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8/11/2019 Asia Society Washington

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Singapore Primary

Mathematics Textbooks

Yeap Ban Har, Ph.D.

National Institute of Education

Nanyang Technological University

Singapore


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SYNOPSIS

This presentation focuses on selected

aspects of mathematics textbooks usedin Singapore primary schools.


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THINKING SCHOOLS

LEARNING NATION

The books are designed for asystem that emphasizes on

thinking and problem solvingfor every student.


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Singapore Mathematics Curriculum 2007

MathematicalProblemSolving

Attitu

des Metacognition

Processe

s

Concepts

Skills

NumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

Reasoning,communication &connectionsThinking skills &heuristics

Application & modelling

Numerical calculation

Algebraic manipulationSpatial visualization

Data analysisMeasurement

Use of mathematical tools

Estimation

Monitoring of ones own thinking

Self-regulation of learning

BeliefsInterest

AppreciationConfidencePerseverance


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70 cm

The figure below is made up of 2 identical squares, 4 identicalrectangles and 3 identical semi-circles. What is the area of thefigure?

STUDENTS ARE EXPECTED TO ENGAGE IN

VISUALIZATON

x


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STUDENTS ARE EXPECTED TO

HANDLE CHALLENGING SITUATIONS

At first, the ratio of Shantis savings to Royssavings was 5 : 4. After each of them

donated $60 to charity, the ratio of Shantissavings to Roys savings became 13 : 10.

What was Shantis savings at first?


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Shantis savings

Roys savings


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Shantis savings

Roys savings


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Shantis savings

Roys savings


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Shantis savings

Roys savings


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Problem-solving strategies are

shown

Problems are varied


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VISUALIZATION

The books uses a lot of visualrepresentations to help

students construct mentalimages.


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Mathematics & Intellectual Competence

It is recognized that mathematics is an

excellent vehicle for the development andimprovement of a persons intellectual

competence in logical reasoning,spatial visualization, analysis and

abstract thought

Ministry of Education Singapore 2006


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PEDAGOGY

The books employ variouspedagogical tools to facilitate

learning.


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The use of

appropriate

manipulatives. Theseare commonmanipulatives thathave inexpensivealternatives

Focus on one key

concept what it is,and what it is not

Definitions aredeveloped through

induction, starting inan informal fashion

Opportunities tomake connections to

previously taughtconcept - half


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Opportunities for immediate

formative assessment

Teachers know the content that

they are assessing.

Teachers have opportunities to

learn content knowledge. Theprogram was designed for

teachers who do not necessarilyhave strong mathematicsbackground.


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Opportunities for the majority to

reach proficient level

.. opportunities to engageadvanced learners


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Provides independent

practice

Serves as pre-test which isintegrated into instruction


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Provides opportunities for

student-constructedresponses


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Practice for the key concept

Moving from informal

treatment to formal treatmentof key concept


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Even as a new concept is

introduced

.. learners are given practice on

recently-learnt materials

Comparing Areas (Biggest)


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Comparing Areas (Smallest & Greatest)


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Comparing Areas (Same Size)

Building upon previously

developed concepts

Emphasis on visual thinking


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Non-standard unit Standard unit

Opportunities to develop abstract ideas

Concrete Pictorial Abstract

Encourages critical thinking


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Providing

challengingmaterials foradvanced learners

while the rest reach alevel of mastery for

basic materials


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NON-SPECIALIST TEACHERS

Today, only about 50% ofSingapore primary teachers

are graduates.


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NON-SPECIALIST TEACHERS

The textbooks were written for non-specialists, non-graduate teachers. It

has an auto professional developmentfeature.


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SELECTION OF PROBLEMS

The textbooks include a collection oftasks which are carefully selected to

provide variation to strong conceptualdevelopment.


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A collection of purposeful, not

random, tasks


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ROLE OF CONCRETE

MATERIALS

The textbooks are based on theconcrete pictorial abstract

approach.


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MAKING CONNECTIONS

The textbooks help students relateddifferent mathematical ideas. Students

are encouraged to engage insynthesis all the time.


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Facts are not isolated, they areconnected


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STRONG FOUNDATION

The textbooks have contributed tosubsequent success in mathematics in

secondary levels.


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International Benchmark Grade 4 MathematicsPerformance

38%

73%

91%

8%

33%

64%

Advanced High Intermediate

Singapore

International Average


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Research Findings

Students who used the program continued todo well in the later grade levels. This is not the

trend internationally.


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Comparison between Grade 4 and Grade 8

Mathematics Performance

38%44%

8% 6%

73% 77%

33%

24%

91% 93%

64%

51%

Grade 4 Grade 8 Grade 4 Grade 8

Singapore International

Advanced

High

Intermediate


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Conclusion

Textbooks contribute significantly tostudents high level of achievement and

enjoyment of mathematics, in particular, and

abstract thinking, in general. It is a tool forthe teachers to teach and to learn.

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