Singapore Math in Rotterdam IOpleiding Singapore rekenspecialist

This set of slides cover three presentations made on the first day:

• Features of Singapore Math

• Theories – Bruner & Dienes

• Teaching for Understanding

Weten en begrijpen hoe de theorieen van o.a J.Bruner, R.Skemp, Z.Dienes zijn uitgewerkt in het ontwerp van een effectief rekenprogramma dat alle leerlingen in staat stelt te leren en bovengemiddlelde leerlingen de kans biedt te excelleren.

Features of Singapore Mathematics Curriculum

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

Introduction

This is a brief overview of the development of the Singapore mathematics curriculum, its framework

and its rationale and underlying goals.

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

Huam

in P

rim

ary

Sch

ool

Advanced

Intermediate

Low

High

199

5

200

3

200

7

38 4138

70 7473

89 9291

96 9897

Grade 4

North Vista Primary School

TIMSS 1995 – 2007 Trends in International Mathematics and Science Studies

Inte

rnati

on

al

5

26

67

90

Advanced

Intermediate

Low

High

Ind

onesi

a

Th

aila

nd

2 30

15 124

46 4414

75 6648

Grade 8

Method Used in Singapore Textbooks

TIMSS 2007Trends in International Mathematics and Science Studies

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Sin

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402

7018

8850

9782

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Why Schools Teach Mathematics

We will engage in activities that are used to help teachers understand the rationale for teaching

mathematics in school.

Problem

Arrange the ten cards so that you can do what is shown to you.

Method 1 – by drawing

Method 2 – by using the cards

Scarsdale Teachers’ Institute, New York

Some participants tried to solve the Dutch-version of the problem.

Wellington Primary School

Problem

Rearrange the sticks to show a given number of squares.

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.

Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”.

Ministry of Education (Singapore) 2006

Focus on Problem Solving

The Singapore curriculum focuses on problem solving. So does the national test. It is no wonder that’s schools place a lot of emphasis on problem

solving.

National Test

Textbooks

Textbooks

Textbooks

Textbooks

The CPA Approach & Principle of Variations

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

Number Bonds

The focus on number sense right from the start. Number bonds is taught before addition.

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

Number Bonds

PCF Telok Blangah Kindergarten

One duck is big. Six ducklings are small.

PCF Telok Blangah Kindergarten

PCF Telok Blangah Kindergarten

PCF Telok Blangah Kindergarten

PCF Telok Blangah Kindergarten

PCF Telok Blangah Kindergarten

Number Bonds continues to receive attention in Grade 1. M

y P

als

Are

Here

! M

ath

em

ati

cs

Addition Facts are given emphasis in the first six months of grade one.

The children learn it in stages as the textbooks distinguished between Numbers to 10 and Numbers to 20.

Count On and Count All are used in Numbers to 10.

Earl

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ird

Kin

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en

Math

em

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Addition Facts

While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.

Pri

nce

ss E

lizab

eth

Pri

mary

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ool

Addition Facts & Number Sense

The topics are arranged in a way that makes learning progressive and systematic – this is part of the idea of a spiral curriculum.

Jerome Bruner

Ideas are introduced using concrete materials. Pictorial representations follow. Finally, children

engage with the abstract symbols. This is called the CPA Approach in Singapore.

bruner’s theoryconcrete

mathz4kidz Learning Centre, Penang, Malaysia

A lesson from Earlybird Kindergarten Mathematics

concreteexperiences

mathz4kidz Learning Centre, Penang, Malaysia

pictorialconcreteto

frommathz4kidz Learning Centre, Penang, Malaysia

abstractpictorialto

from

All Kids Are Intelligent Series

symbols

mathz4kidz Learning Centre, Penang, Malaysia

Variations

Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.

Math in Focus 2A

Math in Focus 2A

Math in Focus 2A

Zoltan Dienes

The three lessons include mathematical variations within the same grade.

This is referred to as a spiral approach.

It is likely that a teacher will start this unit using the sticks. This is followed by the use of base ten blocks. Finally, non-proportionate materials such as coins are used. In each of these lessons, the teacher is likely to introduce the following five notations in turn – place value chart, expanded notation, number in numerals, number in words and the tens and ones notation.

The question is what is an appropriate sequence? Should the place value chart be used first? Or the expanded notation? Give your reasons.

Place Value Chart Expanded Notation

Numerals WordsTens and Ones Notation Primary Mathematics

Zoltan Dienes

The one lesson include perceptual variations. This is Dienes’ idea of multiple embodiment. The

mathematical concept is constant while the materials used to embody it are varied.

Teaching for UnderstandingIdeas from Richard Skemp

Yeap Ban Har, Ph.D.

Marshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

Example 1

Grade 1 Division

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

National Institute of Education

Grade 1 Division

Curriculum DocumentDivision of a quantity (not greater than 20) into equal sets

Given the number of objects in the

set

Given the number of sets

Solving 1-step word problems with pictorial representation

Princess Elizabeth Primary School

Division

Links between concrete and pictorial representation must be carefully constructed.

conceptual

Bina Bangsa School, Semarang, Indonesia

skemp’s

understandingtheory

Example 2

Division in Other Grade Levels

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

My Pals Are Here! Mathematics 3A

Keys Grade School, Manila, The Philippines

Keys Grade School, Manila, The Philippines

Example 3

Division Involving Fractions

Skemp

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

Teaching for conceptual understanding is given emphasis in Singapore Math.

Primary Mathematics Standards Edition Grade 6

Primary Mathematics Standards Edition Grade 6