Seminar at Harvard Graduate School of Education 15 April 2010

1. Theoretical Underpinnings of Singapore Math Seminar at Harvard Graduate School of Education Yeap Ban-Har, Ph.D. National Institute of Education Nanyang Technological University Singapore banhar.yeap@nie.edu.sg

2. Catholic High School (Primary)

3. introduction Wellington Primary School

4. Task Lesson Study Problem Wellington Primary School Move 3 sticks to make 3 squares.

5. Task Move 3 sticks to make 3 squares.

6. Task Move 3 sticks to make 3 squares.

7. Task Move 3 sticks to make 2 squares.

8. Task Move 3 sticks to make 2 squares.

9. Task Move 3 sticks to make 2 squares.

10. A Problem from Singapore Grade 6 National Test Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?

11. Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy? chocolates sweets Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets. 12 Jim 12 18 12 12 12 12 Ken 3 parts  12 + 12 + 12 + 12 + 18 = 66 1 part  22 Half of the sweets Ken bought = 22 + 12 = 34 So Ken bought 68 sweets.`

12. 88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day? A Problem from a Singapore Classroom Fairfield Methodist Primary School

15. 34 – 20 = 14 54 – 34 = 20 34 54

16. 3 x 7 = 21 21 girls wear goggles. A Curriculum That Helps Average Students Reach High Achievement

17. TIMSS 2007 Trends in International Mathematics and Science Studies 1995 2003 2007 Grade 4 Advanced 38 41 38 High 70 74 73 Intermediate 89 92 91 Low 96 98 97 North Vista Primary School

18. TIMSS 2007 Trends in International Mathematics and Science Studies Average Indonesia Thailand Malaysia Singapore Grade 8 Advanced 2 3 0 40 2 High 15 12 4 70 18 Intermediate 46 44 14 88 50 Low 75 66 48 97 82 Method Used in Singapore Textbooks

19. 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

20. Every Child Counts

21. effective mathematics teaching BinaBangsa School, Indonesia

22. Primary Mathematics 1A Pedagogical Principle: Bruner

23. Number Bonds PCF Kindergarten TelokBlangah

24. Number Bonds PCF Kindergarten TelokBlangah

25. Bruner The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. Division National Institute of Education

26. Division Princess Elizabeth Primary School

27. My Pals Are Here! Mathematics 1B

28. Catholic High School (Primary)

29. mathz4kidz Learning Centre, Penang, Malaysia bruner’s theory concrete A lesson from Earlybird Kindergarten Mathematics

30. mathz4kidz Learning Centre, Penang, Malaysia concrete experiences

31. from concrete to pictorial mathz4kidz Learning Centre, Penang, Malaysia

32. from pictorial to abstract All Kids Are Intelligent Series

33. mathz4kidz Learning Centre, Penang, Malaysia symbols

34. using concrete materials Professional Development in AteneoGrade School, Manila, The Philippines Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

35. Primary Mathematics (Standards Edition) 2A Pictorial Before Abstract

36. bruner Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

37. skemp’s theory conceptual understanding BinaBangsa School, Semarang, Indonesia

38. Keys Grade School, Manila, The Philippines

39. Keys Grade School, Manila, The Philippines

40. Skemp Understanding in mathematics relational (conceptual) instrumental (procedural) conventional Teaching for conceptual understanding is given emphasis in Singapore Math. Pedagogical Principle: Skemp Primary Mathematics Standards Edition Grade 6

41. Fraction Division Primary Mathematics Standards Edition Grade 6

42. skemp Scarsdale Middle School New York

43. Dienes Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. Pedagogical Principle: Dienes Primary Mathematics Standards Edition Primary Mathematics Standards Edition Grade 1

44. Pedagogical Principle: Dienes Primary Mathematics Standards Edition Grade 1

45. Pedagogical Principle: Dienes Primary Mathematics Standards Edition Grade 2

46. 1 h = 60 min 60 ÷ 4 = 15 15 x 3 = 45 ¾ x 60 = 45 Primary Mathematics Standards Edition Grade 5

47. Mathematical Variation 16 Primary Mathematics Standards Edition Grade 5

48. 16 Mathematical Variation 30 Primary Mathematics

49. Mathematical Variation Primary Mathematics Standards Edition Grade 2

50. Earlybird Kindergarten Mathematics Standards Edition diene’s theory of variation

51. diene’s theory of variation

52. dienes Princess Elizabeth Primary School, Singapore

53. Emphasis on pictorial representation and systematic variation to enhance conceptual understanding

54. Fuchun Primary School, Singapore interaction Vygotsky’s Theory Children Learn in Social Situations

55. conclusion PCF Kindergarten PasirRis

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

57. Patterns BinaBangsa School Bandung, Indonesia

58. Patterns BinaBangsa School Bandung, Indonesia

59. Visualization Yangzheng Primary School

60. Communication PathlightSchool

61. Primary Mathematics Syllabus 2007 Primary 2 Wellington Primary School

62. Balestier Hill Primary School Fuchun Primary School Primary Mathematics Syllabus 2007

63. Princess Elizabeth Primary School

64. “Children are trulythe future of our nation. “ Irving Harris

65. TEDS-M Elementary Teachers Content Knowledge TEDS-M Elementary Teachers Pedagogical Content Knowledge

66. TEDS-M Middle School Teachers Content Knowledge TEDS-M Middle School Teachers Pedagogical Content Knowledge