Workshop 2

1. Singapore Maths
The Emphasis on Visuals
Multi-Step Problems on Fractions
Harris Federation, London  October 2012
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

2. Jerome Bruner
• Enactive Representation (Concrete)
• Iconic Representation (Pictorial)
• Symbolic Representation (Abstract)
Reference
http://www.theoryfundamentals.com/bruner.htm

3. Howard Gardner
Theory of Multiple Intelligences
• Spatial
• Linguistic
• Logical-mathematical
• Bodily-kinesthetic
• Musical
• Interpersonal
• Intrapersonal
• Naturalistic
Gardner, 1983

4. 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.

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

6. emphasis
visualization

7. Example 1  Primary 5  Year 6
3 units = 18
1 units = 18  3 = 6
6 x 8 = 48
There were 48 coins at first.

8. Example 2  Primary 5  Year 6
Mr Chen had some durians for
sale. He sold 24 durians in the
morning. In the afternoon, he sold
2
of the remainder.
7
1
Then, he had of the total number of durians left.
2
My Pals Are Here! Maths Primary 5
3 units = 24
24
1 units = 24  3 = 8
How many durians did Mr Chen had at first?
10 units = 8 x 10 = 80
At first, Mr Chen had 80 durians for sale.