Singapore Math Administrators Symposium Scottsdale

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Experiencing Singapore MathInitial Concrete Experiences & Building Conceptual Understanding

Yeap Ban HarMarshall Cavendish Institute

Singapore

yeapbanhar@gmail.com

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

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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

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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

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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

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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