This course is offered in Chile as part of a Certificate in Mathematics Teaching programme. This presentation is for MAP101 Fundamentals of Singapore Mathematics Curriculum. It is a study of the problem solving approach and an emphasis on thinking - visualization, generalization and number sense. Plus learning theories such as Dienes and Bruner.

1. Day  DrYeap Ban Har banhar.@sg.marshallcavendish.com Marshall Cavendish Institute Singapore

2. MAP 101 Fundamentals in Singapore Mathematics Curriculum DrYeap Ban Har banhar.@sg.marshallcavendish.com Marshall Cavendish Institute Singapore

3. Singapore Mathematics: Focus on Thinking an excellent vehicle for the development & improvement of a person’s intellectual competencies Ministry of Education Singapore 2006

5. 110 g 180 g 110 g Bella puts 180 g brown sugar on the dish. 290 g

6. on an identical dish 110 g 2 units = 180 g 1 unit = 90 g 110 g 180 g 3 units = 270 g Bella puts 270 g brown sugar on the dish. 290 g

7. Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.

8. Singapore Math Visualization

10. Method 1 The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located. Method 4 The position for 99 can be found by writing out all the numbers but this is not efficient method. Method 3 Numbers ending with 9 are at E. So, 99 is at E too. Method 2 The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.

11. Method 1 The letters under A and I are even. So 99 cannot be there. Method 2 The positions of numbers ending with 9 form a diagonal pattern. Method 3 The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out. Method 4 The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out. Method 5 Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

12. Method 2 The positions of numbers ending with 9 form a diagonal pattern. In December 2010, another group of teachers in Chile who did this course also came up with a similar method.

13. Another Method In a course done in December 2010 with another group of Chilean teachers, there was a method that involves division. For Cheryl it was 99 : 10. For David, it was 99 : 8. Are you able to figure out that method?

14. Singapore Math Patterns & Generalization

15. Singapore Mathematics: Focus on Problem Solving

19. CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.

21. Singapore Math Learn New Concept Through Problem Solving

25. Singapore Math Drill-and-Practice Through Problem Solving

27. Singapore Math Applying Knowledge in Problem Solving

29. Learning Theories

35. How many 4s are there in 12? 12 ÷ 4 = 3