Rotterdam Day 1
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Transcript of Rotterdam Day 1
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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.
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Features of Singapore Mathematics Curriculum
Yeap Ban Har, Ph.D.
Marshall Cavendish InstituteSingapore
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Introduction
This is a brief overview of the development of the Singapore mathematics curriculum, its framework
and its rationale and underlying goals.
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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
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Every Child Counts
Huam
in P
rim
ary
Sch
ool
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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
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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
Mala
ysi
a
Sin
gapor
e
402
7018
8850
9782
Inte
rnati
onal
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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.
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Problem
Arrange the ten cards so that you can do what is shown to you.
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Method 1 – by drawing
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Method 2 – by using the cards
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Scarsdale Teachers’ Institute, New York
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Some participants tried to solve the Dutch-version of the problem.
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Wellington Primary School
Problem
Rearrange the sticks to show a given number of squares.
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Task
• Move 3 sticks to make 3 squares.
Lesson Study Problem Wellington Primary School
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Task
• Move 3 sticks to make 3 squares.
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Task
• Move 3 sticks to make 3 squares.
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Task
• Move 3 sticks to make 2 squares.
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Task
• Move 3 sticks to make 2 squares.
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Task
• Move 3 sticks to make 2 squares.
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Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”.
Ministry of Education (Singapore) 2006
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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.
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National Test
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Textbooks
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Textbooks
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Textbooks
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Textbooks
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The CPA Approach & Principle of Variations
Yeap Ban Har, Ph.D.
Marshall Cavendish InstituteSingapore
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Number Bonds
The focus on number sense right from the start. Number bonds is taught before addition.
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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
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PCF Telok Blangah Kindergarten
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One duck is big. Six ducklings are small.
PCF Telok Blangah Kindergarten
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PCF Telok Blangah Kindergarten
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PCF Telok Blangah Kindergarten
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PCF Telok Blangah Kindergarten
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PCF Telok Blangah Kindergarten
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Number Bonds continues to receive attention in Grade 1. M
y P
als
Are
Here
! M
ath
em
ati
cs
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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
yb
ird
Kin
derg
art
en
Math
em
ati
cs
Addition Facts
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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
Sch
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.
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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.
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bruner’s theoryconcrete
mathz4kidz Learning Centre, Penang, Malaysia
A lesson from Earlybird Kindergarten Mathematics
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concreteexperiences
mathz4kidz Learning Centre, Penang, Malaysia
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pictorialconcreteto
frommathz4kidz Learning Centre, Penang, Malaysia
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abstractpictorialto
from
All Kids Are Intelligent Series
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symbols
mathz4kidz Learning Centre, Penang, Malaysia
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Variations
Tasks are varied in a systematic way to ensure that average and struggling learners can learn well.
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Math in Focus 2A
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Math in Focus 2A
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Math in Focus 2A
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Zoltan Dienes
The three lessons include mathematical variations within the same grade.
This is referred to as a spiral approach.
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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
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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.
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Teaching for UnderstandingIdeas from Richard Skemp
Yeap Ban Har, Ph.D.
Marshall Cavendish InstituteSingapore
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Example 1
Grade 1 Division
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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
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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
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Princess Elizabeth Primary School
Division
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Links between concrete and pictorial representation must be carefully constructed.
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conceptual
Bina Bangsa School, Semarang, Indonesia
skemp’s
understandingtheory
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Example 2
Division in Other Grade Levels
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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My Pals Are Here! Mathematics 3A
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Keys Grade School, Manila, The Philippines
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Keys Grade School, Manila, The Philippines
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Example 3
Division Involving Fractions
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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
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Primary Mathematics Standards Edition Grade 6