This is the presentation on both days of the White Plains event.

1. Singapore
Math
Strategiesfor U.S.
yeap ban har marshall cavendish
Schools institute
White Plains NY  March
2012
SESSION ONE
Overview & Fundamentals
of Singapore Mathematics
Primary 3 Mathematics Lesson Study on
Mass
CHIJ Our Lady of Good Counsel, Singapore

3. Introduction
Anchor Green Primary School, Singapore

4. General Overview of Singapore and
its Education System
 Land
 700 sq km
 People
 4.7 million

5. General Overview of Singapore and
its Education System
 GDP per capita in current U.S. dollars
1965 $510 2010 $43 300

6. 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) Canossa Convent Primary School,
 15 Mixed-Level Schools Singapore
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.

7. 1992 Problem-Solving
Curriculum
1997 Thinking Schools,
Learning Nation
Singapore Mathematics:
2004 Teach Less,
Background Learn More
2010 Professional
Learning
Communities
2011 21st Century
Competencies

9. Singapore Ministry of Education 1992, 2001, 2007, 2013

10. “Mathematics is an excellent
vehicle for the development
and improvement of a person’s
intellectual competencies”
Singapore Ministry of Education 2006

12. What to Teach?
Singapore Mathematics: What &
How
How to Teach?

13. Singapore Examination & Assessment Board 2012
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.

14. Case Study 1 16 units = $120
20 units =
04 units = $120
4 units = $30
04
20 units = $30 x 5
20 units = $150
John had $150 at first.

16. Case Study 1
what is it that the
teacher wants students
to learn

17. SESSION ONE
Singapore Overview & Fundamentals
of Singapore Mathematics
Math Fundamentals of
Strategies for U.S. Singapore
Schools Mathematics
 Focus on Problem Solving
White Plains NY  March
 Focus on Thinking
2012
 Focus on Managing
Information
 Focus on Visualization
 Focus on Generalization
 Focus on Number Sense
 Focus on Communication

18. Singapore
Math
Strategiesfor U.S.
yeap ban har marshall cavendish
Schools institute
White Plains NY  March
2012
SESSION TWO
Mathematical Problem
Solving including Bar
Models
Pathlight School, Singapore

20. Tom has some sweets.
Jerry has 5 sweets more than
Tom.
Later, Tom gives Jerry 2
sweets.
Who has more sweets now?
2
Case Study 3
Primary 3 Lesson Study 2 5 2
Kong Hwa School
Tom Jerry Who has more sweets now?
Before x x+5 How many more?
After x–2 x+7

21. Tom has 9 sweets.
Jerry has 5 sweets more than
Tom.
How many sweets does Jerry
have?
Tom 9
Case Study 3
Jerry 5
9 + 5 = 14
Jerry has 14 sweets.

22. 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?
Tom 9 2
Case Study 3
Jerry 5 2
9–2=7
9 + 5 + 2 =16
16 – 7 = 9
Jerry has 9 more sweets than
Tom.

23. 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
cars 543
Case Study 3
buses 274
543 + 274 = 
cars buses
543 274

24. 543 + 274 = 

25. 543 + 274 = 

26. 543 + 274 = 

27. 543 + 274 = 

28. 543 + 274 = 

29. 543 + 274 = 

30. Multiplication is taught
with a focus on meaning,
visualization, and making
connections.

31. 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
Case Study 6
Terry
72
Vanessa
60 12
72 6= 12
Terry is 12 years old. Sam is 24 years old.
Vanessa is 36 years old.

32. Sam is twice as old as Terry.
Vanessa is three times as old as
Terry.
Their total ages is 72 years. Differentiation for
Find their ages. Struggling Learners
Sam is twice as old as Terry.
Case Study 6 Vanessa is 36 years old.
Their total ages is 72 years.
Find their ages.

33. 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.
Case Study 6 Vanessa is three times as old as
Differentiation for
Terry.
Advanced Learners Their total ages is 72 years.
Find their ages.

34. Primary Mathematics (Standards Edition) Grade 6
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.

37. Singapore
Math
Strategiesfor U.S.
yeap ban har marshall cavendish
Schools institute
White Plains NY  March
2012
REVIEW & CONSOLIDATE
Opening Lecture
Primary 3 Mathematics Lesson Study on
Mass
CHIJ Our Lady of Good Counsel, Singapore

38. Average Learners
High Achievement
International Studies

39. 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
2007
1995
2003
International Benchmark (the
international average is 5% and 2%
respectively). Advanced 38 38 41 5
Grade 4
High 70 73 74 26
Intermediate 89 91 92 67
Low 96 97 98 90

40. Hong Kong
Singapore
S. Korea
Average
Taiwan
TIMSS
Trends in International Mathematics and Science Studies
Advanced 2 31 40 40 45
Grade 8
High 15 64 70 71 71
Intermediate 46 85 88 90 86
Low 75 94 97 98 95
Junyuan Secondary School, Singapore

41. TIMSS
Trends in International Mathematics and Science Studies
Grade 4 1995
Grade 8 1999
Advanced 38 42
High 70 77
Intermediate 89 94
Low 96 99
Fuchun Primary School, Singapore

42. TIMSS
Trends in International Mathematics and Science Studies
Grade 4 2003
Grade 8 2007
Grade 4 1995
Grade 8 1999
Advanced 38 42 38 40
High 70 77 73 70
Intermediate 89 94 91 88
Low 96 99 97 97
Fuchun Primary School, Singapore

43. 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

44. Achievement
Attitude
Singapore 71 41
Hong Kong 67 40
Taiwan 50 24
Grade 4
Japan 62 23
Kazakhstan 89 19
England 62 16
Russia 80 16
International 72 5

45. Achievement
Attitude
Taiwan 37 45
S Korea 33 40
Singapore 60 40
Grade 8
Hong Kong 47 31
Japan 30 26
Hungary 30 10
England 40 8
International 54 2

46. 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

47. All major international tests (literacy, science and mathematics) between 1964
and 2003 were placed on a common scale. Selected countries shown in the table.
Score 1960-1970s 1980s 1990s 2000s
500 Japan Japan Japan Japan
Korea Korea Korea
Hong Kong Singapore Hong Kong
Hong Kong Singapore
400 Thailand Singapore Malaysia Malaysia
Thailand Thailand Thailand
The Philippines
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

48. Average Learners
High Achievement
Pedagogy

49. Math in Focus

50. Pensar sin Limites (Spanish Edition)

51. Pensar sin Limites (Spanish Edition)

52. Maths Champion (Indonesian Edition)

53. Primary Mathematics (Standards Edition)

54. Primary Mathematics (Standards Edition)

55. Singapore
Math
Strategiesfor U.S.
yeap ban har marshall cavendish
Schools institute
White Plains NY  March
2012
SESSION THREE
Differentiated Instruction
Primary 3 Mathematics Lesson Study on
Mass
CHIJ Our Lady of Good Counsel, Singapore

61. “… over-emphasising procedural skills
without understanding the underlying
mathematical principles should be
avoided.”
Ministry of Education 2006

62. My Pals Are Here! Mathematics (Second Edition)

65. Singapore
Math
Strategiesfor U.S.
yeap ban har marshall cavendish
Schools institute
White Plains NY  March
2012
SESSION FOUR
Assessment
Primary 3 Mathematics Lesson Study on
Mass
CHIJ Our Lady of Good Counsel, Singapore

66. Grade Levels Assessment Notes
1–2 Basic Skills Emerging
Informal Familiar Applications Established
Assessment Novel Applications Independently
Scaffolding
With or without
materials
3–4 Basic Skills 40%
Informal Familiar Applications 40%
Assessment Novel Applications 20%
Standardized Test
5–6 Basic Skills 20%
Informal Familiar Applications 30%
Assessment Novel Applications 50%
Standardized Test

67. Jack and Kyla share $300.
Jack gets twice as much as Kyla.
How much does Kyla get?
Jack
Case Study 4
Kyla
$300 3 = $100
Kyla gets $100.

68. 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 12
Case Study 5
Peter
58 – 12 = 46
46 2 = 23
23 + 12 = 35
Natalia’s bag is 35 kg. Peter’s bag is 23 kg.

69. 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

70. 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

71. 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

73. 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

74. 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?

75. Homework for Bar Model 

76. 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.
Case Study 8
Pablo
Wynn
Zena

77. 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?
Case Study 9
Day 1
Day 2 4
Day 3 4 4
Day 4 4 4 4

78. 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?
Case Study 9
Day 1
Day 2 4
Day 3 4 4
Day 4 4 4 4