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LEAP Educators’ Conference 2011<br />Developing Thinking <br />Through High School Mathematics<br />Yeap Ban Har<br />Mars...
Link to Keynote Lectures<br />First lecture raised the question: “Why is the achievement level eroded when students progre...
Introduction<br />Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual compe...
Problem Solving<br />National Test                      <br />
 National Test Grade 10 (Secondary 4)<br />	A fly, F, starts at a point with position vector   (i + 12j) cm and crawls acr...
Problem Solving<br />Textbook                      <br />
Draw a 4-sided polygon.<br />Cut it into triangles.<br />How many triangles can you get?<br />
Example: Algebra<br />Factoring a quadratic expression.                      <br />
Algebra Tiles<br />
Example: Algebra<br />Completing the square.                      <br />
Example: Algebra<br />Solve                      .<br />
Solve                      .<br />
Example: Coordinate Geometry<br />Find the distance between two points.<br />
Problem: Find the distance between points A (2, 3) and B (10, 9).<br />Students working collaboratively on a problem to le...
Every group was able to use their previous learning (Pythagoras Theorem) to solve the main problem.<br />BinaBangsa School...
BinaBangsa School, Indonesia<br />Later they were also asked to find points where the distance is a whole number.<br />
Example: Circles<br />Learning definition and making sense of formulae.<br />
Example<br />To engage pupils in the learning of mathematics.<br />Fuchun Primary School<br />
Task 1 Find the longest distance between two points on a circle.<br />Fuchun Primary School, Singapore<br />
Fuchun Primary School, Singapore<br />
Fuchun Primary School, Singapore<br />
Task 2 Measure circumference and diameter of four circles.<br />Fuchun Primary School, Singapore<br />
Task 3 Draw a circle given that its  circumference is 6 metres.<br />Fuchun Primary School, Singapore<br />
Fuchun Primary School, Singapore<br />
Fuchun Primary School, Singapore<br />
Example: Circles<br />Learning definition and making sense of formulae.<br />
Area > 2r2<br />
Area < 4r2<br />
2r2 < Area < 4r2<br />
Conclusion<br />Mathematics is not just for its content but also for the opportunities to develop generic thinking skills....
Example: Trapezium<br />a<br />c<br />b<br />h<br />d<br />
Example: Trapezium<br />a<br />d<br />c<br />b<br />h<br />d<br />a<br />
International Benchmarks<br />
TIMSS 2007 Achievement<br />Singapore<br />International<br />USA<br />Grade 8<br />Advanced<br />40<br />6<br />2<br />Hi...
TIMSS 2007 Affect<br />PATM<br />SVM<br />SCM<br />Grade 8<br />High<br />60<br />41<br />77<br />Medium<br />20<br />34<b...
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LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

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This plenary lecture on high school mathematics calls for teaching of thinking through mathematics.

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LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

  1. 1. LEAP Educators’ Conference 2011<br />Developing Thinking <br />Through High School Mathematics<br />Yeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Presentation is available on www.banhar.blogspot.com<br />
  2. 2. Link to Keynote Lectures<br />First lecture raised the question: “Why is the achievement level eroded when students progress from elementary to high school?”. The second lecture calls for changing mindset.<br />This lecture attempts to answer the question and suggest an alternate way of looking at school mathematics.<br />
  3. 3. Introduction<br />Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence…<br />Ministry of Education 2006<br />
  4. 4.
  5. 5. Problem Solving<br />National Test <br />
  6. 6.  National Test Grade 10 (Secondary 4)<br /> A fly, F, starts at a point with position vector (i + 12j) cm and crawls across the surface with a velocity of (3i + 2j) cm s-1. At the instant the fly starts crawling, a spider, S, at the point with position vector (85i + 5j) cm, sets off across the surface with a velocity of (-5i + kj) cm s-1, where k is a constant. Given that the spider catches the fly, calculate the value of k. <br /> <br />
  7. 7. Problem Solving<br />Textbook <br />
  8. 8. Draw a 4-sided polygon.<br />Cut it into triangles.<br />How many triangles can you get?<br />
  9. 9.
  10. 10. Example: Algebra<br />Factoring a quadratic expression. <br />
  11. 11. Algebra Tiles<br />
  12. 12.
  13. 13.
  14. 14.
  15. 15.
  16. 16.
  17. 17. Example: Algebra<br />Completing the square. <br />
  18. 18.
  19. 19.
  20. 20.
  21. 21.
  22. 22.
  23. 23.
  24. 24.
  25. 25. Example: Algebra<br />Solve .<br />
  26. 26. Solve .<br />
  27. 27. Example: Coordinate Geometry<br />Find the distance between two points.<br />
  28. 28. Problem: Find the distance between points A (2, 3) and B (10, 9).<br />Students working collaboratively on a problem to learn the coordinate geometry topic on distance between points. Traditionally, students were given a formulae to do this. Instead students had to conduct a mini-inquiry to use what they had previously learned.<br />BinaBangsa School, Indonesia<br />
  29. 29. Every group was able to use their previous learning (Pythagoras Theorem) to solve the main problem.<br />BinaBangsa School, Indonesia<br />
  30. 30. BinaBangsa School, Indonesia<br />Later they were also asked to find points where the distance is a whole number.<br />
  31. 31. Example: Circles<br />Learning definition and making sense of formulae.<br />
  32. 32. Example<br />To engage pupils in the learning of mathematics.<br />Fuchun Primary School<br />
  33. 33. Task 1 Find the longest distance between two points on a circle.<br />Fuchun Primary School, Singapore<br />
  34. 34. Fuchun Primary School, Singapore<br />
  35. 35. Fuchun Primary School, Singapore<br />
  36. 36. Task 2 Measure circumference and diameter of four circles.<br />Fuchun Primary School, Singapore<br />
  37. 37. Task 3 Draw a circle given that its circumference is 6 metres.<br />Fuchun Primary School, Singapore<br />
  38. 38. Fuchun Primary School, Singapore<br />
  39. 39. Fuchun Primary School, Singapore<br />
  40. 40.
  41. 41. Example: Circles<br />Learning definition and making sense of formulae.<br />
  42. 42.
  43. 43.
  44. 44.
  45. 45. Area > 2r2<br />
  46. 46. Area < 4r2<br />
  47. 47. 2r2 < Area < 4r2<br />
  48. 48.
  49. 49.
  50. 50.
  51. 51.
  52. 52.
  53. 53. Conclusion<br />Mathematics is not just for its content but also for the opportunities to develop generic thinking skills.<br />
  54. 54. Example: Trapezium<br />a<br />c<br />b<br />h<br />d<br />
  55. 55. Example: Trapezium<br />a<br />d<br />c<br />b<br />h<br />d<br />a<br />
  56. 56. International Benchmarks<br />
  57. 57. TIMSS 2007 Achievement<br />Singapore<br />International<br />USA<br />Grade 8<br />Advanced<br />40<br />6<br />2<br />High<br />70<br />31<br />15<br />Intermediate<br />88<br />67<br />46<br />Low<br />97<br />92<br />55<br />Photo: Catholic High School (Primary)<br />
  58. 58. TIMSS 2007 Affect<br />PATM<br />SVM<br />SCM<br />Grade 8<br />High<br />60<br />41<br />77<br />Medium<br />20<br />34<br />19<br />Low<br />20<br />25<br />4<br />Photo: Catholic High School (Primary)<br />

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