Rotterdam Day 1

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This is part of the professional development for the team that translate My Pals Are Here into Dutch and also people who are going to provide professionald evelopment for teachers using Singapore textbooks in the future.

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Rotterdam Day 1

  1. 1. Singapore Math in Rotterdam I<br />Opleiding Singapore rekenspecialist<br />This set of slides cover three presentations made on the first day:<br /><ul><li>Features of Singapore Math
  2. 2. Theories – Bruner & Dienes
  3. 3. Teaching for Understanding</li></ul>Weten en begrijpen hoe de theorieen van o.aJ.Bruner, R.Skemp, Z.Dieneszijnuitgewerkt in het ontwerp van eeneffectiefrekenprogrammadatalleleerlingen in staatsteltteleren en bovengemiddleldeleerlingen de kansbiedtteexcelleren.<br />
  4. 4. Features of Singapore Mathematics Curriculum<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  5. 5. Introduction<br />This is a brief overview of the development of the Singapore mathematics curriculum, its framework and its rationale and underlying goals.<br />
  6. 6. 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 />
  7. 7. Every Child Counts<br />Huamin Primary School<br />
  8. 8. TIMSS 1995 – 2007 <br />Trends in International Mathematics and Science Studies<br />1995<br />2003<br />2007<br />International<br />Grade 4<br />5<br />Advanced<br />38<br />41<br />38<br />26<br />High<br />70<br />74<br />73<br />67<br />Intermediate<br />89<br />92<br />91<br />90<br />Low<br />96<br />98<br />97<br />North Vista Primary School<br />
  9. 9. TIMSS 2007<br />Trends in International Mathematics and Science Studies<br />Indonesia<br />Thailand<br />Malaysia<br />Singapore<br />International<br />Grade 8<br />Advanced<br />2<br />3<br />0<br />40<br />2<br />High<br />15<br />12<br />4<br />70<br />18<br />Intermediate<br />46<br />44<br />14<br />88<br />50<br />Low<br />75<br />66<br />48<br />97<br />82<br />Method Used in Singapore Textbooks<br />
  10. 10. Why Schools Teach Mathematics<br />We will engage in activities that are used to help teachers understand the rationale for teaching mathematics in school.<br />
  11. 11. Problem<br />Arrange the ten cards so that you can do what is shown to you.<br />
  12. 12. Method 1 – by drawing<br />
  13. 13. Method 2 – by using the cards<br />
  14. 14. Scarsdale Teachers’ Institute, New York<br />
  15. 15. Some participants tried to solve the Dutch-version of the problem. <br />
  16. 16. Problem<br />Rearrange the sticks to show a given number of squares.<br />Wellington Primary School<br />
  17. 17. Task<br />Lesson Study Problem <br />Wellington Primary School<br />Move 3 sticks to make 3 squares.<br />
  18. 18. Task<br />Move 3 sticks to make 3 squares.<br />
  19. 19. Task<br />Move 3 sticks to make 3 squares.<br />
  20. 20. Task<br />Move 3 sticks to make 2 squares.<br />
  21. 21. Task<br />Move 3 sticks to make 2 squares.<br />
  22. 22. Task<br />Move 3 sticks to make 2 squares.<br />
  23. 23. Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”.<br />Ministry of Education (Singapore) 2006<br />
  24. 24. Focus on Problem Solving<br />The Singapore curriculum focuses on problem solving. So does the national test. It is no wonder that’s schools place a lot of emphasis on problem solving.<br />
  25. 25. National Test<br />
  26. 26. Textbooks<br />
  27. 27. Textbooks<br />
  28. 28. Textbooks<br />
  29. 29. Textbooks<br />
  30. 30. The CPA Approach <br />& Principle of Variations<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  31. 31. Number Bonds<br />The focus on number sense right from the start. Number bonds is taught before addition.<br />
  32. 32. Number Bonds <br />Number Bonds is emphasized prior to the learning of addition.<br />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. <br />Earlybird Kindergarten Mathematics<br />
  33. 33. PCF TelokBlangah Kindergarten<br />
  34. 34. One duck is big. <br />Six ducklings are small.<br />PCF TelokBlangah Kindergarten<br />
  35. 35. PCF TelokBlangah Kindergarten<br />
  36. 36. PCF TelokBlangah Kindergarten<br />
  37. 37. PCF TelokBlangah Kindergarten<br />
  38. 38. PCF TelokBlangah Kindergarten<br />
  39. 39. My Pals Are Here! Mathematics<br />Number Bonds continues to receive attention in Grade 1.<br />
  40. 40. Addition Facts<br />Addition Facts are given emphasis in the first six months of grade one.<br />The children learn it in stages as the textbooks distinguished between Numbers to 10 and Numbers to 20.<br />Count On and Count All are used in Numbers to 10.<br />Earlybird Kindergarten Mathematics<br />
  41. 41. Addition Facts &Number Sense <br />While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.<br />Princess Elizabeth Primary School<br />The topics are arranged in a way that makes learning progressive and systematic – this is part of the idea of a spiral curriculum.<br />
  42. 42. Jerome Bruner<br />Ideas are introduced using concrete materials. Pictorial representations follow. Finally, children engage with the abstract symbols. This is called the CPA Approach in Singapore.<br />
  43. 43. mathz4kidz Learning Centre, Penang, Malaysia<br />bruner’s theory<br />concrete<br />A lesson from Earlybird Kindergarten Mathematics<br />
  44. 44. mathz4kidz Learning Centre, Penang, Malaysia<br />concrete<br />experiences<br />
  45. 45. mathz4kidz Learning Centre, Penang, Malaysia<br />from<br />concrete<br />to<br />pictorial<br />
  46. 46. from<br />pictorial<br />to<br />abstract<br />All Kids Are Intelligent Series<br />
  47. 47. mathz4kidz Learning Centre, Penang, Malaysia<br />symbols<br />
  48. 48. Variations<br />Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.<br />
  49. 49. Math in Focus 2A<br />
  50. 50. Math in Focus 2A<br />
  51. 51. Math in Focus 2A<br />
  52. 52. ZoltanDienes<br />The three lessons include mathematical variations within the same grade. <br />This is referred to as a spiral approach.<br />
  53. 53. 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 />
  54. 54. ZoltanDienes<br />The one 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 />
  55. 55. Teaching for Understanding<br />Ideas from Richard Skemp<br />Yeap Ban Har, Ph.D.<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />
  56. 56. Example 1<br />Grade 1 Division<br />
  57. 57.
  58. 58. The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. <br />Grade 1 Division<br />National Institute of Education<br />
  59. 59.
  60. 60. Curriculum Document<br />Division of a quantity (not greater than 20) into equal sets<br /> Given the number of objects in the <br />set<br />Given the number of sets<br />Solving 1-step word problems with pictorial representation<br />
  61. 61. Princess Elizabeth Primary School<br />Division<br />
  62. 62. Links between concrete and pictorial representation must be carefully constructed.<br />
  63. 63. skemp’s<br />theory<br />conceptual<br />understanding<br />BinaBangsa School, Semarang, Indonesia<br />
  64. 64. Example 2<br />Division in Other Grade Levels<br />
  65. 65. My Pals Are Here! Mathematics 3A<br />
  66. 66. My Pals Are Here! Mathematics 3A<br />
  67. 67. My Pals Are Here! Mathematics 3A<br />
  68. 68. My Pals Are Here! Mathematics 3A<br />
  69. 69. My Pals Are Here! Mathematics 3A<br />
  70. 70. My Pals Are Here! Mathematics 3A<br />
  71. 71. My Pals Are Here! Mathematics 3A<br />
  72. 72. My Pals Are Here! Mathematics 3A<br />
  73. 73. My Pals Are Here! Mathematics 3A<br />
  74. 74.
  75. 75. Keys Grade School, Manila, The Philippines<br />
  76. 76. Keys Grade School, Manila, The Philippines<br />
  77. 77. Example 3<br />Division Involving Fractions<br />
  78. 78. Skemp<br />Understanding in mathematics <br /> relational<br /> (conceptual) <br /> instrumental <br /> (procedural)<br /> conventional <br />Teaching for conceptual understanding is given emphasis in Singapore Math.<br />Primary Mathematics Standards Edition Grade 6<br />
  79. 79. Primary Mathematics Standards Edition Grade 6<br />

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