This document summarizes a presentation on Singapore Math given at Highline Public Schools in March 2013. It discusses key aspects of Singapore Math including the concrete-pictorial-abstract approach, the spiral curriculum, and an emphasis on relational understanding. It also references several educational theorists and compares international test results that show Singapore students performing well. The document contains examples of how Singapore Math concepts and methods are taught.

1. Singapore Math at Highline Public Schools
March 2013  Session 5
Yeap Ban Har
www.banhar.blogspot.com
The Merlion by Yeap Ken Min

2. John had 1.5 m of
copper wire. He cut
some of the wire to
bend into the shape
shown in the figure
below. In the figure,
there are 6 equilateral
triangles and the
length of XY is 19 cm.
How much of the
copper wire was left?

6. 19 cm x 5 = 95 cm
150 cm – 95 cm = 55 cm
55 cm was left.

7. Lesson 6 12th March 2013

8. Lesson 6 12th March 2013

9. Lesson 6 12th March 2013

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

13. Student Achievement
Average Learners Performing
Well
Pathlight School, Singapore

14. 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

15. 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 Hong Kong Hong Kong Hong Kong
Japan Japan Japan
Korea Korea Korea
Singapore Singapore
400 Thailand The Philippines Malaysia Malaysia
Singapore Thailand Thailand
Thailand
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

16. mathematics

17. intermediate
advanced
high
low
average
Singapore 606 43 78 94 99
South Korea 605 39 80 97 100
grade four mathematics
Hong Kong 602 37 80 96 99
Taiwan 591 34 74 93 99
Japan 585 30 70 93 99
Northern Ireland 562 24 59 86 96
Belgium 549 10 50 89 99
Finland 545 12 49 85 98
England 542 18 49 78 93
Russia 542 13 47 82 97
International 500 4 28 69 90

18. intermediate
advanced
high
low
average
South Korea 613 47 77 93 99
Singapore 611 48 78 92 99
grade eight mathematics
Taiwan 609 49 73 88 96
Hong Kong 586 34 71 89 97
Japan 570 27 61 87 97
Russia 539 14 47 78 95
Israel 516 12 40 68 87
Finland 514 4 30 73 96
United States 509 7 30 68 92
England 507 8 32 65 88
International 500 3 17 46 75

19. intermediate
grade eight mathematics
advanced
average
high
low
Singapore 611 48 78 92 99
Malaysia 440 2 12 36 65
Thailand 427 2 8 26 55
Indonesia 386 0 2 15 43
International 500 3 17 46 75

20. Singapore Math
The CPA Approach, The Spiral
Approach and Emphasis on Relational
Understanding
Globe Academy, London

21. J Bruner
Enactive, Iconic, Symbolic
Representations
Edgewood Elementary School, New York

22. Greenville Elementary School, New York

23. Escuela de Guetamala, Chile
6
6
6
6

26. J Bruner
Spiral Curriculum
Greenville Elementary School, New York

27. Z Dienes
Play  Structured Learning
 Practice
Bina Bangsa School, Indonesia

28. x
x x x
x
Jenaplanschool Cleoplas, The Netherlands

29. L Vygotsky
Interaction
Pathlight School, Singapore
Bina Bangsa School, Indonesia

30. R Skemp
Relational and Instrumental
Understanding
Globe Academy, London

31. Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1

32. Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1

33. J Piager
Assimilation, Accommodation
Keys Grade School, Manila

34. H Gardner
Multiple Intelligences
Keys Grade School, Manila

35. Observing patterns and
making generalizations
involves reflection.
Seely Place Elementary School, New York

39. Singapore National Examination
Find the value of 12.2 ÷ 4 .
Answer : 3.05 [B1]
Example 1

40. 3 .05
12.20 4 12.20
12
12 20 hundredths
0.20
0.20
Number Bond Method
0
Long Division Method

41. A show started at 10.55 a.m. and
ended at 1.30 p.m. How long was
the show in hours and minutes?
2 h 30 min
11 a.m. 1.30
p.m.
Answer : 2 h 35 min [B1]
Example 2

42. Find <y in the figure below.
70 o
70 o y
70 o
360o – 210o = 150o
Example 3

43. Cup cakes are sold at 40 cents each.
What is the greatest number of cup
cakes that can be bought with $95?
 $95 ÷ 40 cents = 237.5
Answer: 237 cupcakes
Example 4

44. Mr Tan rented a car for 3 days. He
was charged $155 per day and 60
cents for every km that he travelled.
He paid $767.40. What was the total
distance that he travelled for the 3
days?
$767.40 – 3 x $155 = $302.40
$302.40 ÷ 60 cents per km = 504 km
Example 5

45. “Mathematical problem
solving is central to
mathematics learning.”
Ministry of Education 2006

46. “… including non-routine,
open-ended and real-world
problems.”
Ministry of Education 2006

47. Parents Up In Arms Said Mrs Vivian Weng: "I think the setters
feel it'll be faster for them to compute with a
Over PSLE calculator. So the problems they set are much
more complex; there are more values, more
steps. But it's unfair because this is the first
Mathematics Paper time they can do so and they do not know
what to expect!"
TODAY’S 10 OCT 2009 …
"The introduction of the use of calculators
does not have any bearing on the difficulty of
SINGAPORE: The first thing her son did when he came out from paper. The use of calculators has been
the Primary School Leaving Examination (PSLE) maths paper on introduced into the primary maths curriculum
Thursday this week was to gesture as if he was "slitting his so as to enhance the teaching and learning of
throat". maths by expanding the repertoire of learning
"One look at his face and I thought 'oh no'. I could see that he felt activities, to achieve a better balance between
he was condemned," said Mrs Karen Sng. "When he was telling the time and effort spent developing problem
me about how he couldn't answer some of the questions, he got solving skills and computation skills.
very emotional and started crying. He said his hopes of getting Calculators can also help to reduce
(an) A* are dashed." computational errors."
…
Not for the first time, parents are up in arms over the PSLE Another common gripe: There was not
Mathematics paper, which some have described as "unbelievably enough time for them to complete the paper.
tough" this year. As recently as two years ago, the PSLE A private tutor, who declined to be named,
Mathematics paper had also caused a similar uproar. told MediaCorp she concurred with parents'
The reason for Thursday's tough paper, opined the seven parents opinions. "This year's paper demanded more
whom MediaCorp spoke to, was because Primary 6 students were from students. It required them to read and
allowed to use calculators while solving Paper 2 for the first time. understand more complex questions, and go
… through more steps, so time constraints would
have been a concern," the 28-year-old said.

48. Trends in International
Mathematics and Science
Study TIMSS
Students in the highest international
benchmark are able to apply their
knowledge in a variety of situations
and able to explain themselves.

57. “Skill proficiencies include the
ability to use technology
confidently, where appropriate,
for exploration and problem
solving.”
Ministry of Education 2006

58. 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
Example 6

59. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a
plastic frame that covers exactly 9 squares of Table 1 with the centre
square darkened.

60. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a
plastic frame that covers exactly 9 squares of Table 1 with the centre
square darkened.
(a) Kay puts the frame on 9 squares as shown in the figure below.
3 4 5
11 13
19 20 21
What is the average of the 8 numbers that
can be seen in the frame?

61. Table 1 consists of numbers from 1 to 56. Kay and Lin are given a
plastic frame that covers exactly 9 squares of Table 1 with the centre
square darkened.
(a) Kay puts the frame on 9 squares as shown in the figure below.
3+4+5+11+13+19+20 = 96
3 4 5 96 ÷ 8 = 12
11 13 Alternate Method
4 x 24 = 96
19 20 21 96 ÷ 8 = 12
What is the average of the 8 numbers that
can be seen in the frame?

62. (b) Lin puts the frame on some other 9 squares.
The sum of the 8 numbers that can be seen in the frame is 272.
What is the largest number that can be seen in the frame?
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56

63. 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 puts 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?
Example 7

64. three
keys
to successful
implementation

65. Reference: Department of Education State of New York
assessment

66. assessment
Reference: Department of Education State of Hawaii

67.  Teacher as a learner (professor as a
model)
 Teacher as an observer of learning
(lesson study)
 Teacher as reflective practitioner
(professional learning community)
teacher preparation

68. teacher preparation
National Institute of Education
Singapore
Singapore teachers learn what they need to learn through an
approach that balances content and pedagogy.

69. teacher preparation
National Institute of Education
Singapore
The practice component is given emphasis – micro teaching,
practicum and lesson study.

70. teacher preparation
There is an
emphasis on
teachers
solving the
problems
themselves
during the
course.

71. teacher development
Teachers learn from the
textbooks and teachers
guide.

72. teacher development
We learn from the Japanese method to help teachers
develop better skills in observing students. This is lesson
study. Princess Elizabeth Primary School
Singapore

73. TEDS-M Findings
TEDS-M Elementary Teachers TEDS-M Elementary Teachers
Content Knowledge Pedagogical Content Knowledge

74. National Institute of Education, Singapore
Edgewood Elementary School, New York
Fuchun Primary School, Singapore

75. Bina Bangsa School, Indonesia
Keys Grade School, The Philippines
Kranji Secondary School, Singapore

76. leadership Mayor of Newark gave an inspirational message to
teachers attending professional development on
Singapore Math.

77. • 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

78. Singapore Math at Highline Public Schools
March 2013 
Yeap Ban Har
yeapbanhar@gmail.com
The Merlion by Yeap Ken Min