This was from the professional development course for lower school teachers at a school in Vero Beach, Florida.

1. The ABCDs of Singapore Math Lower School Professional Development St Edward’s School Vero Beach FL www.banhar.blogspot.com Yeap Ban-Har, Ph.D. Singapore banhar.yeap@pathlight.org.sg DaQiao Primary School

2. Catholic High School (Primary)

3. introduction Wellington Primary School

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

5. Move 3 sticks to make 3 squares.

6. Move 3 sticks to make 3 squares.

7. Move 3 sticks to make 2 squares.

8. Move 3 sticks to make 2 squares.

9. Move 3 sticks to make 2 squares.

10. 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? Teacher-Constructed Test Item Fairfield Methodist Primary School

13. 34 – 20 = 14 54 – 34 = 20 34 54

14. 3 x 7 = 21 21 girls wear goggles.

15. 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

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

17. 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

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

19. 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)

20. effective mathematics teaching BinaBangsa School, Indonesia

21. Primary Mathematics 1A Pedagogical Principle: Bruner

22. Number Bonds PCF Kindergarten TelokBlangah

23. Number Bonds PCF Kindergarten TelokBlangah

24. 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

25. Division Princess Elizabeth Primary School

26. Catholic High School (Primary)

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

28. mathz4kidz Learning Centre, Penang, Malaysia concrete experiences

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

30. from pictorial to abstract All Kids Are Intelligent Series

31. mathz4kidz Learning Centre, Penang, Malaysia symbols

32. 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

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

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

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

36. Keys Grade School, Manila, The Philippines

37. Keys Grade School, Manila, The Philippines

38. 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

39. Fraction Division Primary Mathematics Standards Edition Grade 6

40. skemp Scarsdale Middle School New York

41. 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

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

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

44. How is Task 4 different from Task 5? 16 Primary Mathematics Standards Edition Grade 5

45. 16 What is the given in Task 5? What is the given in Task 6? Are these different? 30 Primary Mathematics Standards Edition Grade 5

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

47. dienes Princess Elizabeth Primary School, Singapore

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

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

50. conclusion PCF Kindergarten PasirRis

52. Modeling

53. Providing

54. ExplaningDaQiao Primary School

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

56. This presentation is based on part of one of Singapore pre-service mathematics method courses. 50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists. The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.

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

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