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International Workshop on Philippine and Singapore Mathematics
Hotel Supreme Convention Plaza,
Baguio City
January 28 – 30, 2013
Promoting Critical and Creative Thinking:
Singapore Mathematics
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
Introduction A Glimpse of Singapore Math
Assumption Englsih School, Singapore
What is Singapore Math? A Glimpse – Mathematics Classroom
Bina Bangsa School, Indonesia
What is Singapore Math? A Glimpse – Mathematics Textbooks
x2 x
1
x2 x
1
x2 + 4x + 1
What is Singapore Math? A Glimpse – Mathematics Textbooks
x2 x
x2 + 4x + 1
= x2 + 4x + 1 + 3 – 3
= (x + 2)2 – 3
What is Singapore Math? A Glimpse – Mathematics Textbooks
What is Singapore Math? A Glimpse – Mathematics Examinations
Weiyang started a savings plan by putting 2 coins in a money
box every day. Each coin was either a 20-cent or 50-cent coin.
His mother also put in a $1 coin in the box every 7 days. The
total value of the coins after 182 days was $133.90 .
(a) How many coins were there altogether?
(b) How many of the coins were 50-cent coins?
Reference: Singapore Examination and Assessment Board
What is Singapore Math? A Glimpse – Mathematics Examinations
Weiyang started a savings plan by putting 2 coins in a money
box every day. Each coin was either a 20-cent or 50-cent coin.
His mother also put in a $1 coin in the box every 7 days. The
total value of the coins after 182 days was $133.90 .
182 7 = 20 + 6 = 26
140 42
182 x 2 + 26 = 364 + 26 = 390
There were 390 coins altogether.
40 cents 70 cents $1
7 5 $133.90 – $26 = $107.90
182 101
Hint for Part (b)
What is Singapore Math? A Glimpse – Teacher Preparation
National Institute of Education, Singapore
Learning to teach 34 x 42.
What is Singapore Math? Thinking and Problem Solving
Nanyang Primary School, Singapore
Mathematics is “an excellent vehicle for
the development and improvement of a
person’s intellectual competence”.
Ministry of Education, Singapore (2006)
thinkingschools learningnation
Ministry of Education, Singapore (1991, 2000, 2006, 2012)
The twin goals of mathematics in the
basic education levels, K-10 are
Critical Thinking and Problem Solving.
Mathematical problem solving is
finding a way around a difficulty,
around an obstacle, and finding a
solution to a problem that is unknown.
Department of Education, The Philippines (2012)
Singapore Math The CPA Approach, The Spiral
Approach and Emphasis on Relational
Understanding Globe Academy, London
Singapore Math The CPA Approach
Singapore Math The CPA Approach
6
2 1
3
concrete
pictorial
abstract
Singapore Math The CPA Approach
3
2
2
1
3
1
3
2
2
1
3
1
1
1
Seely Place Elementary School, New York
Seely Place Elementary School, New York
Seely Place Elementary School, New York
5
4
4
3
Seely Place Elementary School, New York
5
4
4
3
Seely Place Elementary School, New York
5
4
4
3
5
1
1
3=
5
13=
Seely Place Elementary School, New York
5
4
4
3 =
1
1 5
1
1
3
Singapore Math Three-Part Lesson Structure
Extended Engagement
with One Task
Teach Less, Learn More
w w w . b a n h a r . b l o g s p o t . c o m
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure
Singapore Math Three-Part Lesson Structure: Guided Practice
Singapore Math Three-Part Lesson Structure
Singapore Math The Spiral Approach
Singapore Math The Spiral Approach
Singapore Math Anchor Task
Guided Practice
Independent Practice
J Bruner Enactive, Iconic, Symbolic
Representations
Edgewood Elementary School, New York
Edgewood Elementary School, New York
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Edgewood Elementary School, New York
A
B
C 20
116 x
x x
x
x + 2x + x + 20 = 116
4x = 116 – 20 = 96
x = 96 4 = …
King Solomon Academy, London
A number is of a second number.
The sum of the two numbers is 120. 5
3
J Bruner Spiral Curriculum
Greenville Elementary School, New York
Seely Place Elementary School, New York
Greenville Elementary School, New York
The CPA Approach
C P A
Students were asked to
make three nests of 2
eggs and, later, 3 nests
of 7 eggs. They were
only given 20 ‘eggs’.
Greenville Elementary School, New York
CPA Approach in Developing Conventional Language
3 nests 3 nests of 2 eggs 3 groups of 2 3 twos
Escuela de Guetamala, Chile
6
6
6
6
Allfarthing Primary School, London
Math in Focus
Da Qiao Primary School, Singapore
Bina Bangsa School, Indonesia
Z Dienes Play Structured Learning
Practice
Jenaplanschool Cleoplas, The Netherlands
x x x
x
x
x
x – 1
x + 1
x – 2
x + 2
L Vygotsky Interaction
Pathlight School, Singapore
Bina Bangsa School, Indonesia
Globe Academy, London
R Skemp Relational and Instrumental
Understanding
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1
J Piager Assimilation, Accommodation
Keys Grade School, Manila
H Gardner Multiple Intelligences
Keys Grade School, Manila
Seely Place Elementary School, New York
Observing patterns and
making generalizations
involves reflection.
Student Achievement Average Learners Performing
Well
Pathlight School, Singapore
Singapore Math allows
average learners perform at
a high level. The following
are some data from some
international research on
math achievement and
attitude.
East Coast Primary School, Singapore
Score 1960-1970s 1980s 1990s 2000s
500 Japan Hong Kong Japan Korea
Hong Kong Japan Korea
Singapore
Hong Kong Japan Korea
Singapore
400 Thailand The Philippines Singapore Thailand
Malaysia Thailand
Malaysia Thailand
300 Indonesia The Philippines
Indonesia The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
All major international tests (literacy, science and mathematics) between 1964 and
2003 were placed on a common scale. Selected countries shown in the table.
mathematics
gra
de f
our
ma
them
atics
Singapore
South Korea
Hong Kong
Taiwan
Japan
Northern Ireland
Belgium
Finland
England
Russia
International
43
39
37
34
30
24
10
12
18
13
4
78
80
80
74
70
59
50
49
49
47
28
94
97
96
93
93
86
89
85
78
82
69
99
100
99
99
99
96
99
98
93
97
90
606
605
602
591
585
562
549
545
542
542
500
adva
nced
hig
h
inte
rmedia
te
low
average
gra
de e
ight
ma
them
atics
South Korea
Singapore
Taiwan
Hong Kong
Japan
Russia
Israel
Finland
United States
England
International
47
48
49
34
27
14
12
4
7
8
3
77
78
73
71
61
47
40
30
30
32
17
93
92
88
89
87
78
68
73
68
65
46
99
99
96
97
97
95
87
96
92
88
75
613
611
609
586
570
539
516
514
509
507
500
adva
nced
hig
h
inte
rmedia
te
low
average
gra
de e
ight
ma
them
atics
Singapore
Malaysia
Thailand
Indonesia
International
48
2
2
0
3
78
12
8
2
17
92
36
26
15
46
99
65
55
43
75
611
440
427
386
500
adva
nced
high
inte
rmedia
te
low
ave
rage
gra
de e
ight
ma
them
atics
Singapore
Malaysia
Thailand
Indonesia
International
48
2
2
0
3
32
39
26
20
26
23
15
16
10
31
611
440
427
386
500
adva
nced
like m
ath
dislik
e m
ath
ave
rage
gra
de e
ight
ma
them
atics
Singapore
South Korea
Taiwan
Hong Kong
Japan
48
47
49
34
27
32
8
14
19
9
23
56
53
37
53
611
613
609
586
570
adva
nced
like m
ath
dislik
e m
ath
ave
rage
International 3 26 31 500
Singapore
International
82
52
pere
ntage
corr
ect
Singapore
International
52
27
pere
ntage
corr
ect
Singapore
International
45
23
pere
ntage
corr
ect
Singapore
International
60
25
pere
ntage
corr
ect
three keys to successful implementation
assessment
Reference: Department of Education State of New York
teacher preparation
Teacher as a learner (professor as a
model)
Teacher as an observer of learning
(lesson study)
Teacher as reflective practitioner
(professional learning community)
Singapore teachers learn what they need to learn through an
approach that balances content and pedagogy.
teacher preparation
National Institute of Education
Singapore
The practice component is given emphasis – micro teaching,
practicum and lesson study.
teacher preparation
National Institute of Education
Singapore
There is an
emphasis on
teachers
solving the
problems
themselves
during the
course.
teacher preparation
Teachers learn from the
textbooks and teachers
guide.
teacher development
We learn from the Japanese method to help teachers
develop better skills in observing students. This is lesson
study.
teacher development
Princess Elizabeth Primary School
Singapore
TEDS-M Elementary Teachers
Content Knowledge TEDS-M Elementary Teachers
Pedagogical Content Knowledge
TEDS-M Findings
National Institute of Education, Singapore
Fuchun Primary School, Singapore
Edgewood Elementary School, New York
Bina Bangsa School, Indonesia
Keys Grade School, The Philippines
Kranji Secondary School, Singapore
leadership Mayor of Newark gave an inspirational message to
teachers attending professional development on
Singapore Math.
International Workshop on Philippine and Singapore Mathematics
Hotel Supreme Convention Plaza,
Baguio City
January 28 – 30, 2013
Promoting Critical and Creative Thinking:
K-12 Mathematics • What can I do as a teacher?
• What can my school do?
• What can the education schools do?
• What government support should be in place?
Slides are available at
www.banhar.blogspot.com