National Singapore Math Summer Institute, Denver

Opening Keynote
The Foundations of Singapore Mathematics
DrYeap Ban Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
www.marshallcavendish.com/education/mci

“Mathematics is
an excellent vehicle
for the development and improvement of a person’s intellectual competence ...”

Singapore Ministry of Education 2006

Source: Mathematics Syllabus Primary
Singapore Ministry of Education 2006

The Bar Model Method
In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?
Source: Primary School Leaving Examination 2006 – 2010

The Bar Model Method
In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?
Source: Primary School Leaving Examination 2006 – 2010
3 units = 15
1 units = 5
15
18 units = 18 x 5 = 90
There are 90 fruits in the basket.

Emphasis on Problem Solving
Some children shared a sum of money. When each child tried to take $11, the last child received only $6. When each child received $8, there was $25 left over.
Find the amount each child received if the sum of money is shared equally among them.

Find the amount each child receives if the sum of money is shared equally among them.
Method 1
$25 + $2 = $27
$27 ÷ $3 = 9
Method 2
There are 9 children who returned $3.
There are 10 children in all.
Total = $8 x 10 + $25 = $105
Each child receives $105 ÷ 10 = $10.50

Find the amount each child receives if the sum of money is shared equally among them.
Method 3
Let there be x children.
$11(x – 1) + $6 = $8x + $25
$11x – $11 + $6 = $8x + $25
3x = 30 or x = 10
The sum of money was 10 x $8 + $25 = $105
Each child receives $105 ÷ 10 = $10.50

The CPA Approach: The Importance of Initial Concrete Experience

Use the base ten materials to show 23.

Use it to find the value of 23 – 11.

23 = 20 + 3

1
1
2 3
1 5
Use the base ten materials to show 23.

Use it to find the value of 23 – 15.

23 = 10 + 13

51 + 12 51 – 17 51 ÷ 3

Using sticks to learn division by grouping.
King Solomon Academy, London

Emphasis on Visualization
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Emphasis on visualization and generalization in problem solving.
High School Attached to Tsukuba University, Japan

“A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.”
Jerome Bruner 1960
The Process of Education

Emphasis on Spiral Approach
Grade 1
Multiplication using drawing

Math in Focus
Singapore Math by Marshall Cavendish

Grade 2
Multiplication of 2, 5, 10 and 3, 4

Math in Focus

Pensar sin Limites
MatematicaMetodoSingapur

Daqiao Primary School
Singapore

Grade 3
Multiplication of 6, 7, 8, 9
2-digit x 1 digit, 3-digit x 1-digit
6
6
6
6

EscuelaNo. 1577 TenienteDagobertoGodoy Chile

Math in Focus

Grade 3
Multiplication of
2-digit x 1 digit
3-digit x 1-digit

National Institute of Education
Singapore

42
4

Grade 4
Multiplication of 4-digit x 1 digit, 2-digit x 2-digit
30

National Institute of Education
Singapore

Emphasis on Systematic Variation

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National Singapore Math Summer Institute, Denver

by Jimmy Keng on Jul 26, 2011

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