1. International Workshop on Philippine and Singapore Mathematics Hotel Supreme Convention Plaza, Baguio City January 28 – 30, 2013Promoting Critical and Creative Thinking:Singapore MathematicsYeap Ban HarMarshall Cavendish InstituteSingaporeyeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
2. Introduction A Glimpse of Singapore MathAssumption Englsih School, Singapore
3. What is Singapore Math? A Glimpse – Mathematics ClassroomBina Bangsa School, Indonesia
4. What is Singapore Math? A Glimpse – Mathematics Textbooksx2 x 1
5. What is Singapore Math?x2 + 4x + 1 A Glimpse – Mathematics Textbooks x2 x 1
6. What is Singapore Math? A Glimpse – Mathematics Textbooksx2 x x2 + 4x + 1 = x2 + 4x + 1 + 3 – 3 = (x + 2)2 – 3
7. What is Singapore Math? A Glimpse – Mathematics ExaminationsWeiyang started a savings plan by putting 2 coins in a moneybox every day. Each coin was either a 20-cent or 50-cent coin.His mother also put in a $1 coin in the box every 7 days. Thetotal value of the coins after 182 days was $133.90 .(a) How many coins were there altogether?(b) How many of the coins were 50-cent coins? Reference: Singapore Examination and Assessment Board
8. What is Singapore Math? A Glimpse – Mathematics Examinations Weiyang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20-cent or 50-cent coin. His mother also put in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90 . 182  7 = 20 + 6 = 26 182 x 2 + 26 = 364 + 26 = 390140 42 There were 390 coins altogether. Hint for Part (b) 40 cents 70 cents $1 $133.90 – $26 = $107.90 5 7 101 182
9. What is Singapore Math? A Glimpse – Teacher Preparation Learning to teach 34 x 42.National Institute of Education, Singapore
10. What is Singapore Math? Thinking and Problem SolvingNanyang Primary School, Singapore
11. thinkingschools learningnation Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”. Ministry of Education, Singapore (2006)
12. Ministry of Education, Singapore (1991, 2000, 2006, 2012)
13. The twin goals of mathematics in thebasic education levels, K-10 areCritical Thinking and Problem Solving.Mathematical problem solving isfinding a way around a difficulty,around an obstacle, and finding asolution to a problem that is unknown. Department of Education, The Philippines (2012)
14. Singapore Math The CPA Approach, The Spiral Approach and Emphasis on Relational UnderstandingGlobe Academy, London
21. 3 4  4 5Seely Place Elementary School, New York
22. Seely Place Elementary School, New York3 4 4 5
23. Seely Place Elementary School, New York3 4 3 1  = 4 5 1 5 1 = 3 5
24. Seely Place Elementary School, New York 1 3 4 3 1  = 14 5 1 5
25. 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
26. Singapore MathThree-Part Lesson Structure
27. Singapore MathThree-Part Lesson Structure
28. Singapore MathThree-Part Lesson Structure
29. Singapore MathThree-Part Lesson Structure
30. Singapore MathThree-Part Lesson Structure
31. Singapore MathThree-Part Lesson Structure
32. Singapore MathThree-Part Lesson Structure
33. Singapore MathThree-Part Lesson Structure
34. Singapore MathThree-Part Lesson Structure
35. Singapore MathThree-Part Lesson Structure
36. Singapore MathThree-Part Lesson Structure: Guided Practice
37. Singapore MathThree-Part Lesson Structure
38. Singapore MathThe Spiral Approach
39. Singapore MathThe Spiral Approach
40. Singapore MathAnchor TaskGuided PracticeIndependent Practice
41. J Bruner Enactive, Iconic, Symbolic RepresentationsEdgewood Elementary School, New York
42. 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
43. 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
44. 3A number is of a second number. 5The sum of the two numbers is 120. King Solomon Academy, London
45. J Bruner Spiral CurriculumGreenville Elementary School, New York
46. Seely Place Elementary School, New York
47. 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’.
48. CPA Approach in Developing Conventional Language3 nests  3 nests of 2 eggs  3 groups of 2  3 twos Greenville Elementary School, New York
49. Escuela de Guetamala, Chile 6 6 6 6
50. Allfarthing Primary School, London
51. Math in Focus
52. Da Qiao Primary School, Singapore
53. Z Dienes Play  Structured Learning  PracticeBina Bangsa School, Indonesia
54. x x x+1x x x x+2 x–1 x x–2 Jenaplanschool Cleoplas, The Netherlands
55. L Vygotsky InteractionPathlight School, Singapore Bina Bangsa School, Indonesia
56. R Skemp Relational and Instrumental UnderstandingGlobe Academy, London
57. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
58. Using bar model to introduce solvingalgebraic equationsSolve 7 – 3y = 1 . 7 3y 1
60. H Gardner Multiple IntelligencesKeys Grade School, Manila
61. Observing patterns andmaking generalizationsinvolves reflection.Seely Place Elementary School, New York
62. Student Achievement Average Learners Performing WellPathlight School, Singapore
63. 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
64. 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)
65. mathematics
66. 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
67. 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
68. 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
69. 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
70. 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
76. Reference: Department of Education State of New Yorkassessment
77. assessment Reference: Department of Education State of Hawaii
78.  Teacher as a learner (professor as a model) Teacher as an observer of learning (lesson study) Teacher as reflective practitioner (professional learning community)teacher preparation
79. teacher preparation National Institute of Education SingaporeSingapore teachers learn what they need to learn through anapproach that balances content and pedagogy.
80. teacher preparationNational Institute of Education SingaporeThe practice component is given emphasis – micro teaching,practicum and lesson study.
81. teacher preparation There is an emphasis on teachers solving the problems themselves during the course.
82. teacher developmentTeachers learn from thetextbooks and teachersguide.
83. teacher developmentWe learn from the Japanese method to help teachersdevelop better skills in observing students. This is lessonstudy. Princess Elizabeth Primary School Singapore
85. National Institute of Education, Singapore Edgewood Elementary School, New York Fuchun Primary School, Singapore
86. Bina Bangsa School, Indonesia Keys Grade School, The Philippines Kranji Secondary School, Singapore
87. leadership Mayor of Newark gave an inspirational message to teachers attending professional development on Singapore Math.
88. International Workshop on Philippine and Singapore Mathematics Hotel Supreme Convention Plaza, Baguio City January 28 – 30, 2013Promoting Critical and Creative Thinking:K-12 Mathematics• What can I do as a teacher?• What can my school do?• What can the education schools do?• What government support should be in place? Slides are available at www.banhar.blogspot.com
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