bala have?
Angela
Bala
Cheng
Hao
50
872

25. Source
Primary Three Examination Item from Henry Park Primary School,
Singapore
Angela, Bala, and Cheng Hao
have 872 marbles altogether.
Angela has 4 times as many
marbles as Bala. Cheng Hao has
50 more marbles than Bala. How
many marbles does Bala have?
Angela
Bala
Cheng
Hao
822
1 unit = 822 ÷ 6
1 unit = 137
Bala has 137
marbles.
600
180
42

26. Source
Primary Three Examination Item from Henry Park Primary School,
Singapore
Angela, Bala, and Cheng Hao
have 872 marbles altogether.
Angela has 4 times as many
marbles as Bala. Cheng Hao has
50 more marbles than Bala. How
many marbles does Bala have?
Angela
Bala
Cheng
Hao
50
872y
y y y y
y
4y + y + (y + 50) = 872
6y + 50 = 872
6y = 872 – 50
y = 822 ÷ 6
y = 137

27. outcomes

28. Students in Singapore have
demonstrated high achievement and
positive attitude towards mathematics.
In Trends in Mathematics and Science
Study, more than 40% of Singapore’s 4th
and 8th graders are in the Advanced
International Benchmark (the
international average is 5% and 2%
respectively). Advanced
Intermediate
Low
High
1995
2003
2007
38 4138
70 7473
89 9291
96 9897
Grade4
International
5
26
67
90

29. Advanced
Intermediate
Low
High
Indonesia
Thailand
2 30
15 124
46 4414
75 6648
Grade 8
Method Used in Singapore Textbooks
TIMSS 2007
Trends in International Mathematics and Science Studies
Malaysia
Singapore
402
7018
8850
9782
International

30. Advanced
Intermediate
Low
High
Average
HongKong
Singapore
2 4031
15 7064
46 8885
75 9794
S.Korea
Taiwan
4540
7171
8690
9598
Grade8
Singapore Math in Indonesia
TIMSS 2007
Trends in International Mathematics and Science Studies

31. Advanced
Intermediate
Low
High
Grade41995
38
70
89
96
TIMSS
Trends in International Mathematics and Science Studies
Grade81999
42
77
94
99
Grade42003
Grade82007
38
73
91
97
40
70
88
97

32. In the PSLE, the national average for
students who are capable of completing
the most challenging items in the
examination is between 40% and 45%.
We saw one such challenging items
earlier.
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate
cookies and the rest were almond cookies. After selling 210 almond
cookies and 5/6 of the chocolate cookies, she had 1/5 of the
cookies left.
How many cookies did Mrs Hoon sell?

33. The attitude index for Singapore
students in TIMSS is also relatively high
compared to other high-performing
countries.
Also, the majority of students in
Singapore opt to study mathematics in
Grades 11 and 12 when they are no
longer required to.

34. Taiwan
Singapore
Hong Kong
S Korea
Attitude
Achievement
37 45
33 40
60 40
47 31
Grade8
Japan
England
International
Hungary
30 26
30 10
40 8
54 2

35. Making the Average Student on Top
• Thinking-oriented Curriculum
• Theoretically-sound Pedagogy
• Assessment that is coherent with the curriculum
• Teacher professional development
• Changing mindset about what mathematics is
• Constructing knowledge
• Enhancing capacity to learn