This document summarizes a seminar on the Singapore Math approach. It discusses key concepts like conceptual understanding, variation theory, concrete-pictorial-abstract instruction, and assessment results that show Singapore student performance. Example word problems are provided to illustrate how Singapore Math teaches for understanding over rote memorization.

1. Seminar on Singapore Math International School Saigon Pearl Ho Chi Minh City www.banhar.blogspot.com Yeap Ban-Har, Ph.D. Singapore banhar.yeap@pathlight.org.sg Da Qiao Primary School, Singapore

2. The examples used in this course are take n from Math in Focus The Singapore Approach unless otherwise specified.

3. Catholic High School (Primary), Singapore

4. introduction Wellington Primary School, Singapore

5. 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

6. Example 1

7. Example 2

8. John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left? 19 cm x 5 = 95 cm 150 cm – 95 cm = 105 cm 105 cm of copper wire was left. Example 3 Singapore Examinations & Assessment Board

10. Conceptual reasoning

11. Strategic competence

12. Adaptive reasoning

13. Productive dispositionKilpatrick, Swafford & Findell 2001

14. Philosophy of the Education System thinking schools learning nation Ministry of Education 1997

15. Rationale for Teaching Mathematics “an excellent vehicle for the development and improvement of a person’s intellectual competence” Ministry of Education 2006

16. mathz4kidz Learning Centre, Penang, Malaysia Trends in Mathematics This whole shape stands for 1. & Science Studies What does this stand for? apply their understanding and knowledge in a variety of complex situations

17. Trends in Mathematics & ScienceStudy explain their reasoning mathz4kidz Learning Centre, Penang, Malaysia

18. mathematical literacy … capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life … OECD Program for International Student Assessment (PISA)

19. Princess Elizabeth Primary School, Singapore basics in early grades

20. Development of Number Sense

21. Number Bonds Number Bonds is emphasized prior to the learning of addition. Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5. Earlybird Kindergarten Mathematics Series

22. PCF TelokBlangahKindergarten, Singapore

23. One duck is big. Six ducklings are small. PCF TelokBlangahKindergarten, Singapore

24. PCF TelokBlangahKindergarten, Singapore

25. PCF TelokBlangahKindergarten, Singapore

26. Number Bonds PCF TelokBlangahKindergarten, Singapore

27. PCF TelokBlangahKindergarten, Singapore

28. Number Bonds PCF TelokBlangahKindergarten, Singapore

29. Number Bonds PCF TelokBlangahKindergarten, Singapore

31. Basic Facts

32. Basic Facts

33. Basic Facts

34. Basic Facts

35. Basic Facts

36. Basic Facts

37. Primary Mathematics Standards Edition

38. National Institute of Education

39. effective mathematics teaching BinaBangsa School, Indonesia

40. Spiral Within and Between Grades

43. effective mathematics teaching BinaBangsa School, Indonesia

45. Bruner

46. 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, Singapore

48. Division Princess Elizabeth Primary School, Singapore

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

50. mathz4kidz Learning Centre, Penang, Malaysia concrete experiences

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

52. from pictorial to abstract All Kids Are Intelligent Series

53. mathz4kidz Learning Centre, Penang, Malaysia symbols

54. 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

55. Multiplication Catholic High School (Primary), Singapore

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

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

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

60. Keys Grade School, Manila, The Philippines

61. Keys Grade School, Manila, The Philippines

62. 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

63. skemp Scarsdale Middle School, New York

64. 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

65. effective mathematics teaching BinaBangsa School, Indonesia

66. Pedagogical Principle: Dienes

67. Pedagogical Principle: Dienes

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

72. Earlybird Kindergarten Mathematics Series Standards Edition Can you see how Dienes’ idea is used in designing these tasks? diene’s theory of variation

73. dienes Princess Elizabeth Primary School, Singapore

74. thinking problem solving bruner’scpa approach conceptual understanding diene’s variations

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

76. conclusion PCF Kindergarten PasirRis, Singapore

78. Modeling

79. Providing

80. ExplaningDa Qiao Primary School, Singapore

81. Grade Six National Test Item 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?

82. 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.`

83. 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

84. 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

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