Theoretical Underpinnings of Singapore Math

Sheraton San Diego Mission Valley Hotel, San Diego CA

SingaporeMath.comProfessional Development

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Yeap Ban-Har, Ph.D.National Institute of Education

Nanyang Technological University Singapore

banhar.yeap@nie.edu.sgDa Qiao Primary School

Catholic High School (Primary)

overview

video of dice problem

solving problems

instructional models

Bruner’s theory

Skemp’s theory

Dienes’ theory

introduction

Wellington Primary School

Task

• Move 3 sticks to make 3 squares.

Lesson Study Problem Wellington Primary School

Task

• Move 3 sticks to make 3 squares.

Task

• Move 3 sticks to make 3 squares.

Task

• Move 3 sticks to make 2 squares.

Task

• Move 3 sticks to make 2 squares.

Task

• Move 3 sticks to make 2 squares.

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

chocolates

Jim

Ken

sweets

12

12

3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22

Half of the sweets Ken bought = 22 + 12 = 34So Ken bought 68 sweets.`

18

12

12

12

12

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?

Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.

• 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

• 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?

34

88

54

• 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?

34

54 – 34 = 2034 – 20 = 14

54

3 x 7 = 21

21 girls wear goggles.

A Curriculum That Helps

Average Students

Reach High Achievement

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

Advanced

Intermediate

Low

High

Aver

age

Indo

nesi

a

Thai

land

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

Mal

aysi

a

Sing

apor

e

402

7018

8850

9782

Mathematics Curriculum Framework

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

SkillsNumericalAlgebraic

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

Every Child Counts

mathematicsteaching

effective

Bina Bangsa School, Indonesia

Pedagogical Principle:

Bruner

Primary Mathematics 1A

Number Bonds

PCF Kindergarten Telok Blangah

Number Bonds

PCF Kindergarten Telok Blangah

Bruner

The concrete pictorial abstract approach is used to help the majority of learners to develop strong foundation in mathematics.

National Institute of Education

Division

Princess Elizabeth Primary School

Division

Catholic High School (Primary)

bruner’s theoryconcrete

mathz4kidz Learning Centre, Penang, Malaysia

A lesson from Earlybird Kindergarten Mathematics

concreteexperiences

mathz4kidz Learning Centre, Penang, Malaysia

pictorialconcreteto

from

mathz4kidz Learning Centre, Penang, Malaysia

abstractpictorialto

from

All Kids Are Intelligent Series

symbols

mathz4kidz Learning Centre, Penang, Malaysia

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

Pictorial Before Abstract

Primary Mathematics (Standards Edition) 2A

bruner

Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

Keys Grade School, Manila, The Philippines

Keys Grade School, Manila, The Philippines

Skemp

Understanding in mathematics • relational (conceptual) • instrumental (procedural)• conventional

Teaching for conceptual understanding is given emphasis in Singapore Math.

Pedagogical Principle:

Skemp

Primary Mathematics Standards Edition Grade 6

Fraction Division

Primary Mathematics Standards Edition Grade 6

skemp

Scarsdale Middle School New York

Primary Mathematics Standards Edition

Pedagogical Principle:

Dienes

Dienes

Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.

Primary Mathematics Standards Edition Grade 1

Pedagogical Principle:

Dienes

Primary Mathematics Standards Edition Grade 1

Pedagogical Principle:

Dienes

Primary Mathematics Standards Edition Grade 2

homeworkAre you able to see how these tasks are varied according to Dienes’ idea of mathematical variability?

16

How is Task 4 different from

Task 5?

Primary Mathematics Standards Edition Grade 5

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

variationtheoryof

diene’s

Earlybird Kindergarten Mathematics Standards Edition

Can you see how Dienes’ idea is used in designing these tasks?

dienes

Princess Elizabeth Primary School, Singapore

Emphasis on pictorial

representation and systematic variation to

enhance conceptual

understanding

conclusion

PCF Kindergarten Pasir Ris

Instructional Models

• Coaching• Modeling• Providing• Explaning

Da Qiao Primary School

“Children are truly the future of our

nation. “Irving Harris

This presentation is based on part of one of Singapore pre-service mathematics method courses.

50% of Singapore elementary teachers are not college graduate and they are not trained to be specialists.

The TEDS-M findings provide some evidence into the effectiveness of this form of professional development.

TEDS-M Elementary TeachersContent Knowledge

TEDS-M Elementary TeachersPedagogical Content Knowledge

TEDS-M Middle School TeachersContent Knowledge

TEDS-M Middle School TeachersPedagogical Content Knowledge