Rotterdam Day 2

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We focus on the bar model.

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Rotterdam Day 2

  1. 1. Singapore Math in Rotterdam 2<br />Opleiding Singapore rekenspecialist<br />Review of Day 1<br />What are some features of Singapore Math and its theoretical underpinnings.<br />On Day 2, we look at the focus on visualization and the model method.<br />
  2. 2. Review of Day 1<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  3. 3. Variations<br />Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.<br />
  4. 4. Math in Focus 2A<br />
  5. 5. Math in Focus 2A<br />
  6. 6. Math in Focus 2A<br />
  7. 7. ZoltanDienes<br />The three lessons include mathematical variations within the same grade. <br />This is referred to as a spiral approach.<br />
  8. 8. 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.<br />The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons.<br />Place Value Chart<br />Expanded Notation<br />Words<br />Numerals<br />Tens and Ones Notation<br />Primary Mathematics<br />
  9. 9. ZoltanDienes<br />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.<br />
  10. 10. Jerome Bruner<br />Bruner advised teachers to use the CPA Approach in teaching mathematics.<br />
  11. 11.
  12. 12. Richard Skemp<br />Skemp distinguished between instrumental understanding from relational understanding to encourage teachers to teach for conceptual understanding.<br />
  13. 13. skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
  14. 14. Example 2<br />Division in Other Grade Levels<br />
  15. 15. My Pals Are Here! Mathematics 3A<br />
  16. 16. My Pals Are Here! Mathematics 3A<br />
  17. 17. My Pals Are Here! Mathematics 3A<br />
  18. 18. My Pals Are Here! Mathematics 3A<br />
  19. 19. My Pals Are Here! Mathematics 3A<br />
  20. 20. My Pals Are Here! Mathematics 3A<br />
  21. 21. My Pals Are Here! Mathematics 3A<br />
  22. 22. My Pals Are Here! Mathematics 3A<br />
  23. 23. My Pals Are Here! Mathematics 3A<br />
  24. 24.
  25. 25. Keys Grade School, Manila, The Philippines<br />
  26. 26. Keys Grade School, Manila, The Philippines<br />
  27. 27. The Bar Model Method<br />de strookmodel<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  28. 28. Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-regulation of learning<br />Attitudes<br />Metacognition<br />Numerical calculation<br />Algebraic manipulation<br />Spatial visualization<br />Data analysis<br />Measurement<br />Use of mathematical tools<br />Estimation<br />Mathematical Problem Solving<br />Reasoning, communication & connections<br />Thinking skills & heuristics<br />Application & modelling<br />Skills<br />Processes<br />Concepts<br />Numerical<br />Algebraic<br />Geometrical<br />Statistical<br />Probabilistic<br />Analytical<br />Mathematics Curriculum Framework<br />
  29. 29. visualization<br />Wellington Primary School<br />
  30. 30. Primary Mathematics Standards Edition <br />
  31. 31.
  32. 32. 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?<br /> <br />19 cm x 5 = 95 cm<br />150 cm – 95 cm = 105 cm<br />
  33. 33. 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. <br /> <br />
  34. 34. The Bar Model Method<br />de strookmodel<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  35. 35. Ali has 3 sweets. <br />Billy has 5 sweets.<br />How many sweets do they have altogether?<br />Ali<br />Billy<br />
  36. 36. Ali has 3 sweets. <br />Billy has 5 sweets.<br />How many sweets do they have altogether?<br />Ali<br />Billy<br />
  37. 37.
  38. 38. Introduction<br />The focus is on the bar model method.<br />
  39. 39. Materials developed by Poon Yain Ping <br />
  40. 40. Materials developed by Poon Yain Ping <br />
  41. 41. Materials developed by Poon Yain Ping <br />
  42. 42. Summary<br />The three basic situations are part-whole, comparison and before-after situations.<br />
  43. 43. Materials developed by Poon Yain Ping <br />
  44. 44. 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.<br />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.<br />Materials developed by Poon Yain Ping <br />
  45. 45. Summary<br />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.<br />
  46. 46. Materials developed by Poon Yain Ping <br />
  47. 47. Materials developed by Poon Yain Ping <br />
  48. 48. Materials developed by Poon Yain Ping <br />
  49. 49. School Assessment<br />women<br />men<br />
  50. 50. School Assessment<br />women<br />45<br />men<br />12<br />
  51. 51. School Assessment<br />women<br />men<br />?<br />women<br />45<br />6<br />6<br />men<br />12<br />
  52. 52. Further Practice for Model Method<br />
  53. 53. Materials developed by Poon Yain Ping <br />
  54. 54. Materials developed by Poon Yain Ping <br />
  55. 55. Materials developed by Poon Yain Ping <br />
  56. 56. Materials developed by Poon Yain Ping <br />
  57. 57. Materials developed by Poon Yain Ping <br />
  58. 58. Materials developed by Poon Yain Ping <br />
  59. 59. Materials developed by Poon Yain Ping <br />
  60. 60. Materials developed by Poon Yain Ping <br />
  61. 61. Materials developed by Poon Yain Ping <br />
  62. 62. Materials developed by Poon Yain Ping <br />
  63. 63. Materials developed by Poon Yain Ping <br />

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