Singapore Maths An Introduction to CPA Approach

H a r r i s F e d e r a t i o n , L o n d o n O c t o b e r 2 0 1 2

Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.com

Slides are available at

www.banhar.blogspot.com

Jerome Bruner

• Enactive Representation (Concrete)

• Iconic Representation (Pictorial)

• Symbolic Representation (Abstract)

Reference

http://www.theoryfundamentals.com/bruner.htm

Concrete Pictorial Abstract

15 3 = 5

enactive

iconic

symbolic

J. Bruner My Pals Are Here! Maths (Second Edition)

Princess Elizabeth Primary School, Singapore

Primary Mathematics (Standards Edition)

My Pals Are Here! Maths (Third Edition)

Bina Bangsa School, Jakarta

Secondary 1 students using concrete materials to understand the idea

of cross-section area x height to give the volume of a prism and

cylinder. This Indonesian group of schools use Singapore textbooks.

How many pieces

does each get?

What’s the name

of each piece?

3 fourths 4 = 12 sixteenths 4 = 3 sixteenths

3 fourths 4 = 1

4×

3

4

Share 3 fourths equally among 3.

3 fourths 3 = 1 fourth

Share 3 fourths equally between 2.

3 fourths 2 = 6 eighths 2 = 3 eighths

Share 3 fourths equally among 4.

3 fourths 4 = 12 sixteenths 4 = 3 sixteenths

Royston Primary School, London

There are 17 more girls than boys

in a group.

John has $34 more than Mary.

Theory of Multiple Intelligences

• Spatial

• Linguistic

• Logical-mathematical

• Bodily-kinesthetic

• Musical

• Interpersonal

• Intrapersonal

• Naturalistic Gardner, 1983