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Yeap Ban Har made three presentations on Day 2 of the symposium.
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Experiencing Singapore MathInitial Concrete Experiences & Building Conceptual Understanding
Yeap Ban HarMarshall Cavendish Institute
Singapore
Slides are available atwww.banhar.blogspot.com
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Land 270 sq miles
People 4.7 million
GDP per capita 1965 USD510 2010 USD43,300
in current USD
Junyuan Secondary School, Singapore
introduction
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Score 1960-1970s 1980s 1990s 2000s
500 Japan JapanKorea
Hong Kong
JapanKorea
SingaporeHong Kong
JapanKorea
Hong KongSingapore
400 Thailand SingaporeThailand
The Philippines
MalaysiaThailand
MalaysiaThailand
300 IndonesiaThe Philippines
IndonesiaThe 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.
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1992Introduction of Problem-
Solving Curriculum
1997Thinking SchoolsLearning Nation
1982Introduction of Singapore mathematics
textbooks as they are known today.
2001Introduction of textbooks published by
private publishers and approved by Ministry of Education.
2007New editions of textbooks are
published with the introduction of the revised curriculum.
Mathematics is “an excellent vehicle for the
development and improvement of a person’s intellectual competence”.
Ministry of Education Singapore 2006
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Conceptual Understanding R Skemp
Concrete Introduction J Bruner
Junyuan Secondary School, Singapore
what & how
Page 08Page 13
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3 fourths 4 = 12 sixteenths 4 = 3 sixteenths 4
3 fourths 4 =
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Share 3 fourths equally among 3.
3 fourths 3 = 1 fourth
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Share 3 fourths equally between 2.
3 fourths 2 = 6 eighths 2= 3 eighths
Share 3 fourths equally among 4.
3 fourths 4 = 12 sixteenths 4= 3 sixteenths
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12 cookies 4
12 pieces 4
12 sixteenths 4
12 tenths 4
12 x 4
12 cookies 4 cookies
12 pieces 4 pieces
12 x 4 x
34
÷1434
÷12
Page 13
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Lim Siong GuanHead, Civil Service
Singapore
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King Solomon Academy, London
King Solomon Academy, London
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King Solomon Academy, London
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Globe Academy, London
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Globe Academy, London
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Globe Academy, London
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Concrete to Visual J Bruner
Variation Z Dienes
Human Intelligences H Gardner
Junyuan Secondary School, Singapore
visualization
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Math in Focus
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Da Qiao Primary School, Singapore
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See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey.See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on Higher-Order Thinking Skills. Paper presented at International Conference on School Mathematics Textbooks Shanghai, China.
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Primary Mathematics (Third Edition)
Visuals are used to teach concepts – distributive property of multiplication – without using formal terms.
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Primary Mathematics (Third Edition)
emphasis variation
tens ones
Page 12
emphasis spiral
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emphasis visualization
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3 units = 181 units = 18 3 = 6
6 x 8 = 48There were 48 coins at first.
110 g
290 g Page 2
110 g
??
2 units = 290 g – 110 g = 180 g
1 units = 180 g 2 = 90 g
3 x 90 g = 270 gBella puts 270 g sugar on the dish.
Escuela de Guetamala, Chile
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x + 2x = 12
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Globe Academy, London
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Edgewood Elementary School, New York
emphasis visualization
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Junyuan Secondary School, Singapore
conclusion
B A N H A R
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Problem 2
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Problem 2
B A N H A R
Which letter is counted 99?
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Problem 2
B A N H A R1 2 3 4 5 6
11 10 9 8 7
12 13 14 15 16
21 20 19 18 17
22 23 24 25 26
31 30 29 28 27
32 33 34 35 36
Which letter in your name is counted 99?
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Problem 2
Number of Letters Which Letter?
6
3
7
5
4
8
3rd
3rd
3rd
3rd
3rd
1st
Which letter in your name is counted 99?
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Globe Academy, London
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3x – 2 = 8
Globe Academy, London
