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Theoretical

Underpinnings of

Singapore Math

Sheraton San Diego Mission

Valley Hotel, San Diego CA

SingaporeMath.com

Professional Development

Please download from

www.mathz4kidz.com

Yeap Ban-Har, Ph.D.

National Institute of Education

Nanyang Technological University

Singapore

[email protected] Qiao Primary School


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Catholic High School (Primary)


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overview

video of dice problem

solving problems

instructional models

Bruners theory

Skempstheory

Dienes theory


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introduction

Wellington Primary School


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Task

Move 3 sticks to make 3 squares.


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Task



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Task



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Task



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Task



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Jim bought some chocolates and gave half of them to

Ken. Ken bought some sweets and gave half of them to

Jim.

Jim ate 12 sweets and Ken ate 18 chocolates. After

that, the number of sweets and chocolates Jim had

were in the ratio 1 : 7 and the number of sweets and

chocolates Ken had were in the ratio 1 : 4.

How many sweets did Ken buy?

A Problem

from Singapore Grade 6 National Test


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88 children took part in a swimming

competition. 1/3 of the boys and 3/7 of the

girls wore swimming goggles. Altogether 34

children wore swimming goggles.

How many girls wore swimming goggles on

that day?

A Problem

from a Singapore Classroom

Fairfield Methodist Primary School


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88 children took part in a swimming competition. 1/3 of the boys and 3/7

of the girls wore swimming goggles. Altogether 34 children wore

swimming goggles.

How many girls wore swimming goggles on that day?


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34

88

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88 children took part in a swimming competition. 1/3 of the boys and 3/7of the girls wore swimming goggles. Altogether 34 children wore

swimming goggles.

How many girls wore swimming goggles on that day?


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34

5434 = 203420 = 14

54


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3 x 7 = 21

21 girls wear goggles.

A Curriculum

That Helps

Average

Students

Reach High

Achievement


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Advanced

Intermediate

Low

High

1995

2003

2007

38 4138

70 7473

89 9291

96 9897

Grade 4

North Vista Primary School

TIMSS 2007Trends in International Mathematics and Science Studies


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Advanced

Intermediate

Low

High

Average

Indonesia

Thailand

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

Malaysia

Singapor

e

402

7018

8850

9782


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Mathematics Curriculum Framework

MathematicalProblemSolving

ConceptsNumericalAlgebraic

GeometricalStatistical

Probabilistic

Analytical

Reasoning,communication &connectionsThinking skills &heuristics

Application & modelling

Numerical calculationAlgebraic manipulation

Spatial visualizationData analysis

MeasurementUse of mathematical tools

Estimation

Monitoring of ones own thinkingSelf-regulation of learning

BeliefsInterest

AppreciationConfidence

Perseverance


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Every Child Counts


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mathematicsteachingeffective

Bina Bangsa School, Indonesia


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Pedagogical

Principle:

Bruner

Primary Mathematics 1A


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Number

Bonds

PCF Kindergarten Telok Blangah
http://localhost/var/www/apps/conversion/tmp/Workshop/04142009/A/Number%20Bonds.MTS


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Number

Bonds

PCF Kindergarten Telok Blangah


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Bruner

The concrete

pictorialabstract

approach is used to

help the majority oflearners to develop

strong foundation in

mathematics.

National Institute of Education

Division


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Princess Elizabeth Primary School

Division


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Catholic High School (Primary)

mathz4kidz Learning Centre Penang Malaysia


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brunerstheory

concrete

mathz4kidz Learning Centre, Penang, Malaysia

A lesson from Earlybird Kindergarten Mathematics



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concreteexperiences



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abstractpictorialtofrom

All Kids Are Intelligent Series



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symbols



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concrete

Lesson Study in a Ministry of Education Seminar on

Singapore Mathematics Teaching Methods in Chile

usingmaterials

Professional Development in Ateneo Grade

School, Manila, The Philippines

Primary Mathematics (Standards Edition) 2A


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Pictorial Before

Abstract

Primary Mathematics (Standards Edition) 2A


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bruner

Lesson Study in a Ministry of Education Seminar on

Singapore Mathematics Teaching Methods in Chile


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conceptual

Bina Bangsa School, Semarang, Indonesia

skemps

understanding

theory


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Keys Grade School, Manila, The Philippines


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Keys Grade School, Manila, The Philippines


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Skemp

Understanding in mathematics

relational

(conceptual)

instrumental

(procedural)

conventional

Teaching for conceptual

understanding is given

emphasis in Singapore Math.

PedagogicalPrinciple:

Skemp

Primary Mathematics Standards Edition Grade 6


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Fraction

Division



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skemp

Scarsdale Middle School New York

Dienes


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Primary Mathematics Standards Edition

Pedagogical

Principle:

Dienes

Dienes

Dienes encouraged the use of

variation in mathematics education

perceptual variability and

mathematical variability.



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Pedagogical

Principle:

Dienes



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PedagogicalPrinciple:

Dienes



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homeworkAre you able to see how these tasks are varied

according to Dienes idea of mathematical

variability?


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16

How is Task 4

different from

Task 5?



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16

30

What is the given

in Task 5? What is

the given in Task

6? Are these

different?Primary Mathematics Standards Edition Grade 5

Earlybird Kindergarten Mathematics


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theoryof

dienes

Standards Edition

Can you see how Dienes idea is

used in designing these tasks?


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Emphasis onpictorial

representation

and systematic

variation toenhance

conceptual

understanding


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conclusion

PCF Kindergarten Pasir Ris


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Instructional Models

Coaching

Modeling

Providing

Explaning

Da Qiao Primary School


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Children are trulythe

future of our nation

Irving Harris


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This presentation is based on part of one of

Singapore pre-service mathematics methodcourses.

50% of Singapore elementary teachers are not

college graduate and they are not trained tobe specialists.

The TEDS-M findings provide some evidence

into the effectiveness of this form ofprofessional development.


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TEDS-M Elementary Teachers

Content KnowledgeTEDS-M Elementary Teachers

Pedagogical Content Knowledge


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TEDS-M Middle School Teachers

Content KnowledgeTEDS-M Middle School Teachers

Pedagogical Content Knowledge

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