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Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
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Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
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Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
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Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
Rekenwonders Bazalt HCO
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Rekenwonders Bazalt HCO

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Teacher trainers received an extension to the three-day course they received in September last year. The focus is on the problem-solving approach.

Teacher trainers received an extension to the three-day course they received in September last year. The focus is on the problem-solving approach.

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  • 1. teaching mathematics<br />focusing on problem solving<br />DrYeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />www.banhar.blogspot.com<br />www.banhar.com<br />Today’s discussion is based on lessons taken from a Singapore textbook series. The goal is to see how mathematics teaching can be made to focus on problem solving and how the lessons can be differentiated for struggling and advanced students.<br />Photographs of the session is available on Facebook<br />
  • 2. fundamental<br />principles<br />mathematics<br />of<br />teaching <br />& learning<br />Review<br />focusing on problem solving<br />
  • 3. concrete<br />
  • 4. pictorial<br />
  • 5. abstract<br />
  • 6. concrete<br />pictorial<br />abstract<br />
  • 7. variations<br />
  • 8. variations<br />
  • 9. variations<br />
  • 10. 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 />
  • 11. one<br />example<br />focusing on problem solving<br />
  • 12. Show 32 using base ten blocks.<br />Do 32 – 9 .<br />focusing on problem solving<br />
  • 13. Show 32 using base ten blocks.<br />Do 32 – 9 .<br />focusing on problem solving<br />
  • 14. focusing on problem solving<br />
  • 15. focusing on problem solving<br />
  • 16. focusing on problem solving<br />
  • 17.
  • 18. Show 32 using base ten blocks.<br />Do 32 – 9 .<br />focusing on problem solving<br />
  • 19.
  • 20.
  • 21. focusing on problem solving<br />
  • 22. two<br />example<br />focusing on problem solving<br />
  • 23. This piece of paper represents 1.<br />Divide it into four equal parts.<br />focusing on problem solving<br />
  • 24. St Edward’s School, Vero Beach, Florida<br />
  • 25. focusing on problem solving<br />
  • 26. focusing on problem solving<br />
  • 27. Initial Concrete Experience<br />Subsequent Pictorial Representation<br />focusing on problem solving<br />
  • 28. Eventual Symbolic Representation<br />
  • 29. focusing on problem solving<br />
  • 30. three<br />example<br />focusing on problem solving<br />
  • 31. Fuchun Primary School, Singapore<br />focusing on problem solving<br />
  • 32. Fuchun Primary School, Singapore<br />focusing on problem solving<br />
  • 33. four<br />example<br />focusing on problem solving<br />
  • 34. focusing on problem solving<br />
  • 35. five<br />example<br />focusing on problem solving<br />
  • 36.
  • 37. focusing on problem solving<br />
  • 38. focusing on problem solving<br />
  • 39. six<br />example<br />focusing on problem solving<br />
  • 40. focusing on problem solving<br />
  • 41.
  • 42. Reference: My Pals Are Here! Maths<br />focusing on problem solving<br />
  • 43. Reference: Primary Mathematics (Standards Edition)<br />focusing on problem solving<br />
  • 44. Reference: Primary Mathematics (Standards Edition)<br />
  • 45. seven<br />example<br />focusing on problem solving<br />
  • 46. focusing on problem solving<br />
  • 47. Kyla<br />?<br />$28 – $9 = $19<br />Kyla has $19.<br />Jake<br />?<br />$9<br />$28<br />focusing on problem solving<br />
  • 48. apples<br />90<br />oranges<br />38<br />pears<br />15<br />
  • 49. apples<br />90<br />oranges<br />pears<br />15<br />23<br />
  • 50. 90 + 15 = 105<br />5 units <br />1 unit  105 ÷ 5 = 21<br />There were (21 + 21 + 23) apples, hence oranges.<br />There were 44 oranges used.<br />apples<br />?<br />oranges<br />pears<br />15<br />23<br />

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