Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Benito School Santiago

Dr Yeap Ban Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
Seminar on Singapore Math in Chile
SANTIAGO  CONCEPTION
This seminar is about how textbooks can help average students learn mathematics well.
Presentation is available at www.banhar.com

Beliefs
Interest
Appreciation
Confidence
Perseverance
Monitoring of one’s own thinking
Self-regulation of learning
Attitudes
Metacognition
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Mathematical Problem Solving
Reasoning, communication & connections
Thinking skills & heuristics
Application & modelling
Skills
Processes
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992.

thinking schools
learning nation
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.

Textbooks that place an emphasis on problem solving and thinking naturally will be able to help many students becoming good in problem solving.
Singapore textbooks do not focus on tedious computations or learning procedures without the corresponding conceptual understanding.

Textbooks place an emphasis on problem solving and thinking.

first day
first day
first day

It focuses on the development of visualization.

The bar model is used extensively to help students represent problems well as well as to develop visualization.

Visuals are used extensively to develop conceptual understanding.

In learning how to write mixed numbers as improper fractions in Grade 4, the visual approach is a common approach in the textbooks.

This visual shows why
It is clear that there are 5 halves in

It focuses on the development of number sense.

There is an emphasis on mental strategies.
Mental strategies help students become flexible thinkers as they need to make decisions on the best strategy to use for a particular computation.

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.

bruner’s theory
concrete
Singapore Math in Malaysia

concrete
experiences
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 ZoltanDienes.

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).
1995
2003
2007
International
5
Advanced
38
41
38
Grade 4
26
High
70
74
73
67
Intermediate
89
92
91
90
Low
96
98
97

Average
Hong Kong
Singapore
S. Korea
Taiwan
Grade 8
Advanced
2
40
31
45
40
High
15
70
64
71
71
Intermediate
46
88
85
86
90
Low
75
97
94
95
98
Singapore Math in Indonesia

TIMSS
Trends in International Mathematics and Science Studies
Grade 4 2003
Grade 8 2007
Grade 4 1995
Grade 8 1999
38
40
Advanced
38
42
73
70
High
70
77
91
88
Intermediate
89
94
97
97
Low
96
99

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

210
MrsHoon sold 960 cookies.

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%.

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?
$78
Number of $5 notes
4
$20
$58
8
Number of $2 notes
$58 ÷ 7 = 8
8
She had eight $2 notes.

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.

Attitude
Achievement
Singapore
71
41
Grade 4
Hong Kong
67
40
Taiwan
50
24
Japan
62
23
Kazakhstan
89
19
England
62
16
Russia
80
16
International
72
5

Attitude
Achievement
Taiwan
37
45
Grade 8
S Korea
33
40
Singapore
60
40
Hong Kong
47
31
Japan
30
26
Hungary
30
10
England
40
8
International
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 Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
Seminar on Singapore Math in Chile
SANTIAGO  CONCEPTION
Singapore Math in Chile
Presentation is available at www.banhar.com

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Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Benito School Santiago

by Jimmy Keng on Sep 28, 2010

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