The document discusses Singapore's approach to mathematics education, known as the CPA Approach. It is based on Bruner's theory of enactive, iconic, and symbolic representations. The CPA Approach focuses on visualization, number sense, generalization, and seeing patterns and connections. It has helped students in Singapore and several other countries perform well in mathematics according to international test results. The approach views mathematics as an excellent way to develop intellectual competence.

1. K-5 CommonCoreMathematics
reviewandreflect| danbury, connecticut |25 June 2013
Yeap Ban Har
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
|meeting instructional demands the singapore way
day two|

2. CPA Approach is fundamental to Singapore Math
Bruner – enactive, iconic and symbolic representations
Dienes – construction principle

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

4. the mind’s ability to see
|visualization

5. flexibility with numbers
and mental math
|number sense

6. seeing patterns and
connections
|generalization

7. outcomes |

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

9. Country
GDP per capita in
current USD
2012
Singapore 60,400
Malaysia 16,900
Thailand 10,100
Philippines 4,400
“Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “

10. In the 1970’s, Singapore needed a way to help
students, most of whom were not performing
well in mathematics, learn mathematics.
CPA Approach based on Bruner’s work and a
host of other learning theories were used to
help students learn. Today, many people refer
to this approach as Singapore Math.

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

12. Mathematics is “an excellent vehicle for
the development and improvement of a
person’s intellectual competence”.
|Ministry of Education, Singapore (2006)
thinkingschool
learningnations

14. K-5 CommonCoreMathematics
numbers in base ten| danbury, connecticut |25 June 2013
Yeap Ban Har
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
|meeting instructional demands the singapore way

17. Using digits 2, 3, 4, 5, 6, 7, 8 and 9.

24. K-5 CommonCoreMathematics
measurement| danbury, connecticut |25 June 2013
Yeap Ban Har
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
|meeting instructional demands the singapore way

29. K-5 CommonCoreMathematics
geometry| danbury, connecticut |25 June 2013
Yeap Ban Har
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
|meeting instructional demands the singapore way