singapore math strategies for u.s. schools

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

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yeap ban har marshall cavendish institute

Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore

SESSION ONEOverview &

Fundamentals of Singapore Mathematics

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. dollars1965 $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) 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.

Canossa Convent Primary School, Singapore

Singapore Mathematics: Background

1992 Problem-Solving Curriculum

1997 Thinking Schools, Learning Nation

2004 Teach Less, Learn More2010 Professional Learning Communities2011 21st Century Competencies

Singapore Ministry of Education 1992, 2001, 2007, 2013

Singapore Ministry of Education 2006

“Mathematics is an excellent vehicle for the development

and improvement of a person’s intellectual competencies”

Singapore Mathematics: What & How

What to Teach?

How to Teach?

Case Study 1

As 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.

Singapore Examination & Assessment Board 2012

Case Study 1 16 units = $120

20 units =

04 units = $120 4 04 units = $30

20 units = $30 x 5 20 units = $150

John had $150 at first.

Case Study 1

what is it that the teacher wants

students to learn

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

2 0 1 2

Fundamentals of Singapore Mathematics

SESSION ONEOverview &

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

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

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yeap ban har marshall cavendish institute

Pathlight School, Singapore

SESSION TWOMathematical Problem Solving including Bar

Models

Case Study 3

Tom has some sweets.Jerry has 5 sweets more than Tom.Later, Tom gives Jerry 2 sweets.Who has more sweets now?

Primary 3 Lesson Study Kong Hwa School

5

2

22

Who has more sweets now?How many more?

Tom Jerry

Before x x + 5

After x – 2 x + 7

Case Study 3

Tom has 9 sweets.Jerry has 5 sweets more than Tom.How many sweets does Jerry have?

9

5

Tom

Jerry

9 + 5 = 14

Jerry has 14 sweets.

Case Study 3

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?

9

5

Tom

Jerry

2

2

9 – 2 = 7

9 + 5 + 2 =16

16 – 7 = 9

Jerry has 9 more sweets than Tom.

Case Study 3

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

543

274

cars

buses

543 + 274 =

543 274

cars buses

543 + 274 =

543 + 274 =

543 + 274 =

543 + 274 =

543 + 274 =

543 + 274 =

Multiplication is taught with a focus on meaning, visualization, and making connections.

Case Study 6

Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.

Sam

Terry

72 6 =

Terry is 12 years old. Sam is 24 years old.

Vanessa

72

60

12 1

2

Vanessa is 36 years old.

Case Study 6

Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.

Sam is twice as old as Terry. Vanessa is 36 years old.Their total ages is 72 years. Find their ages.

Differentiation for Struggling Learners

Case Study 6

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 Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.

Differentiation for Advanced Learners

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 6 textbook to motivate

the learning of algebra.

Primary Mathematics (Standards Edition) Grade 6

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

2 0 1 2

yeap ban har marshall cavendish institute

Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore

REVIEW & CONSOLIDATEOpening Lecture

Average Learners High

Achievement

International Studies

Students in Singapore have demonstrated high achievement and positive attitude towards mathematics.

In Trends in Mathematics and Science Study, about 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively).

Advanced

Intermediate

Low

High

199

5

200

3

200

7

38 4138

70 7473

89 9291

96 9897

Gra

de 4

Inte

rnati

on

al

5

26

67

90

Advanced

Intermediate

Low

High

Aver

age

Hon

g Ko

ng

Sing

apor

e

2 4031

15 7064

46 8885

75 9794

S. K

orea

Taiw

an

4540

7171

8690

9598

Gra

de 8

Junyuan Secondary School, Singapore

TIMSSTrends in International Mathematics and Science Studies

Advanced

Intermediate

Low

High

Gra

de 4

19

95

38

70

89

96

TIMSSTrends in International Mathematics and Science Studies

Gra

de 8

19

9942

77

94

99

Fuchun Primary School, Singapore

Advanced

Intermediate

Low

High

Gra

de 4

19

95

38

70

89

96

TIMSSTrends in International Mathematics and Science Studies

Gra

de 8

19

9942

77

94

99

Gra

de 4

20

03

Gra

de 8

20

07

38

73

91

97

40

70

88

97

Fuchun Primary School, Singapore

The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries.

Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.

Marsiling Secondary School, Singapore

Singapore

Taiwan

Japan

Hong Kong

Att

itude

Ach

ievem

en

t

71 41

67 40

50 24

62 23

Gra

de 4

Kazakhstan

Russia

International

England

89 19

62 16

80 16

72 5

Taiwan

Singapore

Hong Kong

S Korea

Att

itude

Ach

ievem

en

t

37 45

33 40

60 40

47 31

Gra

de 8

Japan

England

International

Hungary

30 26

30 10

40 8

54 2

High achievement was not a given. In 1960, among 30 615 candidates who sat for the first Primary School Leaving Examination, 45% of the candidates passed.

Keon Ming Public School, Singapore

Score 1960-1970s 1980s 1990s 2000s

500 Japan JapanKorea

Hong Kong

JapanKorea

SingaporeHong Kong

JapanKorea

Hong KongSingapore

400 Thailand SingaporeThailand

The Philippines

MalaysiaThailand

MalaysiaThailand

300 IndonesiaThe Philippines

IndonesiaThe Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table.

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)

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

2 0 1 2

yeap ban har marshall cavendish institute

Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore

SESSION THREEDifferentiated

Instruction

“… over-emphasising procedural skills without understanding the underlying

mathematical principles should be avoided.”

Ministry of Education 2006

My Pals Are Here! Mathematics (Second Edition)

Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h

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yeap ban har marshall cavendish institute

Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore

SESSION FOURAssessment

Grade Levels Assessment Notes

1 – 2 Informal Assessment

Basic SkillsFamiliar ApplicationsNovel Applications

EmergingEstablishedIndependentlyScaffoldingWith or without materials

3 – 4Informal Assessment Standardized Test

Basic SkillsFamiliar ApplicationsNovel Applications

40%40%20%

5 – 6 Informal AssessmentStandardized Test

Basic SkillsFamiliar ApplicationsNovel Applications

20%30%50%

Case Study 4

Jack and Kyla share $300.Jack gets twice as much as Kyla.How much does Kyla get?

Jack

Kyla

$300 3 = $100

Kyla gets $100.

Case Study 5

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

Peter

12

58 – 12 = 46

46 2 = 23

23 + 12 = 35

Natalia’s bag is 35 kg. Peter’s bag is 23 kg.

Case Study 7

Mrs. Lee used ¼ of the flour she bought to make cookies and a third of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?

Case Study 7

Mrs. Lee used ¼ of the flour she bought to make cookies and ½ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?

Case Study 7

Mrs. Lee used ¼ of the flour she bought to make cookies and ¼ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?

Case Study 7

Mrs Lee used ¼ of the flour she bought to make cookies and ½ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?

Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward’s money to Sam’s money was 4 : 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 have at first? An example of novel assessment task from a 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 hence Jason’s amount easily. Did you get $360 for Edward and $207 for Jason?

Homework for Bar Model

Case Study 8

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.

Pablo

Wynn

Zena

Case Study 9

Rosa made paper cranes to fill a glass jar. She made 4 more cranes each day than the day before. After 10 days, she has made 250 cranes. How many paper cranes did she make on the last day?

Day 1

Day 2

Day 3

4

4 4

Day 4 4 4 4

Case Study 9

Rosa made paper cranes to fill a glass jar. She made 4 more cranes each day than the day before. After 4 days, she has made 52 cranes. How many paper cranes did she make on the last day?

Day 1

Day 2

Day 3

4

4 4

Day 4 4 4 4