Rotterdam Day 1

Singapore Math in Rotterdam I
Opleiding 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.aJ.Bruner, R.Skemp, Z.Dieneszijnuitgewerkt in het ontwerp van eeneffectiefrekenprogrammadatalleleerlingen in staatsteltteleren en bovengemiddleldeleerlingen de kansbiedtteexcelleren.

Features of Singapore Mathematics Curriculum
Yeap Ban Har, Ph.D.
Marshall Cavendish Institute
Singapore
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.

Beliefs
Interest
Appreciation
Confidence
Perseverance
Monitoring of one’s own thinking
Self-regulation of learning
Attitudes
Metacognition
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Mathematical Problem Solving
Reasoning, communication & connections
Thinking skills & heuristics
Application & modelling
Skills
Processes
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
Mathematics Curriculum Framework

Every Child Counts
Huamin Primary School

TIMSS 1995 – 2007
Trends in International Mathematics and Science Studies
1995
2003
2007
International
Grade 4
5
Advanced
38
41
38
26
High
70
74
73
67
Intermediate
89
92
91
90
Low
96
98
97
North Vista Primary School

TIMSS 2007
Trends in International Mathematics and Science Studies
Indonesia
Thailand
Malaysia
Singapore
International
Grade 8
Advanced
2
3
0
40
2
High
15
12
4
70
18
Intermediate
46
44
14
88
50
Low
75
66
48
97
82
Method Used in Singapore Textbooks

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.

Problem
Rearrange the sticks to show a given number of squares.
Wellington Primary School

Task
Lesson Study Problem
Wellington Primary School
Move 3 sticks to make 3 squares.

Task

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

The CPA Approach
& Principle of Variations
Yeap Ban Har, Ph.D.
Singapore

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

Number Bonds
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

PCF TelokBlangah Kindergarten

One duck is big.
Six ducklings are small.

My Pals Are Here! Mathematics
Number Bonds continues to receive attention in Grade 1.

Addition Facts
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.
Earlybird Kindergarten Mathematics

Addition Facts &Number Sense
While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.
Princess Elizabeth Primary School
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.

mathz4kidz Learning Centre, Penang, Malaysia
bruner’s theory
concrete
A lesson from Earlybird Kindergarten Mathematics

concrete
experiences

from
concrete
to
pictorial

from
pictorial
to
abstract
All Kids Are Intelligent Series

symbols

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

Math in Focus 2A

ZoltanDienes
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
Words
Numerals
Tens and Ones Notation
Primary Mathematics

ZoltanDienes
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 Understanding
Ideas from Richard Skemp
Yeap Ban Har, Ph.D.
Singapore

Example 1
Grade 1 Division

The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics.
Grade 1 Division
National Institute of Education

Curriculum Document
Division 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.

skemp’s
theory
conceptual
understanding
BinaBangsa School, Semarang, Indonesia

Example 2
Division in Other Grade Levels

My Pals Are Here! Mathematics 3A

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

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Rotterdam Day 1

by Jimmy Keng on Sep 15, 2010

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Rotterdam Day 1 — Presentation Transcript