international school saigon pearl

Seminar on Singapore Math

International SchoolSaigon PearlHo Chi Minh City

www.banhar.blogspot.com

Yeap Ban-Har, Ph.D.Singapore

banhar.yeap@pathlight.org.sgDa Qiao Primary School, Singapore

The examples used in this course are take n from Math in Focus The Singapore Approach unless otherwise specified.

Catholic High School (Primary), Singapore

introduction

Wellington Primary School, Singapore

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

Example 1

Example 2

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?  19 cm x 5 = 95 cm150 cm – 95 cm = 105 cm

Example 3Singapore Examinations & Assessment Board

105 cm of copper wire was left.

mathematicalproficiencies

Kilpatrick, Swafford & Findell 2001

• Procedural fluency• Conceptual reasoning• Strategic competence• Adaptive reasoning• Productive disposition

strands of

Philosophy of the Education System

thinking schoolslearning nationMinistry of Education 1997

Rationale for Teaching Mathematics

“an excellent vehiclefor the development and improvement

Ministry of Education 2006

of a person’sintellectual competence”

their understandingin a variety ofcomplex situations

mathz4kidz Learning Centre, Penang, Malaysia

This whole shape

stands for 1.

Trends inMathematics& Science Studiesapply

and knowledge

What does this stand

for?

Trends inMathematics& Science Study

explaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia

mathematicalliteracy

OECD Program for International Student Assessment (PISA)

… capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments, and to use and engage with mathematics in ways that meet the needs of that individual’s life …

in early grades basics

Princess Elizabeth Primary School, Singapore

Development of

Number Sense

Number Bonds is emphasized prior to the learning of addition.

Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5.

Earlybird Kindergarten Mathematics Series

Number Bonds

PCF Telok Blangah Kindergarten, Singapore

One duck is big. Six ducklings are small.

PCF Telok Blangah Kindergarten, Singapore

PCF Telok Blangah Kindergarten, Singapore

PCF Telok Blangah Kindergarten, Singapore

PCF Telok Blangah Kindergarten, Singapore

Number Bonds

PCF Telok Blangah Kindergarten, Singapore

Number Bonds

PCF Telok Blangah Kindergarten, Singapore

Number Bonds

PCF Telok Blangah Kindergarten, Singapore

Basic Facts

Basic Facts

Basic Facts

Basic Facts

Basic Facts

Basic Facts

Primary Mathematics Standards Edition

National Institute of Education

mathematicsteachingeffective

Bina Bangsa School, Indonesia

Spiral Within and

Between Grades

mathematicsteachingeffective

Bina Bangsa School, Indonesia

Bruner

Bruner

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

National Institute of Education, Singapore

Division

Princess Elizabeth Primary School, Singapore

Division

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

Catholic High School (Primary), Singapore

Multiplication

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

skempScarsdale 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

mathematicsteachingeffective

Bina Bangsa School, Indonesia

Pedagogical Principle:

Dienes

Pedagogical Principle:

Dienes

Primary Mathematics Standards Edition

Pedagogical Principle:

Dienes

Dienes

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

Primary Mathematics Series Standards Edition

variationtheoryof

diene’s

Earlybird Kindergarten Mathematics Series Standards Edition

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

dienesPrincess Elizabeth Primary School, Singapore

thinking problem solvingbruner’s cpa approachconceptual understanding

diene’s variations

Emphasis on pictorial

representation and systematic variation to

enhance conceptual

understanding

conclusion

PCF Kindergarten Pasir Ris, Singapore

Instructional Models

• Coaching• Modeling• Providing• Explaning

Da Qiao Primary School, Singapore

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?

Grade SixNational Test Item

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.

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

“Children are truly the future of our

nation. “Irving Harris