Opening Keynote The Foundations of Singapore Mathematics Dr Yeap Ban Har Marshall Cavendish Institute Singapore [email protected] www.marshallcavendish.com/education/mci
Jun 19, 2015
Opening Keynote
The Foundations of Singapore Mathematics
Dr Yeap Ban HarMarshall Cavendish InstituteSingapore
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