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Theoretical
Underpinnings of
Singapore Math
Sheraton San Diego Mission
Valley Hotel, San Diego CA
SingaporeMath.com
Professional Development
Please download from
www.mathz4kidz.com
Yeap Ban-Har, Ph.D.
National Institute of Education
Nanyang Technological University
Singapore
banhar.yeap@nie.edu.sgDa Qiao Primary School
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Catholic High School (Primary)
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overview
video of dice problem
solving problems
instructional models
Bruners theory
Skempstheory
Dienes theory
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introduction
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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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
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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
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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?
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34
88
54
88 children took part in a swimming competition. 1/3 of the boys and 3/7of the girls wore swimming goggles. Altogether 34 children wore
swimming goggles.
How many girls wore swimming goggles on that day?
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34
5434 = 203420 = 14
54
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3 x 7 = 21
21 girls wear goggles.
A Curriculum
That Helps
Average
Students
Reach High
Achievement
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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
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Advanced
Intermediate
Low
High
Average
Indonesia
Thailand
2 30
15 124
46 4414
75 6648
Grade 8
Method Used in Singapore Textbooks
TIMSS 2007Trends in International Mathematics and Science Studies
Malaysia
Singapor
e
402
7018
8850
9782
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Mathematics Curriculum Framework
MathematicalProblemSolving
ConceptsNumericalAlgebraic
GeometricalStatistical
Probabilistic
Analytical
Reasoning,communication &connectionsThinking skills &heuristics
Application & modelling
Numerical calculationAlgebraic manipulation
Spatial visualizationData analysis
MeasurementUse of mathematical tools
Estimation
Monitoring of ones own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
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Every Child Counts
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mathematicsteachingeffective
Bina Bangsa School, Indonesia
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Pedagogical
Principle:
Bruner
Primary Mathematics 1A
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Number
Bonds
PCF Kindergarten Telok Blangah
http://localhost/var/www/apps/conversion/tmp/Workshop/04142009/A/Number%20Bonds.MTS -
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Number
Bonds
PCF Kindergarten Telok Blangah
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Bruner
The concrete
pictorialabstract
approach is used to
help the majority oflearners to develop
strong foundation in
mathematics.
National Institute of Education
Division
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Princess Elizabeth Primary School
Division
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Catholic High School (Primary)
mathz4kidz Learning Centre Penang Malaysia
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brunerstheory
concrete
mathz4kidz Learning Centre, Penang, Malaysia
A lesson from Earlybird Kindergarten Mathematics
mathz4kidz Learning Centre Penang Malaysia
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concreteexperiences
mathz4kidz Learning Centre, Penang, Malaysia
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abstractpictorialtofrom
All Kids Are Intelligent Series
mathz4kidz Learning Centre Penang Malaysia
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symbols
mathz4kidz Learning Centre, Penang, Malaysia
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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
Primary Mathematics (Standards Edition) 2A
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Pictorial Before
Abstract
Primary Mathematics (Standards Edition) 2A
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bruner
Lesson Study in a Ministry of Education Seminar on
Singapore Mathematics Teaching Methods in Chile
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conceptual
Bina Bangsa School, Semarang, Indonesia
skemps
understanding
theory
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Keys Grade School, Manila, The Philippines
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Keys Grade School, Manila, The Philippines
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Skemp
Understanding in mathematics
relational
(conceptual)
instrumental
(procedural)
conventional
Teaching for conceptual
understanding is given
emphasis in Singapore Math.
PedagogicalPrinciple:
Skemp
Primary Mathematics Standards Edition Grade 6
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Fraction
Division
Primary Mathematics Standards Edition Grade 6
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skemp
Scarsdale Middle School New York
Dienes
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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
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Pedagogical
Principle:
Dienes
Primary Mathematics Standards Edition Grade 1
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PedagogicalPrinciple:
Dienes
Primary Mathematics Standards Edition Grade 2
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homeworkAre you able to see how these tasks are varied
according to Dienes idea of mathematical
variability?
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16
How is Task 4
different from
Task 5?
Primary Mathematics Standards Edition Grade 5
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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
Earlybird Kindergarten Mathematics
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theoryof
dienes
Standards Edition
Can you see how Dienes idea is
used in designing these tasks?
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Emphasis onpictorial
representation
and systematic
variation toenhance
conceptual
understanding
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conclusion
PCF Kindergarten Pasir Ris
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Instructional Models
Coaching
Modeling
Providing
Explaning
Da Qiao Primary School
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Children are trulythe
future of our nation
Irving Harris
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This presentation is based on part of one of
Singapore pre-service mathematics methodcourses.
50% of Singapore elementary teachers are not
college graduate and they are not trained tobe specialists.
The TEDS-M findings provide some evidence
into the effectiveness of this form ofprofessional development.
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TEDS-M Elementary Teachers
Content KnowledgeTEDS-M Elementary Teachers
Pedagogical Content Knowledge
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TEDS-M Middle School Teachers
Content KnowledgeTEDS-M Middle School Teachers
Pedagogical Content Knowledge
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