Seminar at Harvard Graduate School of Education 15 April 2010

Theoretical Underpinnings of Singapore Math
Seminar at Harvard Graduate School of Education
Yeap Ban-Har, Ph.D.
National Institute of Education
Nanyang Technological University
Singapore
banhar.yeap@nie.edu.sg

Catholic High School (Primary)

introduction
Wellington Primary School

Task
Lesson Study Problem
Move 3 sticks to make 3 squares.

Task

A Problem from Singapore Grade 6 National Test
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?

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?
chocolates
sweets
Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.
12
Jim
12
18
12
12
12
12
Ken
3 parts  12 + 12 + 12 + 12 + 18 = 66
1 part  22
Half of the sweets Ken bought = 22 + 12 = 34
So Ken bought 68 sweets.`

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

88
34
54

34 – 20 = 14
54 – 34 = 20
34
54

3 x 7 = 21
21 girls wear goggles.
A Curriculum That Helps Average Students Reach High Achievement

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

TIMSS 2007
Trends in International Mathematics and Science Studies
Average
Indonesia
Thailand
Malaysia
Singapore
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

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

effective
mathematics
teaching
BinaBangsa School, Indonesia

Primary Mathematics 1A
Pedagogical Principle:
Bruner

Number Bonds
PCF Kindergarten TelokBlangah

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

Division
Princess Elizabeth Primary School

My Pals Are Here! Mathematics 1B

Catholic High School (Primary)

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

using
concrete
materials
Professional Development in AteneoGrade School, Manila, The Philippines
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

Primary Mathematics (Standards Edition) 2A
Pictorial Before Abstract

bruner
Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile

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

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.
Skemp
Primary Mathematics Standards Edition Grade 6

Fraction Division

skemp
Scarsdale Middle School New York

Dienes
Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability.
Dienes
Primary Mathematics Standards Edition

Dienes

1 h = 60 min
60 ÷ 4 = 15
15 x 3 = 45
¾ x 60 = 45

Mathematical Variation
16

16
30
Primary Mathematics

Earlybird Kindergarten Mathematics
Standards Edition
diene’s
theory
of
variation

diene’s
theory
of
variation

dienes
Princess Elizabeth Primary School, Singapore

Emphasis on pictorial representation and systematic variation to enhance conceptual understanding

Fuchun Primary School, Singapore
interaction
Vygotsky’s Theory
Children Learn in Social Situations

conclusion
PCF Kindergarten PasirRis

Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence ..
Ministry of Education 2006
DaQiao Primary School

Patterns
BinaBangsa School Bandung, Indonesia

Visualization
Yangzheng Primary School

Communication
PathlightSchool

Primary Mathematics Syllabus 2007
Primary 2

Balestier Hill
Primary School
Fuchun Primary School
Primary Mathematics Syllabus 2007

Princess Elizabeth Primary School

“Children are trulythe future of our nation. “
Irving Harris

TEDS-M Elementary Teachers
Content Knowledge
TEDS-M Elementary Teachers
Pedagogical Content Knowledge

TEDS-M Middle School Teachers
Content Knowledge
TEDS-M Middle School Teachers
Pedagogical Content Knowledge

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Seminar at Harvard Graduate School of Education 15 April 2010

by Jimmy Keng on Apr 23, 2010

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