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Singapore Maths<br />THE ESSENTIALS<br />London  June 2011<br />DrYeap Ban Har<br />banhar@sg.marshallcavendish.com<br />...
Kembangan PCF Kindergarten<br />
Curriculum for all learners<br /><ul><li>Struggling students learn enough
Average students perform advanced skills
Advanced students are challenged</li></ul>Kembangan PCF Kindergarten<br />
TIMSS<br />Trends in International Mathematics and Science Studies<br />Grade  4   2003<br />Grade  8   2007<br />Grade  4...
Singapore Mathematics: Focus on Thinking<br />an<br />excellent<br />vehicle<br />for<br />the development<br />&<br />imp...
Allan puts some brown sugar on a dish.<br />The total weight of the brown sugar and the dish is 110 g.<br />Bella puts thr...
Allan puts some brown sugar on a dish.<br />The total weight of the brown sugar and the dish is 110 g.<br />Bella puts thr...
110 g<br />3 units = 180 g<br />1 unit = 60 g<br />110 g<br />180 g<br />3 units = 180 g<br />Bella puts 180 g brown sugar...
Singapore Math<br />Visualization<br />
1	 2	 3	 4	 5	 6<br />11	10	 9	 8	 7	<br />	12	13	14	15	16<br /> 21	20	19	18	17	<br />22	23	24	25	26	<br />
1	   2	     3	    4	    5	<br />9	   8	     7	    6	    	<br />	    10	     11	     12	    13	<br />17	    16	     15	    ...
Professional Development in Santiago de Chile<br />
Singapore Math<br />Patterns<br />
Archipelschool<br />De Tweemaster – Kameleon<br />The Netherlands<br />
Beliefs<br />Interest<br />Appreciation<br />Confidence<br />Perseverance<br />Monitoring of one’s own thinking<br />Self-...
Professional Development in ARK Schools, London<br />
Problem Solving in Learning Basic Concepts and Skills<br />Professional Development in Santiago de Chile<br />
Reference: Primary Mathematics (Standards Edition)<br />
Reference: Primary Mathematics (Standards Edition)<br />
Singapore Math<br />Learn New Concept Through <br />Problem Solving<br />
Singapore Math<br />Drill-and-Practice Through <br />Problem Solving<br />
<br /><br /><br />
Singapore Math<br />Applying Knowledge in <br />Problem Solving<br />
makes abstract concepts accessible to learners who are not  yet  ready  for  abstraction<br />The CPA Approach<br />Focus ...
Textbook <br />
Reference: My Pals Are Here! Maths<br />
1. Setting Up the Task<br />Each person should get 12 animals. I have given you some. How many more do you need?<br />Pupi...
2. Development (1)<br />Put four animals into one cup. Note only one cup is given.<br />This mirrors drawing rings around ...
Students should have positive experiences during the lesson.<br />Put four animals into a second cup.<br />
How many animals are there altogether? <br />How many animals are there in one cup? How many cups do we use?<br />
3. Development (2)<br />This is like the workbook tasks except that the magnets can be moved. Built-in remedial strategy.<...
Pupils needs to monitor the number of magnets as well as to manage their visualization process.<br />Variations on the arr...
4. Extension<br />
5. Development (3) The use of colour to show the group. <br />Built-in remedial strategy.<br />
CPA Approach<br />Links between concrete and pictorial representation must be carefully constructed.<br />Remedial steps a...
Reference: Primary Mathematics (Standards Edition)<br />
51 – 17<br />51 x 3<br />51 + 26<br />
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ARK Schools, London

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This is a one-day course on Essentials of Singapore Maths which is equivalent to MAP101 Fundamentals of Singapore Mathematics. About 60 participants attended this session.

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Transcript of "ARK Schools, London "

  1. 1. Singapore Maths<br />THE ESSENTIALS<br />London  June 2011<br />DrYeap Ban Har<br />banhar@sg.marshallcavendish.com<br />Marshall Cavendish Institute Singapore<br />Presentation slides are available at www.banhar.blogspot.com<br />
  2. 2. Kembangan PCF Kindergarten<br />
  3. 3. Curriculum for all learners<br /><ul><li>Struggling students learn enough
  4. 4. Average students perform advanced skills
  5. 5. Advanced students are challenged</li></ul>Kembangan PCF Kindergarten<br />
  6. 6. TIMSS<br />Trends in International Mathematics and Science Studies<br />Grade 4 2003<br />Grade 8 2007<br />Grade 4 1995<br />Grade 8 1999<br />38<br />40<br />Advanced<br />38<br />42<br />73<br />70<br />High<br />70<br />77<br />91<br />88<br />Intermediate<br />89<br />94<br />97<br />97<br />Low<br />96<br />99<br />
  7. 7. Singapore Mathematics: Focus on Thinking<br />an<br />excellent<br />vehicle<br />for<br />the development<br />&<br />improvement of<br />a person’s intellectual<br />competencies<br />Ministry of Education Singapore 2006<br />
  8. 8. Allan puts some brown sugar on a dish.<br />The total weight of the brown sugar and the dish is 110 g.<br />Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.<br />Find the weight of the brown sugar that Bella puts on the dish.<br />an identical<br />
  9. 9. Allan puts some brown sugar on a dish.<br />The total weight of the brown sugar and the dish is 110 g.<br />Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.<br />Find the weight of the brown sugar that Bella puts on the dish.<br />an identical<br />110 g<br />2 units = 180 g<br />1 unit = 90 g<br />110 g<br />180 g<br />3 units = 270 g<br />Bella puts 270 g brown sugar on the dish.<br />290 g<br />
  10. 10. 110 g<br />3 units = 180 g<br />1 unit = 60 g<br />110 g<br />180 g<br />3 units = 180 g<br />Bella puts 180 g brown sugar on the dish.<br />290 g<br />
  11. 11. Singapore Math<br />Visualization<br />
  12. 12.
  13. 13. 1 2 3 4 5 6<br />11 10 9 8 7 <br /> 12 13 14 15 16<br /> 21 20 19 18 17 <br />22 23 24 25 26 <br />
  14. 14. 1 2 3 4 5 <br />9 8 7 6 <br /> 10 11 12 13 <br />17 16 15 14 <br /> 18 19 20 21 <br />
  15. 15. Professional Development in Santiago de Chile<br />
  16. 16. Singapore Math<br />Patterns<br />
  17. 17. Archipelschool<br />De Tweemaster – Kameleon<br />The Netherlands<br />
  18. 18. 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 />In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992. <br />
  19. 19.
  20. 20. Professional Development in ARK Schools, London<br />
  21. 21. Problem Solving in Learning Basic Concepts and Skills<br />Professional Development in Santiago de Chile<br />
  22. 22.
  23. 23.
  24. 24. Reference: Primary Mathematics (Standards Edition)<br />
  25. 25. Reference: Primary Mathematics (Standards Edition)<br />
  26. 26. Singapore Math<br />Learn New Concept Through <br />Problem Solving<br />
  27. 27.
  28. 28. Singapore Math<br />Drill-and-Practice Through <br />Problem Solving<br />
  29. 29.
  30. 30.
  31. 31. <br /><br /><br />
  32. 32. Singapore Math<br />Applying Knowledge in <br />Problem Solving<br />
  33. 33. makes abstract concepts accessible to learners who are not yet ready for abstraction<br />The CPA Approach<br />Focus on Thinking<br />builds fundamental intellectual competencies required for learners to handle abstraction<br />
  34. 34. Textbook <br />
  35. 35. Reference: My Pals Are Here! Maths<br />
  36. 36. 1. Setting Up the Task<br />Each person should get 12 animals. I have given you some. How many more do you need?<br />Pupils had opportunities to work independently as the teacher attended to other pupils.<br />
  37. 37. 2. Development (1)<br />Put four animals into one cup. Note only one cup is given.<br />This mirrors drawing rings around four objects.<br />
  38. 38. Students should have positive experiences during the lesson.<br />Put four animals into a second cup.<br />
  39. 39. How many animals are there altogether? <br />How many animals are there in one cup? How many cups do we use?<br />
  40. 40. 3. Development (2)<br />This is like the workbook tasks except that the magnets can be moved. Built-in remedial strategy.<br />
  41. 41. Pupils needs to monitor the number of magnets as well as to manage their visualization process.<br />Variations on the arrangements of magnets to increase the level of visualization required.<br />
  42. 42.
  43. 43. 4. Extension<br />
  44. 44. 5. Development (3) The use of colour to show the group. <br />Built-in remedial strategy.<br />
  45. 45.
  46. 46.
  47. 47.
  48. 48. CPA Approach<br />Links between concrete and pictorial representation must be carefully constructed.<br />Remedial steps are built into instruction<br />
  49. 49. Reference: Primary Mathematics (Standards Edition)<br />
  50. 50.
  51. 51.
  52. 52.
  53. 53. 51 – 17<br />51 x 3<br />51 + 26<br />
  54. 54. 3 units = 18<br />1 unit = 6<br />8 units = 8 x 6 = 48<br />There were 48 coins at first.<br />
  55. 55. SingaporeMaths<br />The Essentials<br />Da Qiao Primary School, Singapore<br />
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