singapore math strategies for u.s. schools
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Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore
SESSION ONE
Overview & Fundamentals of
Singapore Mathematics
Introduction
Anchor Green Primary School, Singapore
General Overview of Singapore and its
Education System
Land 700 sq km
People 4.7 million
General Overview of Singapore and its
Education System
GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
General Overview of Singapore and its
Education System
Students 500 000
Teachers 30 000
Principals & Vice-Principals 900
Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
Canossa Convent Primary School, Singapore
Singapore Mathematics: Background
1992 Problem-Solving
Curriculum
1997 Thinking Schools,
Learning Nation
2004 Teach Less,
Learn More
2010 Professional Learning
Communities
2011 21st Century
Competencies
Singapore Ministry of Education 1992, 2001, 2007, 2013
Singapore Ministry of Education 2006
“Mathematics is an excellent
vehicle for the development
and improvement of a person’s
intellectual competencies”
Singapore Mathematics: What & How
What to Teach?
How to Teach?
Case Study 1
As the instructor demonstrates the
lesson, study what is it that the teacher
wants students to learn. This is a Grade
6 problem involving fraction and ratio.
Singapore Examination & Assessment Board 2012
Case Study 1 16 units = $120
20 units =
04 units = $120 4
04 units = $30
20 units = $30 x 5
20 units = $150
John had $150 at first.
Case Study 1
what is it that the teacher
wants students to learn
Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
Fundamentals of
Singapore Mathematics
SESSION ONE
Overview & Fundamentals of
Singapore Mathematics
Focus on Problem Solving
Focus on Thinking
Focus on Managing Information
Focus on Visualization
Focus on Generalization
Focus on Number Sense
Focus on Communication
Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
yeap ban har marshall cavendish institute
Pathlight School, Singapore
SESSION TWO
Mathematical Problem Solving
including Bar Models
Case Study 3
Tom has some sweets.
Jerry has 5 sweets more than Tom.
Later, Tom gives Jerry 2 sweets.
Who has more sweets now?
Primary 3 Lesson Study Kong Hwa School
5
2
2 2
Who has more sweets now?
How many more?
Tom Jerry
Before x x + 5
After x – 2 x + 7
Case Study 3
Tom has 9 sweets.
Jerry has 5 sweets more than Tom.
How many sweets does Jerry have?
9
5
Tom
Jerry
9 + 5 = 14
Jerry has 14 sweets.
Case Study 3
Tom has 9 sweets.
Jerry has 5 sweets more than Tom.
Later, Tom gives Jerry 2 sweets.
Who has more sweets now?
How many more?
9
5
Tom
Jerry
2
2
9 – 2 = 7
9 + 5 + 2 =16
16 – 7 = 9
Jerry has 9 more sweets than Tom.
Case Study 3
One day, 543 cars and 274 buses pass
through a toll booth. How many cars and
buses pass through the toll booth? Math in Focus Grade 2
543
274
cars
buses
543 + 274 =
543 274
cars buses
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
Multiplication is taught with
a focus on meaning,
visualization, and making
connections.
Case Study 6
Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Their total ages is 72 years.
Find their ages.
Sam
Terry
72 6 =
Terry is 12 years old. Sam is 24 years old.
Vanessa
72
60 12 12
Vanessa is 36 years old.
Case Study 6
Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Their total ages is 72 years.
Find their ages.
Sam is twice as old as Terry.
Vanessa is 36 years old.
Their total ages is 72 years.
Find their ages.
Differentiation for Struggling
Learners
Case Study 6
Sam is twice as old as Terry.
Vanessa is three times as old as Terry Sam.
Their total ages is 72 years.
Find their ages.
Terry Sam
Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Their total ages is 72 years.
Find their ages.
Differentiation for Advanced
Learners
Case Study 2
As the instructor demonstrates the
lesson, study what is it that the teacher
wants students to learn. This is a task
from a Grade 6 textbook to motivate
the learning of algebra.
Primary Mathematics (Standards Edition) Grade 6
Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore
REVIEW & CONSOLIDATE
Opening Lecture
Average Learners High Achievement
International Studies
Students in Singapore have demonstrated
high achievement and positive attitude
towards mathematics.
In Trends in Mathematics and Science Study,
about 40% of Singapore’s 4th and 8th
graders are in the Advanced International
Benchmark (the international average is 5%
and 2% respectively).
Advanced
Intermediate
Low
High
19
95
20
03
20
07
38 41 38
70 74 73
89 92 91
96 98 97
Gra
de
4
Inte
rna
tio
na
l
5
26
67
90
Advanced
Intermediate
Low
High
Ave
rage
Ho
ng
Ko
ng
Sin
gap
ore
2 40 31
15 70 64
46 88 85
75 97 94
S. K
ore
a
Taiw
an
45 40
71 71
86 90
95 98
Gra
de
8
Junyuan Secondary School, Singapore
TIMSS Trends in International Mathematics and Science Studies
Advanced
Intermediate
Low
High
Gra
de
4
19
95
38
70
89
96
TIMSS Trends in International Mathematics and Science Studies
Gra
de
8
19
99
42
77
94
99
Fuchun Primary School, Singapore
Advanced
Intermediate
Low
High
Gra
de
4
19
95
38
70
89
96
TIMSS Trends in International Mathematics and Science Studies
Gra
de
8
19
99
42
77
94
99
Gra
de
4
20
03
Gra
de
8
20
07
38
73
91
97
40
70
88
97
Fuchun Primary School, Singapore
The attitude index for Singapore students in
TIMSS is also relatively high compared to
other high-performing countries.
Also, the majority of students in Singapore
opt to study mathematics in Grades 11 and
12 when they are no longer required to.
Marsiling Secondary School, Singapore
Singapore
Taiwan
Japan
Hong Kong
Att
itu
de
Ac
hie
ve
me
nt
71 41
67 40
50 24
62 23
Gra
de
4
Kazakhstan
Russia
International
England
89 19
62 16
80 16
72 5
Taiwan
Singapore
Hong Kong
S Korea
Att
itu
de
Ac
hie
ve
me
nt
37 45
33 40
60 40
47 31
Gra
de
8
Japan
England
International
Hungary
30 26
30 10
40 8
54 2
High achievement was not a given. In 1960,
among 30 615 candidates who sat for the
first Primary School Leaving Examination,
45% of the candidates passed.
Keon Ming Public School, Singapore
Score 1960-1970s 1980s 1990s 2000s
500 Japan Japan Korea
Hong Kong
Japan Korea
Singapore Hong Kong
Japan Korea
Hong Kong Singapore
400 Thailand Singapore Thailand
The Philippines
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.
Average Learners High Achievement
Pedagogy
Math in Focus
Pensar sin Limites (Spanish Edition)
Pensar sin Limites (Spanish Edition)
Maths Champion (Indonesian Edition)
Primary Mathematics (Standards Edition)
Primary Mathematics (Standards Edition)
Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore
SESSION THREE
Differentiated Instruction
“… over-emphasising procedural skills without understanding the underlying
mathematical principles should be avoided.”
Ministry of Education 2006
My Pals Are Here! Mathematics (Second Edition)
Singapore Math Strategies for U.S. Schools W h i t e P l a i n s N Y M a r c h 2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore
SESSION FOUR
Assessment
Grade Levels Assessment Notes
1 – 2 Informal Assessment
Basic Skills Familiar Applications Novel Applications
Emerging Established
Independently Scaffolding
With or without materials
3 – 4 Informal Assessment Standardized Test
Basic Skills Familiar Applications Novel Applications
40% 40% 20%
5 – 6 Informal Assessment Standardized Test
Basic Skills Familiar Applications Novel Applications
20% 30% 50%
Case Study 4
Jack and Kyla share $300.
Jack gets twice as much as Kyla.
How much does Kyla get?
Jack
Kyla
$300 3 = $100
Kyla gets $100.
Case Study 5
Natalia’s bag is 12 kg heavier than Peter’s.
The total mass of the two bags is 58 kg.
How heavy is Natalia’s bag?
How heavy is Peter’s bag?
Natalia
Peter
12
58 – 12 = 46
46 2 = 23
23 + 12 = 35
Natalia’s bag is 35 kg. Peter’s bag is 23 kg.
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and a third
of the remainder to bake a cake. She then has 3.6 kg of flour left.
How much flour did she buy?
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and ½ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and ¼ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Case Study 7
Mrs Lee used ¼ of the flour she bought to make cookies and ½ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Jason, Edward and Sam had a total of $837. Jason had the least
amount of money. The ratio of Edward’s money to Sam’s money was
4 : 3 at first. Jason and Edward each spent a third of their money.
Given that the three boys had $648 left, how much did Jason have
at first?
An example of novel assessment task from
a Singapore school. This is for Grade 6.
$837 - $648 = $189
$189 x 3 = $567
This is Jason and Edward’s money at first.
$837 - $567 = $270
This is Sam’s money at first.
With this it is possible to find Edward’s hence
Jason’s amount easily. Did you get $360 for
Edward and $207 for Jason?
Homework for Bar Model
Case Study 8
Pablo is twice as tall as Wynn. Wynn is 20 cm taller than Zena.
Pablo is 100 cm taller than Zena.
Find their heights in meters.
Pablo
Wynn
Zena
Case Study 9
Rosa made paper cranes to fill a glass jar. She made 4 more cranes
each day than the day before. After 10 days, she has made 250
cranes. How many paper cranes did she make on the last day?
Day 1
Day 2
Day 3
4
4 4
Day 4 4 4 4
Case Study 9
Rosa made paper cranes to fill a glass jar. She made 4 more cranes
each day than the day before. After 4 days, she has made 52
cranes. How many paper cranes did she make on the last day?
Day 1
Day 2
Day 3
4
4 4
Day 4 4 4 4
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