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 MathInternational SchoolSaigon PearlHo Chi Minh Citywww.banhar.blogspot.comYeap Ban-Har, Ph.D.Singaporebanhar.yeap@pathlight.org.sgDa 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. introductionWellington Primary School, Singapore

5. BeliefsInterestAppreciationConfidencePerseveranceMonitoring of one’s own thinkingSelf-regulation of learningAttitudesMetacognitionNumerical calculationAlgebraic manipulationSpatial visualizationData analysisMeasurementUse of mathematical toolsEstimationMathematical Problem SolvingReasoning, communication & connectionsThinking skills & heuristicsApplication & modellingSkillsProcessesConceptsNumericalAlgebraicGeometricalStatisticalProbabilisticAnalyticalMathematics 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 cm150 cm – 95 cm = 105 cm105 cm of copper wire was left.Example 3Singapore Examinations & Assessment Board

9. strands ofmathematicalproficienciesProcedural fluency

10. Conceptual reasoning

11. Strategic competence

12. Adaptive reasoning

13. Productive dispositionKilpatrick, Swafford & Findell 2001

14. Philosophy of the Education Systemthinking schoolslearning nationMinistry of Education 1997

15. Rationale for Teaching Mathematics“an excellent vehiclefor the development and improvementof a person’sintellectual competence”Ministry of Education 2006

16. mathz4kidz Learning Centre, Penang, MalaysiaTrends inMathematicsThis whole shape stands for 1.& Science StudiesWhat does this stand for?applytheir understandingand knowledgein a variety ofcomplex situations

17. Trends inMathematics& ScienceStudyexplaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia

18. mathematicalliteracy… 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, Singaporebasicsin early grades

20. Development ofNumber 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 BondsPCF TelokBlangahKindergarten, Singapore

27. PCF TelokBlangahKindergarten, Singapore

28. Number BondsPCF TelokBlangahKindergarten, Singapore

29. Number BondsPCF 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. effectivemathematicsteachingBinaBangsa School, Indonesia

40. Spiral Within and Between Grades

43. effectivemathematicsteachingBinaBangsa School, Indonesia

45. Bruner

46. BrunerThe concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. DivisionNational Institute of Education, Singapore

48. DivisionPrincess Elizabeth Primary School, Singapore

49. mathz4kidz Learning Centre, Penang, Malaysiabruner’s theoryconcreteA lesson from Earlybird Kindergarten Mathematics

50. mathz4kidz Learning Centre, Penang, Malaysiaconcreteexperiences

51. mathz4kidz Learning Centre, Penang, Malaysiafromconcretetopictorial

52. frompictorialtoabstractAll Kids Are Intelligent Series

53. mathz4kidz Learning Centre, Penang, Malaysiasymbols

54. usingconcretematerialsProfessional Development in AteneoGrade School, Manila, The PhilippinesLesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

55. MultiplicationCatholic High School (Primary), Singapore

56. Primary Mathematics (Standards Edition) 2APictorial Before Abstract

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

59. skemp’stheoryconceptualunderstandingBinaBangsa School, Semarang, Indonesia

60. Keys Grade School, Manila, The Philippines

61. Keys Grade School, Manila, The Philippines

62. SkempUnderstanding in mathematics relational (conceptual) instrumental (procedural) conventional Teaching for conceptual understanding is given emphasis in Singapore Math.Pedagogical Principle:SkempPrimary Mathematics Standards Edition Grade 6

63. skempScarsdale Middle School, New York

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

65. effectivemathematicsteachingBinaBangsa School, Indonesia

66. Pedagogical Principle:Dienes

67. Pedagogical Principle:Dienes

71. DienesDienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. Pedagogical Principle:DienesPrimary 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’stheoryofvariation

73. dienesPrincess Elizabeth Primary School, Singapore

74. thinkingproblem solvingbruner’scpa approachconceptual understandingdiene’s variations

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

76. conclusionPCF Kindergarten PasirRis, Singapore

77. Instructional Models Coaching

78. Modeling