1. BollesM4thodology
openingsession| jacksonville, florida |19 June 2013
Yeap Ban Har
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
constructivist approach problem solving computational fluency theoretical underpinnings
differentiated instruction number sense assessment small group work multiple
strategies journal writing multiple intelligences lesson structure common core state standards
scope and sequence pacing anchor task conceptual understanding homework workbook
textbook questioning technique |role of mathematics

2. introduction |

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

4. 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
96
97
97
95
87
96
92
88
75
613
611
609
586
570
539
516
514
509
507
500
advanced
high
intermediate
low
average
gradeeightmathematics

5. | Hanusek, Jamison, Jamison & Woessmann 2008

6. | Hanusek, Jamison, Jamison & Woessmann 2008
Score 1960-1970s 1980s 1990s 2000s
500’s Japan Hong Kong
Japan
Korea
Hong Kong
Japan
Korea
Singapore
Hong Kong
Japan
Korea
Singapore
400’s Thailand Philippines
Singapore
Thailand
Malaysia
Thailand
Malaysia
Thailand
300’s Indonesia
Philippines
Indonesia
Philippines

7. “Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “
singapore math
a response to low student
achievement and dismal economic
performance

8. focus on conceptual
understanding |

9. 51 ÷ 3

10. 51 ÷ 3
30 21
= 17

11. 3|51
30
21
21
0
17

12. Conceptual or Relational Understanding refers to
knowing how ideas are related … how number
bonds are connected to dividing
Skemp – instrumental and relational understanding

13. 









2 x 7

14. 









14 + 7

15. 









14 + 14

16. 










14 + 35

17. 









70

18. 









70 - 7

19. Mathematics is “an excellent vehicle for
the development and improvement of a
person’s intellectual competence”.
|Ministry of Education, Singapore (2006)
thinkingschool
learningnations

21. focus on concrete and
pictorial representations|

23. CPA Approach is fundamental to Singapore Math
Bruner – enactive, iconic and symbolic representations
Dienes – construction principle

24. In the 1970’s, Singapore needed a way to help
students, most of whom were not performing
well in mathematics, learn mathematics.
CPA Approach based on Bruner’s work and a
host of other learning theories were used to
help students learn. Today, many people refer
to this approach as Singapore Math.