This session is on early grade mathematics. It focuses on key ideas in early grades mathematics. I have previously done a keynote lecture on this topic at Erikson Institute, Chicago (First International Symposium on Early Mathematics).

1. National Conference on Singapore Math Strategies Las Vegas PCF Kindergarten Telok Blangah Singapore Session A4 Teaching Kindergarten and First Grade Math Yeap Ban Har banhar.yeap@pathlight.org.sg Slides are available at www.banhar.blogspot.com Princess Elizabeth Primary School Singapore

2. PCF Kindergarten Telok Blangah Singapore In Singapore, formal education starts at Primary 1 (Grade 1). Compulsory education is for the first six grades.

3. overview Theories Behind Singapore Math Jerome Bruner Zoltan Dienes Richard Skemp Big Ideas in Early Mathematics Number Bonds & Basic Facts Visualization Connections Communication PCF Kindergarten Telok Blangah Singapore

4. introduction PART 2 PCF Kindergarten Telok Blangah Singapore

5. The formal education system in Singapore is uniform with only public schools, a national curriculum, and a single teacher-training institute. The gaps among children in the first year of primary school are large depending on the kindergarten education they have received. Some children have not attended kindergartens. St Anthony’s Canossian Primary School, Singapore

6. Conscious effort not to put the disadvantage children in a position of greater disadvantage. Textbooks are written for learners of the language, yet challenging for advanced learners. My Pals Are Here! Mathematics 1

7. Textbooks are also written simply so that non-specialist teachers can understand the mathematics they are teaching. Hopefully, it is not complicated to put the less educated parents off helping their kids. Children bring their books home every day. My Pals Are Here! Mathematics 1

8. Since 2005, Grade 1 and Grade 2 teachers have been asked to adopt the SEED Approach. SEED is the acronym for Strategies for Effective Engagement and Development. More holistic assessment approaches are favored over written tests. Hands-on learning have been given added emphasis. Catholic High School (Primary), Singapore

10. Learning through Inquiry

11. Learning by Collaborating

12. Learning by Reflecting

14. 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

15. PCF Kindergarten Telok Blangah Singapore

16. PCF Kindergarten Telok Blangah Singapore One duck is big. Six ducklings are small.

17. PCF Kindergarten Telok Blangah Singapore

18. PCF Kindergarten Telok Blangah Singapore

19. PCF Kindergarten Telok Blangah Singapore

20. PCF Kindergarten Telok Blangah Singapore

21. My Pals Are Here! Mathematics 1 Number Bonds continues to receive attention in Grade 1.

22. concrete  pictorial  abstractBRUNER’S THEORY PART 2 PCF Kindergarten Telok Blangah Singapore

24. Addition Facts Addition Facts are given emphasis in the first six months of grade one. The children learn it in stages as the textbooks distinguished between Numbers to 10, Numbers to 20, Numbers to 40 and Numbers to 100. Count On and Count All are used in Numbers to 10. Kindergarten Textbook

25. Addition Facts &Number Sense While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20. Princess Elizabeth Primary School

26. 7 + 8

27. 7 + 8

28. mathematical variationDIENES’ THEORY PART 2 PCF Kindergarten Telok Blangah Singapore

31. perceptual variationDIENES’ THEORY PART 2 PCF Kindergarten Telok Blangah Singapore

32. Example on Place Value

33. Example on Number Bonds

34. Why are the illustrations in three consecutive tasks are as such?

36. spiral approach PART 2 PCF Kindergarten Telok Blangah Singapore

37. An Example Study how students get to revisit ideas of number bonds as the deal with number bonds for 6 through 9.

42. spiral approach PART 2 PCF Kindergarten Telok Blangah Singapore

43. Between Grades: Division Primary 1 without symbol Primary 2 with symbol, no remainder Primary 3 with symbol, with remainder long division to 3-digit Primary 4 long division to 4-digit Primary 5 include continuous quantities

44. Within Grade: Whole Numbers Number to 10 Numbers to 20 Numbers to 40 Numbers to 100 Within each unit, numbers, place value, comparing, adding and subtracting are dealt with. This allows students to review materials as they learn new ideas.

45. spiral approach PART 2 PCF Kindergarten Telok Blangah Singapore

46. Whole Numbers in Grade 1 Basic Review Children count shapes in the unit on Shapes Review to Extend Knowledge Children learn another use of whole numbers in the unit on Ordinal Numbers Pre-requisite Children apply counting, comparing, addingand subtracting in the unit on Picture Graphs

49. conceptual understandingSKEMP’S THEORY PART 2 PCF Kindergarten Telok Blangah Singapore

50. 17 + 19 Number Sense 16 + 20

51. Connections Looking for Patterns is introduced through exploration with Shapes. Subsequently, this is done using numbers – in a more abstract context. Princess Elizabeth Primary School MakeConnections to Generalize

52. Visualization In the learning of Numbers to 10, children use square tiles to form patterns of 3 and patterns of 4, for instance. Illustrations in textbooks were also carefully varied to develop this competency.

53. Connections Princess Elizabeth Primary School

54. Communication Articulating one’s thoughts orally, at first, and in written forms using words, pictures, diagrams and symbols is important. Maris Stella High (Primary) School