These are the sldies for MAP101 conducted in Hilo,

1. Professional Development
Singapore Mathematics
Big Island of Hawai’i  5 – 9 June 2012
Dr Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com
Day 1
www.mcinstitute.com.sg
www.facebook.com/MCISingapore

2. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

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

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

5. 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.

6. Universities
National Examination
Institutes of
Poly
Technical
technics
Junior Education
Colleges
Integrated
National Examination
Programmes
Secondary Schools
National Examination
Primary Schools
A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest
http://www.moe.gov.sg/education/education-statistics-digest/

8. Curriculum document is available at http://www.moe.gov.sg/

9. THINKING SCHOOLS
LEARNING NATION
Singapore Ministry of Education 1997

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

11. 21st Century Competencies Framework
Singapore Ministry of Education 2011

12. what
is singapore
mathematics

13. Singapore Mathematics: Focus on Thinking
an
excellent
vehicle
for the development
&improvement of
a person’s intellectual
competencies
Ministry of Education Singapore 2006

14. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

16. 110 g
180 g 110 g
Bella puts 180 g brown sugar on the dish.
290 g

17. on an identical dish
110 g
2 units = 180 g
1 unit = 90 g
180 g 110 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
290 g

18. Singapore Mathematics
focuses on the ability to
visualize. For example,
bar models are used
extensively.
Bar models were introduced to overcome the
pervasive problems students had with word problems
– even the basic ones.

19. Such word problems are used to
help students
 Deal with information
 Handle and clarify ambiguity –
one dish or two
 Develop visualization – bar
models are used extensively
 Practice mental strategies –
numbers used are not difficult to
compute

20. Singapore Math
Visualization

22. C H E R Y L

23. C H E R Y L
1

24. C H E R Y L
2

25. C H E R Y L
3

26. C H E R Y L
4

27. C H E R Y L
5

28. C H E R Y L
6

29. C H E R Y L
7

30. C H E R Y L
8

31. C H E R Y L
9

32. C H E R Y L

33. C H E R Y L

34. C H E R Y L

35. C H E R Y L

36. C H E R Y L

37. C H E R Y L
Which letter is 99?

39. Method 1
The positions of 11, 22, 33 are at C, H, E respectively.
Positions of multiples of 11 can be located.
Method 4
The position
for 99 can be
found by
writing out all
the numbers
Method 3 but this is not
Numbers ending with 9 efficient
are at E. So, 99 is at E method.
Method 2 too.
The positions of numbers ending with 1 and 6 can
be located ta either ends. Thus 91 or 96 can be
located. Subsequently, 99 can be located.

40. D A V I D

42. Method 1
The letters under A and I are
even. So 99 cannot be there.
Method 2
The positions of numbers ending
with 9 form a diagonal pattern.
Method 3
The numbers under first D
increases by 8. Thus 17 + 80 = 97
is under first D. The position for
99 can be worked out.
Method 4
The positions of multiples of 8 I is
definitely under A. 8 x 12 = 96 is
under A. The position of 99 can
be worked out.
Method 5
Numbers under V is 1 less than
multiples of 4. So, 2011 (1 less
than 2012) is under V. 99 is less
than 100.

43. Method 2
The positions of numbers ending with 9
form a diagonal pattern.
The methods were the ones that
participants in Chile came up with.

44. Another Method
In a course done in December 2010 with a group of
Chilean teachers, there was a method that involves
division. For Cheryl, it was 99 : 10.
For David, it was 99 : 8. Are you able to figure out that
method?

45. We did this version in Big Island of Hawai’i.
Singapore Math at Kamehameha Schools, Hawai’i USA
Kamehameha Schools, Hawaii

46. Singapore Math
Patterns & Generalization

47. Singapore Mathematics: Focus on Problem Solving

48. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

54. CPA Approach based on
Jerome Bruner was used
to learn division of
fractions – using paper
folding and subsequent
drawing.

56. Singapore Mathematics: Focus on Conceptual Understanding

57. Singapore Math at Kamehameha Schools, Hawai’i USA
Kamehameha Schools, Hawaii

58. Singapore Math at Kamehameha Schools, Hawai’i USA
Kamehameha Schools, Hawaii

60. Singapore Math
Learn New Concept Through
Problem Solving

61. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

65. Singapore Math at Kamehameha Schools, Hawai’i USA
Kamehameha Schools, Hawaii

66. Singapore Math
Drill-and-Practice Through
Problem Solving

67. Singapore Math
Problem Solving Lesson
Anchorvale Primary School,

68. FUNDAMENTALS
of singapore
math
Further Examples
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

76. Singapore Math
Applying Knowledge in
Problem Solving

78. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

79. Learning Theories

85. How many 4s are there in 12? 12 ÷ 4 = 3

87. Marcus gave ¼ of his coin collection to his
sister and ½ of the remainder to his
brother.
As a result, Marcus had 18 coins.
Find the number of coins in his collection
at first.
3 units = 18
8 units = ???
Marcus had 48 coins at first.