Chile MOE Seminar English

This seminar is about mathematics teaching and learning that focuses on helping average and struggling learners do well in mathematics while maintaining a suitable challenge for advanced learners.

Dr Yeap Ban HarMarshall Cavendish Institute

Singapore

banhar@sg.marshallcavendish.com

Presentation is available at www.banhar.com

Seminar on Singapore Math in

ChileSANTIAGO CONCEPTION

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

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

The assessment reflects the focus of the curriculum. For example, the Grade 6 national examination (Primary School Leaving Examination or PSLE) includes a significant section that requires problem solving.

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?

210

5

1

8

3

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?

210

5

1

8

3210

40

7

5

1

8

3

3040

1

96040

32

5

4

Mrs Hoon sold 960 cookies.

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?

Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE. Grade 3 Examination Item (Raffles Girls’ Primary School 2009)

Devi had some $2 notes and $5 notes.She had a total of $76.She had 4 more $5 notes than $2 notes.How many $2 notes did she have?

Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE. Grade 3 Examination Item (Raffles Girls’ Primary School 2009)

Devi had some $2 notes and $5 notes.She had a total of $76.She had 4 more $5 notes than $2 notes.How many $2 notes did she have?Number of $5 notes

Number of $2 notes

4 $20

$78

$58

$58 ÷ 7 = 8

8

8She had eight $2 notes.

Textbooks place an emphasis on problem solving and thinking.

Mr Khan

Mr Chen

2740 + 3560= 6300

5 units = 6300

1 unit = 1260

4 units = 4 x 12604 units = 5040

In the end, Mr Chen had 5040 sacks and Mr Khan had 1260 sacks.

Textbooks place an emphasis on problem solving and thinking.

first day

first day

first day

A strong foundation is necessary for the students to do well in mathematics. In the Singapore textbooks, such a strong foundation is achieved through the application of a few learning principles. Singapore Math in Chile

bruner’s theoryconcrete

Singapore Math in Malaysia

concreteexperiences

Singapore Math in Malaysia

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.

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.

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

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

Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of Zoltan Dienes.

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

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

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.

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

Other than the curriculum, assessment and textbooks, another important factor is the teachers.

Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.

 Teachers are expected to engage in professional development throughout their career.

 Some study for certification while others just for improvement. It is also an expectation.

  Textbooks are designed for teachers to learn the mathematics that they teach.

Dr Yeap Ban HarMarshall Cavendish Institute

Singapore

banhar@sg.marshallcavendish.com

Presentation is available at www.banhar.com

Seminar on Singapore Math in

ChileSANTIAGO CONCEPTION

Singapore Math in Chile