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The Average Student on TopThe High School Renewal Committee

27 October 2010

Yeap Ban HarMarshall Cavendish Institute

Singapore

banhar@sg.marshallcavendish.com

Slides are available at www.banhar.com

vision and focus

Singapore mathematics curriculum has its focus mathematical problem solving and it is set within an education system that emphasizes thinking.

mathematical problem solving

In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992.

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

Skills

NumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling

Numerical calculationAlgebraic

manipulationSpatial visualization

Data analysisMeasurement

Use of mathematical tools

Estimation

Monitoring of one’s own thinkingSelf-regulation of learning

BeliefsInterest

AppreciationConfidence

Perseverance

thinking

The emphasis on thinking continues in the late 1990s with the introduction of Thinking School, Learning Nation philosophy to the entire education system in 1997.

thinking schoolslearning nation

strong fundamentals

Princess Elizabeth Primary School, Singapore

24

6

3 5

Princess Elizabeth Primary School, Singapore

pedagogy

Pedagogy that focuses on visuals, patterning and number sense.

The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner.

Fuchun Primary School, Singapore

For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in groups of 4 before progressing to using drawings to solve division problems. Later they learn to use division sentence 12 ÷ 4 = 3. Princess Elizabeth Primary School, Singapore

For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1.

The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also one of Jerome Bruner’s ideas.

Singapore Math in the Netherlands

 In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers.

Singapore Math in USA

In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1.

Singapore Math in The Philippines

assessment

SourcePSLE Mathematics Singapore Examination and Assessment Board

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

50

872

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

822

1 unit = 822 ÷ 61 unit = 137Bala has 137 marbles.

600180

42

SourcePrimary Three Examination Item from Henry Park Primary School, Singapore

Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?

Angela

Bala

Cheng Hao

50

872y

y y y y

y

4y + y + (y + 50) = 872

6y + 50 = 872

6y = 872 – 50

y = 822 ÷ 6

y = 137

outcomes

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

In Trends in Mathematics and Science Study, more than 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

Ind

onesi

a

Th

aila

nd

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

Mala

ysi

a

Sin

gapor

e

402

7018

8850

9782

Inte

rnati

onal

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

Singapore Math in Indonesia

TIMSS 2007Trends 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

Gra

de 4

20

03

Gra

de 8

20

07

38

73

91

97

40

70

88

97

In the PSLE, the national average for students who are capable of completing the most challenging items in the examination is between 40% and 45%. We saw one such challenging items earlier.

Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.

How many cookies did Mrs Hoon sell?

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.

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

Making the Average Student on Top • Thinking-oriented Curriculum• Theoretically-sound Pedagogy• Assessment that is coherent with the curriculum• Teacher professional development• Changing mindset about what mathematics is• Constructing knowledge• Enhancing capacity to learn