national singapore math summer institute, denver

Opening Keynote

The Foundations of Singapore Mathematics

Dr Yeap Ban HarMarshall Cavendish InstituteSingapore

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

15

3 units = 15

1 units = 5

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. 

Emphasis on Problem SolvingSome 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  receives  if  the  sum  of money  is  shared  equally among them. 

Method 1

$25 + $2 = $27

$27 ÷ $3 = 9

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

Method 2

Children $11 $8

3 $22+$6 $24+$25

4 $33+$6 $32+$25

5 $44+$6 $40+$25

…

10 $99+$6 $80+$25

Emphasis on Problem SolvingSome 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  receives  if  the  sum  of money  is  shared  equally among them. 

Method 3

Let there be x children.

$11(x – 1) + $6 = $8x + $25

The sum of money was 10 x $8 + $25 = $105Each child receives $105 ÷ 10 = $10.50

$11x – $11 + $6 = $8x + $25

3x = 30 or x = 10

The CPA Approach: The Importance of Initial Concrete Experience

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Use the base ten materials to show 23. Use it to find the value of 23 – 11.  

23 = 20 + 3

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Use the base ten materials to show 23. Use it to find the value of 23 – 15.  

23 = 10 + 13

2 31 5

11

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51 + 12 51 – 17 51 ÷ 3

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51 + 12 51 – 17 51 ÷ 3

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51 + 12 51 – 17 51 ÷ 3

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51 + 12 51 – 17 51 ÷ 3

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51 + 12 51 – 17 51 ÷ 3

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

Emphasis on Visualization

Emphasis on Visualization

Emphasis on Visualization

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

Emphasis on Spiral Approach

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

 Math in Focus

Singapore Math by Marshall Cavendish

 Pensar sin Limites

Matematica Metodo Singapur

 Daqiao Primary School

Singapore

Emphasis on Spiral Approach

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

6 6 66

 Math in Focus

Singapore Math by Marshall Cavendish

Escuela No. 1577 Teniente Dagoberto Godoy Chile

Emphasis on Spiral Approach

Grade 3 Multiplication of 2-digit x 1 digit3-digit x 1-digit

National Institute of EducationSingapore

Emphasis on Spiral Approach

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

42

30

  4

National Institute of EducationSingapore

Emphasis on Systematic Variation