Singapore Math in Rotterdam 2 Opleiding Singapore rekenspecialist

1. Singapore Math in Rotterdam 2 Opleiding Singapore rekenspecialist • This set of slides cover the presentation made on the second day: • The Model Method De centralelaats van visualisatie in het rekenonderwijskunnenplaatsen. Leren hoe je de Model Methodekunttoepassenbij het oplossen van redactieopgaven. Begrijpen hoe dezeModelbenaderinghelptomzakentevisualiseren en omverbadentezientussen de feiten en de informatie die in de opgavengegevenwordt.

2. Singapore Math in Rotterdam 2 Opleiding Singapore rekenspecialist Review of Day 1 What are some features of Singapore Math and its theoretical underpinnings. On Day 2, we look at the focus on visualization and the model method.

3. Review of Day 1 Yeap Ban Har, Ph.D. Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com

4. Variations Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.

5. Math in Focus 2A

6. Math in Focus 2A

7. Math in Focus 2A

8. ZoltanDienes The three lessons include mathematical variations within the same grade. This is referred to as a spiral approach.

9. It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation. The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons. Place Value Chart Expanded Notation Words Numerals Tens and Ones Notation Primary Mathematics

10. ZoltanDienes This lesson include perceptual variations. This is Dienes’ idea of multiple embodiment. The mathematical concept is constant while the materials used to embody it are varied.

11. Jerome Bruner Bruner advised teachers to use the CPA Approach in teaching mathematics.

13. Richard Skemp Skemp distinguished between instrumental understanding from relational understanding to encourage teachers to teach for conceptual understanding.

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

15. Example 2 Division in Other Grade Levels

16. My Pals Are Here! Mathematics 3A

17. My Pals Are Here! Mathematics 3A

18. My Pals Are Here! Mathematics 3A

19. My Pals Are Here! Mathematics 3A

20. My Pals Are Here! Mathematics 3A

21. My Pals Are Here! Mathematics 3A

22. My Pals Are Here! Mathematics 3A

23. My Pals Are Here! Mathematics 3A

24. My Pals Are Here! Mathematics 3A

26. Keys Grade School, Manila, The Philippines

27. Keys Grade School, Manila, The Philippines

28. The Bar Model Method de strookmodel Yeap Ban Har, Ph.D. Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com

29. 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

30. visualization Wellington Primary School

31. Primary Mathematics Standards Edition

33. 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

34. There was an interesting discussion on this problem. There was an explanation that a + b + c = 19 cm. Then there was an assumption that a : b : c = 4 : 2 : 1 which was met with rebuttals such as there is no need to know a : b : c as well as the point that a : b : c can be determined by measuring or folding.

35. The Bar Model Method de strookmodel Yeap Ban Har, Ph.D. Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com

36. Ali has 3 sweets. Billy has 5 sweets. How many sweets do they have altogether? Ali Billy

37. Ali has 3 sweets. Billy has 5 sweets. How many sweets do they have altogether? Ali Billy

39. Introduction The focus is on the bar model method.

40. Materials developed by Poon Yain Ping

41. Materials developed by Poon Yain Ping

42. Materials developed by Poon Yain Ping

43. Summary The three basic situations are part-whole, comparison and before-after situations.

44. Materials developed by Poon Yain Ping

45. The class decided that this was impossible. The teacher asked the class to change this to another number to make the situation possible. We discussed when it is 3, 4 and 5 times. A student gave an incorrect solution for the second part. The teacher asked students to write a question for which this would be a correct solution. Materials developed by Poon Yain Ping

46. Summary We discussed how to use students’ responses to make the lesson focus on depth. We also saw how a problem can be modified to challenge learners.

47. Materials developed by Poon Yain Ping

48. Materials developed by Poon Yain Ping

49. Materials developed by Poon Yain Ping

50. School Assessment women men