Singapore Math at Highline Public SchoolsMarch 2013  Session 2 at ERACYeap Ban Harwww.banhar.blogspot.com                ...
 Land                                         270 sq miles                                         700 sq km           ...
What is Singapore Math?                              Thinking and Problem SolvingNanyang Primary School, Singapore
thinkingschools    learningnationMathematics is “an excellent vehicle forthe development and improvement of a      person’...
Ministry of Education, Singapore (1991, 2000, 2006, 2012)
Singapore Math                        The CPA Approach, The Spiral                        Approach and Emphasis on Relatio...
Singapore MathThe CPA Approach
Singapore MathThe CPA Approach        2   1                  6   3
Singapore MathThe CPA Approach      1 2        1                 2 3        3     1 2 1 1             2 3 1 3
concretepictorialabstract
Seely Place Elementary School, New York
Seely Place Elementary School, New York
3 4                                                   4 5Seely Place Elementary School, New York
Seely Place Elementary School, New York3 4 4 5
Seely Place Elementary School, New York3 4       3 1     =    4 5       1 5             1      =   3             5
Seely Place Elementary School, New York    1 3 4         3 1        =    14   5       1 5
Singapore Math  Three-Part Lesson Structure         Extended        Engagement         with One           Task            ...
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure
Singapore MathThree-Part Lesson Structure: Guided Practice
Singapore MathThree-Part Lesson Structure
Singapore MathThe Spiral Approach
Singapore MathThe Spiral Approach
Singapore MathAnchor TaskGuided PracticeIndependent Practice
J Bruner                               Enactive, Iconic, Symbolic                               RepresentationsEdgewood El...
Box B contains twice as manybooks as Box A. Box Ccontains 20 more books thanBox A. Together, the threeboxes contains 116 b...
x + 2x + x + 20 = 116      4x = 116 – 20 = 96      x = 96  4 = …                   B   x        x                        ...
3A number is     of a second number.            5The sum of the two numbers is 120.                                      K...
J Bruner                                         Spiral CurriculumGreenville Elementary School, New York
Seely Place Elementary School, New York
Greenville Elementary School, New YorkThe CPA Approach      CPAStudents were asked tomake three nests of 2eggs and, late...
CPA Approach in Developing Conventional Language3 nests  3 nests of 2 eggs  3 groups of 2  3 twos                      ...
Escuela de Guetamala, Chile                              6                              6                              6  ...
Z Dienes                                Play  Structured Learning                                 PracticeBina Bangsa Sc...
x            x                  x+1x   x   x               x+2            x–1    x             x–2                        ...
L Vygotsky                              InteractionPathlight School, Singapore                              Bina Bangsa Sc...
R Skemp                        Relational and Instrumental                        UnderstandingGlobe Academy, London
Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 .             7     3y              1
Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 .             7           3y              1
J Piager                            Assimilation, AccommodationKeys Grade School, Manila
H Gardner                            Multiple IntelligencesKeys Grade School, Manila
Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
Student Achievement                              Average Learners Performing                              WellPathlight Sc...
Singapore      Math   allows                               average learners perform at                               a hig...
All major international tests (literacy, science and mathematics) between 1964 and2003 were placed on a common scale. Sele...
mathematics
intermediate                                                      advanced                                                ...
intermediate                                                    advanced                                                  ...
intermediategrade eight mathematics                                                    advanced                           ...
grade eight mathematics                                                                           dislike math            ...
grade eight mathematics                                                                           dislike math            ...
perentage                 correct Singapore       52International    27
perentage                 correct Singapore       45International    23
Singapore Math at Highline Public SchoolsMarch 2013 Yeap Ban Haryeapbanhar@gmail.com                                     ...
Highline Session 2
Highline Session 2
Highline Session 2
Highline Session 2
Highline Session 2
Highline Session 2
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Highline Session 2

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Highline Session 2

  1. 1. Singapore Math at Highline Public SchoolsMarch 2013  Session 2 at ERACYeap Ban Harwww.banhar.blogspot.com The Merlion by Yeap Ken Min
  2. 2.  Land  270 sq miles  700 sq km  People  5.3 million  GDP per capita  1965 USD500  2011 USD50 000Junyuan Secondary School, Singapore in current USD
  3. 3. What is Singapore Math? Thinking and Problem SolvingNanyang Primary School, Singapore
  4. 4. thinkingschools learningnationMathematics is “an excellent vehicle forthe development and improvement of a person’s intellectual competence”. Ministry of Education, Singapore (2006)
  5. 5. Ministry of Education, Singapore (1991, 2000, 2006, 2012)
  6. 6. Singapore Math The CPA Approach, The Spiral Approach and Emphasis on Relational UnderstandingGlobe Academy, London
  7. 7. Singapore MathThe CPA Approach
  8. 8. Singapore MathThe CPA Approach 2 1  6 3
  9. 9. Singapore MathThe CPA Approach 1 2 1    2 3 3 1 2 1 1    2 3 1 3
  10. 10. concretepictorialabstract
  11. 11. Seely Place Elementary School, New York
  12. 12. Seely Place Elementary School, New York
  13. 13. 3 4  4 5Seely Place Elementary School, New York
  14. 14. Seely Place Elementary School, New York3 4 4 5
  15. 15. Seely Place Elementary School, New York3 4 3 1  = 4 5 1 5 1 = 3 5
  16. 16. Seely Place Elementary School, New York 1 3 4 3 1  = 14 5 1 5
  17. 17. Singapore Math Three-Part Lesson Structure Extended Engagement with One Task Teach Less, Learn Morew w w. b a n h a r. b l o g s p o t . c o m
  18. 18. Singapore MathThree-Part Lesson Structure
  19. 19. Singapore MathThree-Part Lesson Structure
  20. 20. Singapore MathThree-Part Lesson Structure
  21. 21. Singapore MathThree-Part Lesson Structure
  22. 22. Singapore MathThree-Part Lesson Structure
  23. 23. Singapore MathThree-Part Lesson Structure
  24. 24. Singapore MathThree-Part Lesson Structure
  25. 25. Singapore MathThree-Part Lesson Structure: Guided Practice
  26. 26. Singapore MathThree-Part Lesson Structure
  27. 27. Singapore MathThe Spiral Approach
  28. 28. Singapore MathThe Spiral Approach
  29. 29. Singapore MathAnchor TaskGuided PracticeIndependent Practice
  30. 30. J Bruner Enactive, Iconic, Symbolic RepresentationsEdgewood Elementary School, New York
  31. 31. Box B contains twice as manybooks as Box A. Box Ccontains 20 more books thanBox A. Together, the threeboxes contains 116 books. Edgewood Elementary School, New York
  32. 32. x + 2x + x + 20 = 116 4x = 116 – 20 = 96 x = 96  4 = … B x x A x 116 C x 20Edgewood Elementary School, New York
  33. 33. 3A number is of a second number. 5The sum of the two numbers is 120. King Solomon Academy, London
  34. 34. J Bruner Spiral CurriculumGreenville Elementary School, New York
  35. 35. Seely Place Elementary School, New York
  36. 36. Greenville Elementary School, New YorkThe CPA Approach CPAStudents were asked tomake three nests of 2eggs and, later, 3 nestsof 7 eggs. They wereonly given 20 ‘eggs’.
  37. 37. CPA Approach in Developing Conventional Language3 nests  3 nests of 2 eggs  3 groups of 2  3 twos Greenville Elementary School, New York
  38. 38. Escuela de Guetamala, Chile 6 6 6 6
  39. 39. Z Dienes Play  Structured Learning  PracticeBina Bangsa School, Indonesia
  40. 40. x x x+1x x x x+2 x–1 x x–2 Jenaplanschool Cleoplas, The Netherlands
  41. 41. L Vygotsky InteractionPathlight School, Singapore Bina Bangsa School, Indonesia
  42. 42. R Skemp Relational and Instrumental UnderstandingGlobe Academy, London
  43. 43. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
  44. 44. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
  45. 45. J Piager Assimilation, AccommodationKeys Grade School, Manila
  46. 46. H Gardner Multiple IntelligencesKeys Grade School, Manila
  47. 47. Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
  48. 48. Student Achievement Average Learners Performing WellPathlight School, Singapore
  49. 49. Singapore Math allows average learners perform at a high level. The following are some data from some international research on math achievement and attitude.East Coast Primary School, Singapore
  50. 50. All major international tests (literacy, science and mathematics) between 1964 and2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Hong Kong Hong Kong Hong Kong Japan Japan Japan Korea Korea Korea Singapore Singapore 400 Thailand The Philippines Malaysia Malaysia Singapore Thailand Thailand Thailand 300 Indonesia Indonesia The Philippines The PhilippinesReference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  51. 51. mathematics
  52. 52. intermediate advanced high low average Singapore 606 43 78 94 99 South Korea 605 39 80 97 100grade four mathematics Hong Kong 602 37 80 96 99 Taiwan 591 34 74 93 99 Japan 585 30 70 93 99 Northern Ireland 562 24 59 86 96 Belgium 549 10 50 89 99 Finland 545 12 49 85 98 England 542 18 49 78 93 Russia 542 13 47 82 97 International 500 4 28 69 90
  53. 53. intermediate advanced high low average South Korea 613 47 77 93 99 Singapore 611 48 78 92 99grade eight mathematics Taiwan 609 49 73 88 96 Hong Kong 586 34 71 89 97 Japan 570 27 61 87 97 Russia 539 14 47 78 95 Israel 516 12 40 68 87 Finland 514 4 30 73 96 United States 509 7 30 68 92 England 507 8 32 65 88 International 500 3 17 46 75
  54. 54. intermediategrade eight mathematics advanced average high low Singapore 611 48 78 92 99 Malaysia 440 2 12 36 65 Thailand 427 2 8 26 55 Indonesia 386 0 2 15 43 International 500 3 17 46 75
  55. 55. grade eight mathematics dislike math advanced like math average Singapore 611 48 32 23 Malaysia 440 2 39 15 Thailand 427 2 26 16 Indonesia 386 0 20 10 International 500 3 26 31
  56. 56. grade eight mathematics dislike math advanced like math average Singapore 611 48 32 23 South Korea 613 47 8 56 Taiwan 609 49 14 53 Hong Kong 586 34 19 37 Japan 570 27 9 53 International 500 3 26 31
  57. 57. perentage correct Singapore 52International 27
  58. 58. perentage correct Singapore 45International 23
  59. 59. Singapore Math at Highline Public SchoolsMarch 2013 Yeap Ban Haryeapbanhar@gmail.com The Merlion by Yeap Ken Min

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