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

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

  • SingaporeMathStrategiesfor U.S. yeap ban har marshall cavendishSchools instituteWhite Plains NY  March2012 SESSION ONE Overview & Fundamentals of Singapore MathematicsPrimary 3 Mathematics Lesson Study onMassCHIJ Our Lady of Good Counsel, Singapore
  • Introduction Anchor Green Primary School, Singapore
  • General Overview of Singapore and its Education System  Land  700 sq km  People  4.7 million
  • General Overview of Singapore and its Education System  GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
  • 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.
  • 1992 Problem-Solving Curriculum 1997 Thinking Schools, Learning NationSingapore Mathematics: 2004 Teach Less, Background Learn More 2010 Professional Learning Communities 2011 21st Century Competencies
  • Singapore Ministry of Education 1992, 2001, 2007, 2013
  • “Mathematics is an excellent vehicle for the developmentand improvement of a person’s intellectual competencies” Singapore Ministry of Education 2006
  • What to Teach?Singapore Mathematics: What & How How to Teach?
  • Singapore Examination & Assessment Board 2012 Case Study 1As the instructor demonstrates the lesson, study what is it that the teacher wants students to learn.This is a Grade 6 problem involving fraction and ratio.
  • Case Study 1 16 units = $120 20 units = 04 units = $120 4 units = $30 04 20 units = $30 x 5 20 units = $150John had $150 at first.
  • Case Study 1 what is it that theteacher wants students to learn
  • SESSION ONESingapore Overview & Fundamentals of Singapore MathematicsMath Fundamentals ofStrategies for U.S. SingaporeSchools Mathematics  Focus on Problem SolvingWhite Plains NY  March  Focus on Thinking2012  Focus on Managing Information  Focus on Visualization  Focus on Generalization  Focus on Number Sense  Focus on Communication
  • SingaporeMathStrategiesfor U.S. yeap ban har marshall cavendishSchools instituteWhite Plains NY  March2012 SESSION TWO Mathematical Problem Solving including Bar Models Pathlight School, Singapore
  • 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
  • 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.
  • 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.
  • 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
  • 543 + 274 = 
  • 543 + 274 = 
  • 543 + 274 = 
  • 543 + 274 = 
  • 543 + 274 = 
  • 543 + 274 = 
  • Multiplication is taughtwith a focus on meaning,visualization, and makingconnections.
  • 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.
  • Sam is twice as old as Terry.Vanessa is three times as old asTerry.Their total ages is 72 years. Differentiation forFind their ages. Struggling 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.
  • Sam is twice as old as Terry.Vanessa is three times as old as TerrySam.Their total ages is 72 years.Find their ages. Terry Sam Sam is twice as old as Terry. Case Study 6 Vanessa is three times as old as Differentiation for Terry. Advanced Learners Their total ages is 72 years. Find their ages.
  • Primary Mathematics (Standards Edition) Grade 6 Case Study 2 As the instructor demonstrates the lesson, study what is it that the teacher wants students to learn. This is a task from a Grade 6textbook to motivate the learning of algebra.
  • SingaporeMathStrategiesfor U.S. yeap ban har marshall cavendishSchools instituteWhite Plains NY  March2012REVIEW & CONSOLIDATE Opening LecturePrimary 3 Mathematics Lesson Study onMassCHIJ Our Lady of Good Counsel, Singapore
  • Average Learners High Achievement International Studies
  • Students in Singapore havedemonstrated high achievement andpositive attitude towards mathematics.In Trends in Mathematics and ScienceStudy, about 40% of Singapore’s 4th and8th graders are in the Advanced International 2007 1995 2003International Benchmark (theinternational average is 5% and 2%respectively). Advanced 38 38 41 5 Grade 4 High 70 73 74 26 Intermediate 89 91 92 67 Low 96 97 98 90
  • 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
  • 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
  • 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
  • The attitude index for Singaporestudents in TIMSS is also relatively highcompared to other high-performingcountries.Also, the majority of students inSingapore opt to study mathematics inGrades 11 and 12 when they are nolonger required to. Marsiling Secondary School, Singapore
  • 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
  • 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
  • High achievement was not a given. In1960, among 30 615 candidates whosat for the first Primary School LeavingExamination, 45% of the candidatespassed. Keon Ming Public School, Singapore
  • 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)
  • Average Learners High Achievement Pedagogy
  • Math in Focus
  • Pensar sin Limites (Spanish Edition)
  • Pensar sin Limites (Spanish Edition)
  • Maths Champion (Indonesian Edition)
  • Primary Mathematics (Standards Edition)
  • Primary Mathematics (Standards Edition)
  • SingaporeMathStrategiesfor U.S. yeap ban har marshall cavendishSchools instituteWhite Plains NY  March2012 SESSION THREE Differentiated InstructionPrimary 3 Mathematics Lesson Study onMassCHIJ Our Lady of Good Counsel, Singapore
  • “… over-emphasising procedural skillswithout understanding the underlying mathematical principles should be avoided.” Ministry of Education 2006
  • My Pals Are Here! Mathematics (Second Edition)
  • SingaporeMathStrategiesfor U.S. yeap ban har marshall cavendishSchools instituteWhite Plains NY  March2012 SESSION FOUR AssessmentPrimary 3 Mathematics Lesson Study onMassCHIJ Our Lady of Good Counsel, Singapore
  • 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
  • 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.
  • 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.
  • Mrs. Lee used ¼ of the flour she bought to make cookies anda third of the remainder to bake a cake. She then has 3.6 kgof flour left. How much flour did she buy? Case Study 7
  • Mrs. Lee used ¼ of the flour she bought to make cookies and½ of the remainder to bake a cake. She then has 3.6 kg offlour left. How much flour did she buy? Case Study 7
  • Mrs. Lee used ¼ of the flour she bought to make cookies and¼ of the remainder to bake a cake. She then has 3.6 kg offlour left. How much flour did she buy? Case Study 7
  • Mrs Lee used ¼ of the flour she bought to make cookies and½ of the remainder to bake a cake. She then has 3.6 kg offlour left. How much flour did she buy? Case Study 7
  • Jason, Edward and Sam had a total of $837. Jason had theleast amount of money. The ratio of Edward’s money to Sam’smoney was 4 : 3 at first. Jason and Edward each spent a thirdof their money. Given that the three boys had $648 left, howmuch did Jason have at first?An example of novel assessment taskfrom a Singapore school. This is forGrade 6.$837 - $648 = $189$189 x 3 = $567This is Jason and Edward’s money atfirst.$837 - $567 = $270This is Sam’s money at first.With this it is possible to find Edward’shence Jason’s amount easily. Did you get$360 for Edward and $207 for Jason?
  • Homework for Bar Model 
  • Pablo is twice as tall as Wynn. Wynn is 20 cm taller thanZena.Pablo is 100 cm taller than Zena.Find their heights in meters. Case Study 8 Pablo Wynn Zena
  • Rosa made paper cranes to fill a glass jar. She made 4 morecranes each day than the day before. After 10 days, she hasmade 250 cranes. How many paper cranes did she make onthe last day? Case Study 9 Day 1 Day 2 4 Day 3 4 4 Day 4 4 4 4
  • Rosa made paper cranes to fill a glass jar. She made 4 morecranes each day than the day before. After 4 days, she hasmade 52 cranes. How many paper cranes did she make onthe last day? Case Study 9 Day 1 Day 2 4 Day 3 4 4 Day 4 4 4 4