This was presented at the NCTM Annual Meeting and Exposition. It provides participants with features of math program that make mathematics accessible to average and struggling learners.

1. Making Mathematics Accessible The Singapore Method DrYeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com Slides are available at www.banhar.blogspot.com

2. MCI-WSU Singapore Math Summer Institute 6 – 8 July 2011 Comprehensive program taught collaboratively by Singapore mathematics educators and WSU’s professors.

3. makes abstract concepts accessible to learners who are not yet ready for abstraction The CPA Approach Focus on Thinking builds fundamental intellectual competencies required for learners to handle abstraction

4. Grade 2 Multiplication Example Singapore

5. Woodlands Primary School, Singapore Grade 2 Multiplication

6. Pictorial to Symbolic Concrete to Pictorial Symbolic Reference: Primary Mathematics

7. Reference: Math in Focus

8. Reference: Math in Focus

9. Grade 4 Division of Large Numbers Example Philippines

10. Keys Grade School, Manila, The Philippines

11. Grade 8 Volume of Pyramid Example Indonesia

12. BinaBangsa School, Semarang, Indonesia

13. Grade 2 Fractions Example Florida

14. St Edward’s School, Vero Beach, Florida

16. Initial Concrete Experience Subsequent Pictorial Representation

17. Eventual Symbolic Representation

19. Primary 6 Circumference of Circles Example Singapore

20. Fuchun Primary School, Singapore

21. Fuchun Primary School, Singapore

22. Kindergarten Subtraction Example Malaysia

23. mathz4kidz Learning Centre, Penang, Malaysia bruner’s theory concrete

24. mathz4kidz Learning Centre, Penang, Malaysia concrete experiences

25. from concrete to pictorial Reference: Earlybird Kindergarten Mathematics

26. from pictorial to abstract Reference: All Kids Are Intelligent Series

27. mathz4kidz Learning Centre, Penang, Malaysia symbols

28. Primary 1 Division Example Singapore

30. Reference: My Pals Are Here! Maths

31. Reference: Primary Mathematics (Standards Edition)

32. Reference: Primary Mathematics (Standards Edition)

33. Scarsdale Middle School, New York

35. Primary 5 Multiplication of Fractions Example Singapore

36. Da Qiao Primary School, Singapore

37. Allan spent ¼ of his allowance on a gift and ¼ of the remainder on a book. The book cost $18. Find the amount of Allan’s allowance. Allan’s allowance = 4 x $24 = $96 $72 ÷ 3 = $24 4 x $18 = $72

38. Student’s Initial Solution Student’s Alternate Solution

39. The Curriculum (Ministry of Education 2006)

40. The Curriculum (Ministry of Education 2006)

41. The Curriculum (Ministry of Education 2006)

42. makes abstract concepts accessible to learners who are not yet ready for abstraction The CPA Approach Focus on Thinking builds fundamental intellectual competencies required for learners to handle abstraction

43. MCI-WSU Singapore Math Summer Institute 6 – 8 July 2011 Comprehensive program taught collaboratively by Singapore mathematics educators and WSU’s professors.