MAP101 Hilo, Hawai'i

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These are the sldies for MAP101 conducted in Hilo,

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MAP101 Hilo, Hawai'i

  1. 1. Professional Development Singapore Mathematics Big Island of Hawai’i  5 – 9 June 2012 Dr Yeap Ban Har yeapbanhar@gmail.com Marshall Cavendish Institute Singapore Presentation slides are available at www.banhar.blogspot.com Day 1 www.mcinstitute.com.sg www.facebook.com/MCISingapore
  2. 2. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  3. 3. General Overview of Singapore and its Education System  Land  700 sq km  People  4.7 million
  4. 4. General Overview of Singapore and its Education System GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
  5. 5. General Overview of Singapore and its Education System Students  500 000 Teachers  30 000 Principals & Vice-Principals  900 Schools  173 Primary Schools (Primary 1 – 6)  155 Secondary Schools (Secondary 1 – 4)  13 Junior Colleges (JC 1 – 2) Canossa Convent Primary School  15 Mixed-Level Schools Singapore The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
  6. 6. Universities National Examination Institutes of Poly Technical technics Junior Education Colleges Integrated National Examination Programmes Secondary Schools National Examination Primary SchoolsA detailed schematic diagram of Singapore’s education system is available in Education Statistics Digesthttp://www.moe.gov.sg/education/education-statistics-digest/
  7. 7. Curriculum document is available at http://www.moe.gov.sg/
  8. 8. THINKING SCHOOLSLEARNING NATION Singapore Ministry of Education 1997
  9. 9. “Mathematics is an excellent vehicle for the developmentand improvement of a person’s intellectual competencies” Singapore Ministry of Education 2006
  10. 10. 21st Century Competencies FrameworkSingapore Ministry of Education 2011
  11. 11. whatis singapore mathematics
  12. 12. Singapore Mathematics: Focus on Thinking anexcellent vehicle for the development &improvement of a person’s intellectual competencies Ministry of Education Singapore 2006
  13. 13. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  14. 14. 110 g180 g 110 g Bella puts 180 g brown sugar on the dish. 290 g
  15. 15. on an identical dish 110 g 2 units = 180 g 1 unit = 90 g 180 g 110 g 3 units = 270 g Bella puts 270 g brown sugar on the dish. 290 g
  16. 16. Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.Bar models were introduced to overcome thepervasive problems students had with word problems– even the basic ones.
  17. 17. Such word problems are used tohelp students Deal with information Handle and clarify ambiguity – one dish or two Develop visualization – bar models are used extensively Practice mental strategies – numbers used are not difficult to compute
  18. 18. Singapore Math Visualization
  19. 19. C H E R Y L
  20. 20. C H E R Y L1
  21. 21. C H E R Y L 2
  22. 22. C H E R Y L 3
  23. 23. C H E R Y L 4
  24. 24. C H E R Y L 5
  25. 25. C H E R Y L 6
  26. 26. C H E R Y L 7
  27. 27. C H E R Y L 8
  28. 28. C H E R Y L 9
  29. 29. C H E R Y L
  30. 30. C H E R Y L
  31. 31. C H E R Y L
  32. 32. C H E R Y L
  33. 33. C H E R Y L
  34. 34. C H E R Y L Which letter is 99?
  35. 35. Method 1The positions of 11, 22, 33 are at C, H, E respectively.Positions of multiples of 11 can be located. Method 4 The position for 99 can be found by writing out all the numbers Method 3 but this is not Numbers ending with 9 efficient are at E. So, 99 is at E method. Method 2 too. The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.
  36. 36. D A V I D
  37. 37. Method 1The letters under A and I areeven. So 99 cannot be there.Method 2The positions of numbers endingwith 9 form a diagonal pattern.Method 3The numbers under first Dincreases by 8. Thus 17 + 80 = 97is under first D. The position for99 can be worked out.Method 4The positions of multiples of 8 I isdefinitely under A. 8 x 12 = 96 isunder A. The position of 99 canbe worked out.Method 5Numbers under V is 1 less thanmultiples of 4. So, 2011 (1 lessthan 2012) is under V. 99 is lessthan 100.
  38. 38. Method 2The positions of numbers ending with 9form a diagonal pattern.The methods were the ones thatparticipants in Chile came up with.
  39. 39. Another MethodIn a course done in December 2010 with a group ofChilean teachers, there was a method that involvesdivision. For Cheryl, it was 99 : 10.For David, it was 99 : 8. Are you able to figure out thatmethod?
  40. 40. We did this version in Big Island of Hawai’i.Singapore Math at Kamehameha Schools, Hawai’i USA Kamehameha Schools, Hawaii
  41. 41. Singapore MathPatterns & Generalization
  42. 42. Singapore Mathematics: Focus on Problem Solving
  43. 43. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  44. 44. CPA Approach based onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.
  45. 45. Singapore Mathematics: Focus on Conceptual Understanding
  46. 46. Singapore Math at Kamehameha Schools, Hawai’i USA Kamehameha Schools, Hawaii
  47. 47. Singapore Math at Kamehameha Schools, Hawai’i USA Kamehameha Schools, Hawaii
  48. 48. Singapore MathLearn New Concept Through Problem Solving
  49. 49. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  50. 50. Singapore Math at Kamehameha Schools, Hawai’i USA Kamehameha Schools, Hawaii
  51. 51. Singapore MathDrill-and-Practice Through Problem Solving
  52. 52. Singapore MathProblem Solving LessonAnchorvale Primary School,
  53. 53. FUNDAMENTALS of singapore math Further Examples Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  54. 54. Singapore MathApplying Knowledge in Problem Solving
  55. 55. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
  56. 56. Learning Theories
  57. 57. How many 4s are there in 12? 12 ÷ 4 = 3
  58. 58. Marcus gave ¼ of his coin collection to hissister and ½ of the remainder to hisbrother.As a result, Marcus had 18 coins.Find the number of coins in his collectionat first. 3 units = 18 8 units = ??? Marcus had 48 coins at first.

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