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Seminar on Mathematics Learning
Yeap Ban Har
Marshall Cavendish Institute
Singapore

yeapbanhar@gmail.com
Slides are available at

www.banhar.blogspot.com
Singapore
 Land
 270 sq miles
 700 sq km

introduction

 People
 5.3 million
 GDP per capita
 1965 USD500
 2011 USD50 000

Junyuan Secondary School, Singapore

in current USD
High achievement was
not a given. In 1960, among the
30,615 candidates who sat for the first
Primary School Leaving Examination, 45%
of the candidates passed.
Today, about the
same proportion
achieve
the
highest grade in
each of the four
subjects tested.

Keon Ming Public School, Singapore
Southeast Asian nations did not
do well …
Score

1960-1970s

500

Japan

Japan
Korea
Hong Kong

400

Thailand

1990s
2000s
… in science,
Japan
Japan
Korea
Korea
mathematics
Singapore
Hong Kong
Hong Kong
Singapore
and literacy.
Malaysia
Malaysia

1980s

Singapore
Thailand
The Philippines

300

Thailand

Thailand

Indonesia
Indonesia
The Philippines The Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
1982
Introduction of Singapore mathematics
textbooks as they are known today.
1992
Introduction of ProblemSolving Curriculum
1997
Thinking Schools
Learning Nation

Mathematics is “an excellent
vehicle for the development and
improvement of a person’s
intellectual competence”.
Ministry of Education Singapore 2006
We started off badly but we
have managed to help our
students in learning math.
By 1990’s, Singapore has
buckled the trend …
Score

1960-1970s

1980s

1990s

2000s

500

Japan

Japan
Korea
Hong Kong

Japan
Korea
Hong Kong
Singapore

Japan
Korea
Hong Kong
Singapore

400

Thailand

Singapore
Thailand
The Philippines

Malaysia
Thailand

Malaysia
Thailand

300

Indonesia
Indonesia
The Philippines The 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.
Score

1960-1970s

1980s

1990s

2000s

500

Japan

Japan
Korea
Hong Kong

Japan
Korea
Singapore
Hong Kong

Japan
Korea
Hong Kong
Singapore

400

Thailand

Singapore
Thailand
The Philippines

Malaysia
Thailand

Malaysia
Thailand

300

Indonesia
Indonesia
The Philippines The Philippines

Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
Attitude

Achievement

Singapore

71

41

Hong Kong

67

40

Taiwan

50

24

Japan

62

23

Kazakhstan

89

19

England

62

16

Russia

80

16

International

72

5

TIMSS

Grade 4

Boston College
Attitude

Achievement

Taiwan

37

45

S Korea

33

40

Singapore

60

40

Hong Kong

47

31

Japan

30

26

Hungary

30

10

England

40

8

International

54

2

TIMSS

Grade 8

Boston College
Mean

PISA
OECD

600

Singapore

562

Hong Kong

15 year-olds

Shanghai

555

S Korea

546

Taiwan

543

Finland

541

Liechtenstein

536

International

496
Singapore Math focuses on
the use of visuals and initial
concrete experiences..
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
Let the piece of paper
represents a cake.

3 fourths  3 =

3
1
3 
4
4

Archipel Basisschool Tweemaster-Kameleon, The Netherlands
3
6
2  2
4
8
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
Let the piece of paper
represents a cake.

3 fourths  2 =

3
6
3
2  2 
4
8
8
Let the piece of paper
represents a cake.

3 fourths  2 =

3
1 3
2  
4
2 4
Let the piece of paper
represents a cake.

3 fourths  2 =

3
1 3 3
2   
4
2 4 8
Let the piece of paper
represents a cake.

3 fourths  2 =
2 fourths  2 =
1 fourths  2 =

3
1 1 3
2   
4
4 8 8
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
3
5

A number (x) is
of a second number (y).
The sum of the two numbers (x and y) is 120.

King Solomon Academy, London UK
3
5

A number is
of a second number.
The sum of the two numbers is 120.

120
80
8 units = 120
1 units = 120  8
1 units = 15
One of the numbers is 3 x 15 = 45.
The greater number is 5 x 15 = 75.

40
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.

Edgewood Elementary School, New York
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Box C

Box A

Box B

20

116
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Box C

x

Box A

x

Box B

x

116

20

x
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Box C

Box A

24

116 – 20 = 116 – 16 – 4 = 96

20

4 units = 96
4 units = 80 + 16

24

1 units = 96  4 =
Box B

24

24

Box A ….
Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.

x + 20 + x + 2x = 116
4x + 20 = 116
4x = 116 – 20 = 96

Box C

x

Box A

x

Box A …
Box B …
Box C …

x

Box B

x = 96  4 = 24

20

x
The Blake School's Seminar for Parents

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The Blake School's Seminar for Parents

  • 1. Seminar on Mathematics Learning Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 2.
  • 4.  Land  270 sq miles  700 sq km introduction  People  5.3 million  GDP per capita  1965 USD500  2011 USD50 000 Junyuan Secondary School, Singapore in current USD
  • 5. High achievement was not a given. In 1960, among the 30,615 candidates who sat for the first Primary School Leaving Examination, 45% of the candidates passed. Today, about the same proportion achieve the highest grade in each of the four subjects tested. Keon Ming Public School, Singapore
  • 6. Southeast Asian nations did not do well … Score 1960-1970s 500 Japan Japan Korea Hong Kong 400 Thailand 1990s 2000s … in science, Japan Japan Korea Korea mathematics Singapore Hong Kong Hong Kong Singapore and literacy. Malaysia Malaysia 1980s Singapore Thailand The Philippines 300 Thailand Thailand Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12. 1982 Introduction of Singapore mathematics textbooks as they are known today. 1992 Introduction of ProblemSolving Curriculum 1997 Thinking Schools Learning Nation Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”. Ministry of Education Singapore 2006
  • 13. We started off badly but we have managed to help our students in learning math.
  • 14. By 1990’s, Singapore has buckled the trend … Score 1960-1970s 1980s 1990s 2000s 500 Japan Japan Korea Hong Kong Japan Korea Hong Kong Singapore Japan Korea Hong Kong Singapore 400 Thailand Singapore Thailand The Philippines Malaysia Thailand Malaysia Thailand 300 Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  • 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 Japan Korea Hong Kong Japan Korea Singapore Hong Kong Japan Korea Hong Kong Singapore 400 Thailand Singapore Thailand The Philippines Malaysia Thailand Malaysia Thailand 300 Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  • 18. Mean PISA OECD 600 Singapore 562 Hong Kong 15 year-olds Shanghai 555 S Korea 546 Taiwan 543 Finland 541 Liechtenstein 536 International 496
  • 19.
  • 20. Singapore Math focuses on the use of visuals and initial concrete experiences..
  • 22. Let the piece of paper represents a cake. 3 fourths  3 = 3 1 3  4 4 Archipel Basisschool Tweemaster-Kameleon, The Netherlands
  • 23. 3 6 2  2 4 8 Archipel Basisschool Tweemaster-Kameleon, The Netherlands
  • 24. Let the piece of paper represents a cake. 3 fourths  2 = 3 6 3 2  2  4 8 8
  • 25. Let the piece of paper represents a cake. 3 fourths  2 = 3 1 3 2   4 2 4
  • 26. Let the piece of paper represents a cake. 3 fourths  2 = 3 1 3 3 2    4 2 4 8
  • 27. Let the piece of paper represents a cake. 3 fourths  2 = 2 fourths  2 = 1 fourths  2 = 3 1 1 3 2    4 4 8 8
  • 29.
  • 30. 3 5 A number (x) is of a second number (y). The sum of the two numbers (x and y) is 120. King Solomon Academy, London UK
  • 31. 3 5 A number is of a second number. The sum of the two numbers is 120. 120 80 8 units = 120 1 units = 120  8 1 units = 15 One of the numbers is 3 x 15 = 45. The greater number is 5 x 15 = 75. 40
  • 32. Box B contains twice as many books as Box A. Box C contains 20 more books than Box A. Together, the three boxes contains 116 books. Edgewood Elementary School, New York
  • 33. Box B contains twice as many books as Box A. Box C contains 20 more books than Box A. Together, the three boxes contains 116 books. Box C Box A Box B 20 116
  • 34. Box B contains twice as many books as Box A. Box C contains 20 more books than Box A. Together, the three boxes contains 116 books. Box C x Box A x Box B x 116 20 x
  • 35. Box B contains twice as many books as Box A. Box C contains 20 more books than Box A. Together, the three boxes contains 116 books. Box C Box A 24 116 – 20 = 116 – 16 – 4 = 96 20 4 units = 96 4 units = 80 + 16 24 1 units = 96  4 = Box B 24 24 Box A ….
  • 36. Box B contains twice as many books as Box A. Box C contains 20 more books than Box A. Together, the three boxes contains 116 books. x + 20 + x + 2x = 116 4x + 20 = 116 4x = 116 – 20 = 96 Box C x Box A x Box A … Box B … Box C … x Box B x = 96  4 = 24 20 x