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Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
Singapore Math Strategies for U.S. Schools
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Singapore Math Strategies for U.S. Schools

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Two-day institute in White Plains.

Two-day institute in White Plains.

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  • 1. Singapore MathStrategies for U.S. SchoolsWhite Plains NY  March 2012yeap ban har  marshall cavendish institute SESSION ONE Overview & Fundamentals of Singapore MathematicsPrimary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
  • 2. Introduction Anchor Green Primary School, Singapore
  • 3. General Overview of Singapore and its Education System  Land  700 sq km  People  4.7 million
  • 4. General Overview of Singapore and its Education System GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
  • 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, Singapore  15 Mixed-Level Schools 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. 1992 Problem-Solving Curriculum 1997 Thinking Schools, Learning Nation 2004 Teach Less,Singapore Mathematics: Background Learn More 2010 Professional Learning Communities 2011 21st Century Competencies
  • 7. Singapore Ministry of Education 1992, 2001, 2007, 2013
  • 8. “Mathematics is an excellent vehicle for the developmentand improvement of a person’s intellectual competencies” Singapore Ministry of Education 2006
  • 9. What to Teach?Singapore Mathematics: What & How How to Teach?
  • 10. Singapore Examination & Assessment Board 2012 Case Study 1 As the instructor demonstrates thelesson, study what is it that the teacherwants students to learn. This is a Grade6 problem involving fraction and ratio.
  • 11. Case Study 1 16 units = $120 20 units = 04 units = $120  4 04 units = $30 20 units = $30 x 5 20 units = $150John had $150 at first.
  • 12. Case Study 1what is it that the teacher wants students to learn
  • 13. SESSION ONESingapore Math Overview & Fundamentals of Singapore MathematicsStrategies for U.S. SchoolsWhite Plains NY  March 2012 Fundamentals of Singapore Mathematics  Focus on Problem Solving  Focus on Thinking  Focus on Managing Information  Focus on Visualization  Focus on Generalization  Focus on Number Sense  Focus on Communication
  • 14. Singapore MathStrategies for U.S. SchoolsWhite Plains NY  March 2012yeap ban har  marshall cavendish institute SESSION TWOMathematical Problem Solving including Bar Models Pathlight School, Singapore
  • 15. Tom has some sweets. Jerry has 5 sweets more than Tom. Later, Tom gives Jerry 2 sweets. Who has more sweets now? 2 Case Study 3 Primary 3 Lesson Study 2 5 2 Kong Hwa School Tom Jerry Who has more sweets now?Before x x+5 How many more?After x–2 x+7
  • 16. Tom has 9 sweets. Jerry has 5 sweets more than Tom. How many sweets does Jerry have? Tom 9Case Study 3 Jerry 5 9 + 5 = 14 Jerry has 14 sweets.
  • 17. Tom has 9 sweets. Jerry has 5 sweets more than Tom. Later, Tom gives Jerry 2 sweets. Who has more sweets now? How many more? Tom 9 2Case Study 3 Jerry 5 2 9–2=7 9 + 5 + 2 =16 16 – 7 = 9 Jerry has 9 more sweets than Tom.
  • 18. One day, 543 cars and 274 buses pass through a toll booth. How many cars and buses pass through the toll booth? Math in Focus Grade 2 cars 543 Case Study 3 buses 274 543 + 274 = cars buses543 274
  • 19. 543 + 274 = 
  • 20. 543 + 274 = 
  • 21. 543 + 274 = 
  • 22. 543 + 274 = 
  • 23. 543 + 274 = 
  • 24. 543 + 274 = 
  • 25. Multiplication is taught witha focus on meaning,visualization, and makingconnections.
  • 26. Sam is twice as old as Terry. Vanessa is three times as old as Terry. Their total ages is 72 years. Find their ages. SamCase Study 6 Terry 72 Vanessa 60 12 72  6 = 12 Terry is 12 years old. Sam is 24 years old. Vanessa is 36 years old.
  • 27. Sam is twice as old as Terry.Vanessa is three times as old as Terry.Their total ages is 72 years. Differentiation for StrugglingFind their ages. Learners Sam is twice as old as Terry. Case Study 6 Vanessa is 36 years old. Their total ages is 72 years. Find their ages.
  • 28. Sam is twice as old as Terry.Vanessa is three times as old as Terry Sam.Their total ages is 72 years.Find their ages. Terry Sam Case Study 6 Sam is twice as old as Terry. Vanessa is three times as old as Terry. Differentiation for Advanced Their total ages is 72 years. Learners Find their ages.
  • 29. Primary Mathematics (Standards Edition) Grade 6 Case Study 2 As the instructor demonstrates thelesson, study what is it that the teacher wants students to learn. This is a task from a Grade 6 textbook to motivate the learning of algebra.
  • 30. Singapore MathStrategies for U.S. SchoolsWhite Plains NY  March 2012yeap ban har  marshall cavendish institute REVIEW & CONSOLIDATE Opening LecturePrimary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
  • 31. Average Learners High Achievement International Studies
  • 32. Students in Singapore have demonstratedhigh achievement and positive attitudetowards mathematics.In Trends in Mathematics and Science Study,about 40% of Singapore’s 4th and 8thgraders are in the Advanced International International 1995 2003 2007Benchmark (the international average is 5%and 2% respectively). Grade 4 Advanced 38 38 41 5 High 70 73 74 26 Intermediate 89 91 92 67 Low 96 97 98 90
  • 33. Hong Kong Singapore S. Korea Average TaiwanTIMSSTrends in International Mathematics and Science Studies Advanced 2 31 40 40 45 Grade 8 High 15 64 70 71 71 Intermediate 46 85 88 90 86 Low 75 94 97 98 95Junyuan Secondary School, Singapore
  • 34. TIMSSTrends in International Mathematics and Science Studies Grade 4 1995 Grade 8 1999 Advanced 38 42 High 70 77 Intermediate 89 94 Low 96 99 Fuchun Primary School, Singapore
  • 35. TIMSSTrends in International Mathematics and Science Studies Grade 4 2003 Grade 8 2007 Grade 4 1995 Grade 8 1999 Advanced 38 42 38 40 High 70 77 73 70 Intermediate 89 94 91 88 Low 96 99 97 97 Fuchun Primary School, Singapore
  • 36. The attitude index for Singapore students inTIMSS is also relatively high compared toother high-performing countries.Also, the majority of students in Singaporeopt to study mathematics in Grades 11 and12 when they are no longer required to. Marsiling Secondary School, Singapore
  • 37. Achievement Attitude Singapore 71 41 Hong Kong 67 40 Taiwan 50 24Grade 4 Japan 62 23 Kazakhstan 89 19 England 62 16 Russia 80 16 International 72 5
  • 38. Achievement Attitude Taiwan 37 45 S Korea 33 40 Singapore 60 40Grade 8 Hong Kong 47 31 Japan 30 26 Hungary 30 10 England 40 8 International 54 2
  • 39. High achievement was not a given. In 1960,among 30 615 candidates who sat for thefirst Primary School Leaving Examination,45% of the candidates passed. Keon Ming Public School, Singapore
  • 40. All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Japan Japan Japan Korea Korea Korea Hong Kong Singapore Hong Kong Hong Kong Singapore 400 Thailand Singapore Malaysia Malaysia Thailand Thailand Thailand The Philippines 300 Indonesia Indonesia The Philippines The PhilippinesReference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  • 41. Average Learners High Achievement Pedagogy
  • 42. Math in Focus
  • 43. Pensar sin Limites (Spanish Edition)
  • 44. Pensar sin Limites (Spanish Edition)
  • 45. Maths Champion (Indonesian Edition)
  • 46. Primary Mathematics (Standards Edition)
  • 47. Primary Mathematics (Standards Edition)
  • 48. Singapore MathStrategies for U.S. SchoolsWhite Plains NY  March 2012yeap ban har  marshall cavendish institute SESSION THREE Differentiated InstructionPrimary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
  • 49. “… over-emphasising procedural skillswithout understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006
  • 50. My Pals Are Here! Mathematics (Second Edition)
  • 51. Singapore MathStrategies for U.S. SchoolsWhite Plains NY  March 2012yeap ban har  marshall cavendish institute SESSION FOUR AssessmentPrimary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
  • 52. Grade Levels Assessment Notes1–2 Basic Skills EmergingInformal Familiar Applications EstablishedAssessment Novel Applications Independently Scaffolding With or without materials3–4 Basic Skills 40%Informal Familiar Applications 40%Assessment Novel Applications 20%Standardized Test5–6 Basic Skills 20%Informal Familiar Applications 30%Assessment Novel Applications 50%Standardized Test
  • 53. Jack and Kyla share $300. Jack gets twice as much as Kyla. How much does Kyla get? JackCase Study 4 Kyla $300  3 = $100 Kyla gets $100.
  • 54. Natalia’s bag is 12 kg heavier than Peter’s. The total mass of the two bags is 58 kg. How heavy is Natalia’s bag? How heavy is Peter’s bag? Natalia 12Case Study 5 Peter 58 – 12 = 46 46  2 = 23 23 + 12 = 35 Natalia’s bag is 35 kg. Peter’s bag is 23 kg.
  • 55. Mrs. Lee used ¼ of the flour she bought to make cookies and a thirdof the remainder to bake a cake. She then has 3.6 kg of flour left.How much flour did she buy? Case Study 7
  • 56. Mrs. Lee used ¼ of the flour she bought to make cookies and ½ ofthe remainder to bake a cake. She then has 3.6 kg of flour left. Howmuch flour did she buy? Case Study 7
  • 57. Mrs. Lee used ¼ of the flour she bought to make cookies and ¼ ofthe remainder to bake a cake. She then has 3.6 kg of flour left. Howmuch flour did she buy? Case Study 7
  • 58. Mrs Lee used ¼ of the flour she bought to make cookies and ½ ofthe remainder to bake a cake. She then has 3.6 kg of flour left. Howmuch flour did she buy? Case Study 7
  • 59. Jason, Edward and Sam had a total of $837. Jason had the leastamount of money. The ratio of Edward’s money to Sam’s money was4 : 3 at first. Jason and Edward each spent a third of their money.Given that the three boys had $648 left, how much did Jason haveat first?An example of novel assessment task froma Singapore school. This is for Grade 6.$837 - $648 = $189$189 x 3 = $567This is Jason and Edward’s money at first.$837 - $567 = $270This is Sam’s money at first.With this it is possible to find Edward’s henceJason’s amount easily. Did you get $360 forEdward and $207 for Jason?
  • 60. Homework for Bar Model 
  • 61. Pablo is twice as tall as Wynn. Wynn is 20 cm taller than Zena.Pablo is 100 cm taller than Zena.Find their heights in meters. Case Study 8 Pablo Wynn Zena
  • 62. Rosa made paper cranes to fill a glass jar. She made 4 more craneseach day than the day before. After 10 days, she has made 250cranes. How many paper cranes did she make on the last day? Case Study 9 Day 1 Day 2 4 Day 3 4 4 Day 4 4 4 4
  • 63. Rosa made paper cranes to fill a glass jar. She made 4 more craneseach day than the day before. After 4 days, she has made 52cranes. How many paper cranes did she make on the last day? Case Study 9 Day 1 Day 2 4 Day 3 4 4 Day 4 4 4 4

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