Presentation at NCTM Annual Meeting & Exposition

1. Photo:: Catholic High School (Primary) NCTM 2009 Annual Meeting & Exposition Washington D. C.

2. Every Child Counts Every Child Can Count Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore [email_address]

3. TIMSS 2007 Photo: Catholic High School (Primary) Advanced Intermediate Low High 38 41 38 70 74 73 89 92 91 96 98 97 Grade 4

4. Curriculum Framework

5. Every Child Counts

6. This initiative has been in place since 2005. It provides a roadmap for schools and parents to help each child maximize his or her potential in general and do well in chosen field.

7. Kindergarten is not part of the formal education system in Singapore. As such Grade 1 students have extremely varied competency in English and mathematics. Learning Support in Mathematics caters to students who do not have the basic numeracy experiences for one reason or another. There is a parallel learning support program for English (LSP). Photo: Princess Elizabeth Primary School

8. Photo: Catholic High School (Primary) Advanced Intermediate Low High 38 41 38 70 74 73 89 92 91 96 98 97 Grade 4 A c h i e v e m e n t L e v e l s

9. By the end of Grade 4, students who still have not mastered the basics have the option to do Foundation Mathematics, instead of the regular Mathematics program. Foundation Mathematics allows students in Grades 5 and 6 to revisit the basics they missed in the first four grades using age-appropriate materials and also allows them to acquire sufficient fifth and sixth grade content to proceed to secondary school. Photo: Princess Elizabeth Primary School

10. A c h i e v e m e n t L e v e l s Photo: Catholic High School (Primary) Advanced Intermediate Low High 38 41 38 70 74 73 89 92 91 96 98 97 Grade 4

11. Vision A mathematics programme that prepares youth at work and in community Mission To equip students with mathematical skills and attitudes at vocational level of competency and confidence that can be applied in life. The four core vocational modules are electrical, mechanical, retail and food preparation. Photo: Northlight School Students who did not managed to achieve the minimum competencies required to proceed to a course of study in secondary school can enrol in one of two schools - Northlight & Pathway Assumption Schools

12. Every Child Counts

13. Every Child Can Count

14. .. but teachers got to help them

15. There is no substitute for knowing the number facts.

16. Photo: PCF Telok Blangah Kindergarten

19. Photo: PCF Telok Blangah Kindergarten Number Bonds

20. One duck is big. Six ducklings are small. Photo: PCF Telok Blangah Kindergarten Number Bonds

21. Photo: PCF Telok Blangah Kindergarten Number Bonds

22. Photo: PCF Telok Blangah Kindergarten Number Bonds

23. Photo: PCF Telok Blangah Kindergarten Number Bonds

24. Number Bonds Photo: PCF Telok Blangah Kindergarten

25. Formal treatment is delayed. Example: Addition is done only after children are familiar with number bonds. Informal Treatment

26. Photo: Princess Elizabeth Primary School Informal Treatment

28. Formal treatment is delayed. Example: The formula to find the area of squares and rectangles are dealt with only at the end of a long unit of area. Informal Treatment

29. Formal treatment is delayed. Example: The idea of division of a whole number / fraction by a fraction is introduced two years before the formal treatment. Informal Treatment

30. Visuals

31. Emphasis on Visualization

32. Visualization Primary Mathematics Standards Edition

33. Visualization

34. Visualization

35. Gilbert and Hazel have some postcards. After Gilbert gives 18 postcards to Hazel, he has 20 postcards more than her. How many more postcards than Hazel does Gilbert have at first? Singapore Examination & Assessment Board Hazel Gilbert 20 18

36. Gilbert and Hazel have some postcards. After Gilbert gives 18 postcards to Hazel, he has 20 postcards more than her. How many more postcards than Hazel does Gilbert have at first? Singapore Examination & Assessment Board Hazel Gilbert 20 18 Visualization

37. Gilbert and Hazel have some postcards. After Gilbert gives 18 postcards to Hazel, he has 20 postcards more than her. How many more postcards than Hazel does Gilbert have at first? Singapore Examination & Assessment Board Hazel Gilbert 20 18 Visualization 18

38. Princess Elizabeth Primary School Practicing Basics & Engaging in Higher Thinking

39. Singapore Examination & Assessment Board Expectations

40. Singapore Examination & Assessment Board

41. Singapore Examination & Assessment Board

42. In a box, there are yellow, red and green beads. 1/3 of the beads in the box are yellow. There are 30 more red beads than yellow beads. The rest of the 15 beads are green. How many beads are there altogether? Ai Tong Primary School Primary 4 Examination Expectations

43. Number Bonds Initial Informal Treatment Visualization Expectations Combining Basics & Higher Thinking Every Child Can Count Every Child Counts

44. [email_address] www.banhar.blogspot.com math.nie.edu.sg/T3 “ C hild r e n a r e t rul y t h e futu r e o f o u r nati o n . “ Irving Harris Bina Bangsa School, Indonesia

45. Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence .. Ministry of Education 2006