Opening Keynote<br />The Foundations of Singapore Mathematics<br />DrYeap Ban Har<br />Marshall Cavendish Institute<br />S...
“Mathematics is <br />an excellent vehicle <br />for the development and improvement of a person’s intellectual competence...
 <br />Source: Mathematics Syllabus Primary <br />Singapore Ministry of Education 2006<br />
The Bar Model Method<br />In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green...
The Bar Model Method<br />In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green...
Emphasis on Problem Solving<br />Some children shared a sum of money. When each child tried to take $11, the last child re...
Emphasis on Problem Solving<br />Some children shared a sum of money. When each child tried to take $11, the last child re...
Emphasis on Problem Solving<br />Some children shared a sum of money. When each child tried to take $11, the last child re...
The CPA Approach: The Importance of Initial Concrete Experience<br />
www.marshallcavendish.com/education/mci<br />
www.marshallcavendish.com/education/mci<br />
www.marshallcavendish.com/education/mci<br />
www.marshallcavendish.com/education/mci<br />
Use the base ten materials to show 23.<br /> <br />Use it to find the value of 23 – 11. <br /> <br />23 = 20 + 3<br />www....
1<br />1<br />2 3<br />1 5<br />Use the base ten materials to show 23.<br /> <br />Use it to find the value of 23 – 15. <b...
51 + 12		51 – 17 		51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
51 + 12		51 – 17 		51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
51 + 12		51 – 17 		51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
51 + 12		51 – 17 		51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
51 + 12		51 – 17 		51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
Using sticks to learn division by grouping.<br />King Solomon Academy, London<br />www.marshallcavendish.com/education/mci...
Emphasis on Visualization<br /><br /><br /><br />
Emphasis on Visualization<br /><br /><br /><br /><br /><br /><br /><br />
Emphasis on Visualization<br /><br /> <br /><br /><br /><br />
Emphasis on Visualization<br /><br /> <br /><br /> <br /><br /> <br ...
Emphasis on visualization and generalization in problem solving.<br />High School Attached to Tsukuba University, Japan<br...
“A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped ...
Emphasis on Spiral Approach<br />Grade 1 <br />Multiplication using drawing<br /> <br />Math in Focus<br />Singapore Math ...
Emphasis on Spiral Approach<br />Grade 2 <br />Multiplication of 2, 5, 10 and 3, 4<br /> <br />Math in Focus<br />Singapor...
 <br />Pensar sin Limites<br />MatematicaMetodoSingapur<br />
 <br />Daqiao Primary School<br />Singapore<br />
Emphasis on Spiral Approach<br />Grade 3 <br />Multiplication of 6, 7, 8, 9 <br />2-digit x 1 digit, 3-digit x 1-digit<br ...
Emphasis on Spiral Approach<br />Grade 3 <br />Multiplication of <br />2-digit x 1 digit<br />3-digit x 1-digit<br /> <br ...
 <br />42<br />Emphasis on Spiral Approach<br />4<br /> <br /> <br /> <br /> <br />Grade 4 <br />Multiplication of 4-digit...
 <br />National Institute of Education<br />Singapore<br />
Emphasis on Systematic Variation<br />
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National Singapore Math Summer Institute, Denver

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National Singapore Math Summer Institute, Denver

  1. 1. Opening Keynote<br />The Foundations of Singapore Mathematics<br />DrYeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />www.marshallcavendish.com/education/mci<br />
  2. 2. “Mathematics is <br />an excellent vehicle <br />for the development and improvement of a person’s intellectual competence ...”<br /> <br />Singapore Ministry of Education 2006<br />
  3. 3.  <br />Source: Mathematics Syllabus Primary <br />Singapore Ministry of Education 2006<br />
  4. 4. The Bar Model Method<br />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?<br />Source: Primary School Leaving Examination 2006 – 2010<br />
  5. 5. The Bar Model Method<br />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?<br />Source: Primary School Leaving Examination 2006 – 2010<br />3 units = 15<br />1 units = 5<br />15<br />18 units = 18 x 5 = 90<br />There are 90 fruits in the basket.<br />
  6. 6. Emphasis on Problem Solving<br />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. <br />Find the amount each child received if the sum of money is shared equally among them. <br />
  7. 7. Emphasis on Problem Solving<br />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. <br />Find the amount each child receives if the sum of money is shared equally among them. <br />Method 1<br />$25 + $2 = $27<br />$27 ÷ $3 = 9<br />Method 2<br />There are 9 children who returned $3.<br />There are 10 children in all.<br />Total = $8 x 10 + $25 = $105<br />Each child receives $105 ÷ 10 = $10.50<br />
  8. 8. Emphasis on Problem Solving<br />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. <br />Find the amount each child receives if the sum of money is shared equally among them. <br />Method 3<br />Let there be x children.<br />$11(x – 1) + $6 = $8x + $25<br />$11x – $11 + $6 = $8x + $25<br />3x = 30 or x = 10<br />The sum of money was 10 x $8 + $25 = $105<br />Each child receives $105 ÷ 10 = $10.50<br />
  9. 9. The CPA Approach: The Importance of Initial Concrete Experience<br />
  10. 10. www.marshallcavendish.com/education/mci<br />
  11. 11. www.marshallcavendish.com/education/mci<br />
  12. 12. www.marshallcavendish.com/education/mci<br />
  13. 13. www.marshallcavendish.com/education/mci<br />
  14. 14. Use the base ten materials to show 23.<br /> <br />Use it to find the value of 23 – 11. <br /> <br />23 = 20 + 3<br />www.marshallcavendish.com/education/mci<br />
  15. 15. 1<br />1<br />2 3<br />1 5<br />Use the base ten materials to show 23.<br /> <br />Use it to find the value of 23 – 15. <br /> <br />23 = 10 + 13<br />www.marshallcavendish.com/education/mci<br />
  16. 16. 51 + 12 51 – 17 51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
  17. 17. 51 + 12 51 – 17 51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
  18. 18. 51 + 12 51 – 17 51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
  19. 19. 51 + 12 51 – 17 51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
  20. 20. 51 + 12 51 – 17 51 ÷ 3<br />www.marshallcavendish.com/education/mci<br />
  21. 21. Using sticks to learn division by grouping.<br />King Solomon Academy, London<br />www.marshallcavendish.com/education/mci<br />
  22. 22. Emphasis on Visualization<br /><br /><br /><br />
  23. 23. Emphasis on Visualization<br /><br /><br /><br /><br /><br /><br /><br />
  24. 24. Emphasis on Visualization<br /><br /> <br /><br /><br /><br />
  25. 25. Emphasis on Visualization<br /><br /> <br /><br /> <br /><br /> <br /><br /><br /> <br /><br /> <br /><br /> <br /><br />
  26. 26. Emphasis on visualization and generalization in problem solving.<br />High School Attached to Tsukuba University, Japan<br />www.marshallcavendish.com/education/mci<br />
  27. 27. “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.” <br />Jerome Bruner 1960 <br />The Process of Education<br /> <br />
  28. 28. Emphasis on Spiral Approach<br />Grade 1 <br />Multiplication using drawing<br /> <br />Math in Focus<br />Singapore Math by Marshall Cavendish<br />
  29. 29. Emphasis on Spiral Approach<br />Grade 2 <br />Multiplication of 2, 5, 10 and 3, 4<br /> <br />Math in Focus<br />Singapore Math by Marshall Cavendish<br />
  30. 30.  <br />Pensar sin Limites<br />MatematicaMetodoSingapur<br />
  31. 31.  <br />Daqiao Primary School<br />Singapore<br />
  32. 32. Emphasis on Spiral Approach<br />Grade 3 <br />Multiplication of 6, 7, 8, 9 <br />2-digit x 1 digit, 3-digit x 1-digit<br />6<br />6<br />6<br />6<br /> <br />EscuelaNo. 1577 TenienteDagobertoGodoy Chile<br /> <br />Math in Focus<br />Singapore Math by Marshall Cavendish<br />
  33. 33. Emphasis on Spiral Approach<br />Grade 3 <br />Multiplication of <br />2-digit x 1 digit<br />3-digit x 1-digit<br /> <br />National Institute of Education<br />Singapore<br />
  34. 34.  <br />42<br />Emphasis on Spiral Approach<br />4<br /> <br /> <br /> <br /> <br />Grade 4 <br />Multiplication of 4-digit x 1 digit, 2-digit x 2-digit<br />30<br />
  35. 35.  <br />National Institute of Education<br />Singapore<br />
  36. 36. Emphasis on Systematic Variation<br />

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