Teacher trainers received an extension to the three-day course they received in September last year. The focus is on the problem-solving approach.

1. teaching mathematics focusing on problem solving DrYeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com www.banhar.blogspot.com www.banhar.com Today’s discussion is based on lessons taken from a Singapore textbook series. The goal is to see how mathematics teaching can be made to focus on problem solving and how the lessons can be differentiated for struggling and advanced students. Photographs of the session is available on Facebook

2. fundamental principles mathematics of teaching & learning Review focusing on problem solving

3. concrete

4. pictorial

5. abstract

6. concrete pictorial abstract

7. variations

8. variations

9. variations

10. Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Mathematics Curriculum Framework

11. one example focusing on problem solving

12. Show 32 using base ten blocks. Do 32 – 9 . focusing on problem solving

13. Show 32 using base ten blocks. Do 32 – 9 . focusing on problem solving

14. focusing on problem solving

15. focusing on problem solving

16. focusing on problem solving

18. Show 32 using base ten blocks. Do 32 – 9 . focusing on problem solving

21. focusing on problem solving

22. two example focusing on problem solving

23. This piece of paper represents 1. Divide it into four equal parts. focusing on problem solving

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

25. focusing on problem solving

26. focusing on problem solving

27. Initial Concrete Experience Subsequent Pictorial Representation focusing on problem solving

28. Eventual Symbolic Representation

29. focusing on problem solving

30. three example focusing on problem solving

31. Fuchun Primary School, Singapore focusing on problem solving

32. Fuchun Primary School, Singapore focusing on problem solving

33. four example focusing on problem solving

34. focusing on problem solving

35. five example focusing on problem solving

37. focusing on problem solving

38. focusing on problem solving

39. six example focusing on problem solving

40. focusing on problem solving

42. Reference: My Pals Are Here! Maths focusing on problem solving

43. Reference: Primary Mathematics (Standards Edition) focusing on problem solving

44. Reference: Primary Mathematics (Standards Edition)

45. seven example focusing on problem solving

46. focusing on problem solving

47. Kyla ? $28 – $9 = $19 Kyla has $19. Jake ? $9 $28 focusing on problem solving

48. apples 90 oranges 38 pears 15

49. apples 90 oranges pears 15 23

50. 90 + 15 = 105 5 units  1 unit  105 ÷ 5 = 21 There were (21 + 21 + 23) apples, hence oranges. There were 44 oranges used. apples ? oranges pears 15 23