Singapore Math at Edgemont School District New York
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Edgemont Union Free School District
Superintendent’s Professional
Development Day
January 2013
MAP101 Fundamentals of Singapore Math E d g e m o n t U n i o n F r e e S c h o o l D i s t r i c t
Yeap Ban Har
Marshall Cavendish Institute Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
Page 1
1992 Introduction of Problem-
Solving Curriculum
1997 Thinking Schools Learning Nation
1982 Introduction of Singapore mathematics
textbooks as they are known today. 2001 Introduction of textbooks published by
private publishers and approved by Ministry of Education.
2007 New editions of textbooks are
published with the introduction of the revised curriculum.
Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”. Ministry of Education Singapore 2006
Page 1
2013 New editions of textbooks are
published with the revision of the curriculum.
Page 4
Singapore Math allows
average learners perform at
a high level. The following
are some data from some
international research on
math achievement and
attitude.
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
United States
International
43
39
37
34
30
24
10
12
18
13
13
4
78
80
80
74
70
59
50
49
49
47
47
28
94
97
96
93
93
86
89
85
78
82
81
69
99
100
99
99
99
96
99
98
93
97
96
90
606
605
602
591
585
562
549
545
542
542
541
500
adv high int low ave
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
Let’s solve a typical word
problem from the Singapore
classroom.
Page 2
110 g
290 g
Page 2
110 g
? ?
2 units = 290 g – 110 g = 180 g
1 units = 180 g 2 = 90 g
3 x 90 g = 270 g Bella puts 270 g sugar on the dish.
Professional Development in London, UK
Exp
erie
nci
ng
Si
nga
po
re M
ath
110 g
290 g
Page 2
the same dish
Page 2
Not necessary to find
the mass that Bella
puts on the dish
Professional Development in St. Louis, USA
The brown sugar problem
demonstrates the importance
of visualization.
Page 5
Share 3 fourths equally among 3.
3 fourths 3 = 1 fourth
Share 3 fourths equally between 2.
3 fourths 2 = 6 eighths 2 = 3 eighths
Share 3 fourths equally among 4.
3 fourths 4 = 12 sixteenths 4 = 3 sixteenths
3 fourths 4 = 12 sixteenths 4 = 3 sixteenths
3 fourths 4 = 1
4×
3
4
Summary of Session 1
Problem solving and thinking as well as
holistic development of the child are the
twin key features of Singapore Math.
CPA Approach is used to achieve the
development of visualization and
provides an impetus for making
generalization.
Escuela de Guetamala, Chile
x + 2x = 12
Seely Place Elementary School, New York
Seely Place Elementary School, New York
Observing patterns and
making generalizations
involves reflection.
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
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 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
Seely Place Elementary School, New York
For students who already
know a procedure, they
should be able to explain the
procedure visually.
Ideally, the visuals are
employed to help students
develop both procedural and
conceptual understanding at
the same time
MAP101 Fundamentals of Singapore Math incorporating differentiated instruction
Yeap Ban Har Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
King Solomon Academy, London
Anchor Task Guided Practice Independent Practice
King Solomon Academy, London
Anchor Task Guided Practice Independent Practice
Globe Academy, London
Anchor Task Guided Practice Independent Practice
Globe Academy, London
Anchor Task Guided Practice Independent Practice
Exp
erie
nci
ng
Si
nga
po
re M
ath
Relational Understanding
R Skemp
Concrete Introduction J Bruner
Junyuan Secondary School, Singapore
what & how
Page 08
Page 13
Differentiated Instruction
30 3 21 3 51 = 50 + 1 51 = 40 + 11 51 = 30 + 21 51 = 20 + 31 51 = 10 + 51
King Solomon Academy, London
60 3 = 20 51 3 = 54 3 =
51 3 = 17 50 3 = Write three story problems for 50 3 .
= Use digit tiles 0 to 9 without repeating.
Write a note to Marc who is absent today. Explain to him how to figure out 51 3 .
Singapore Math
Drill-and-Practice Through
Problem Solving
Summary of Session 2
How we can provide challenge to
advanced learners is discussed in the
51 3. We can also provide
challenge to all students, as
demonstrated in the x=.
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
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