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This seminar is for parents at The Blake School in Minneapolis.
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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
People 5.3 million
GDP per capita 1965 USD500
2011 USD50 000 in current USD
Junyuan Secondary School, Singapore
introduction
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.
Keon Ming Public School, Singapore
Today, about the
same proportion
achieve the
highest grade in
each of the four
subjects tested.
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 The Philippines
Indonesia The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
Southeast Asian nations did not
do well … … in science,
mathematics
and literacy.
1992 Introduction of Problem-
Solving Curriculum
1997 Thinking Schools Learning Nation
1982 Introduction of Singapore mathematics
textbooks as they are known today.
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.
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 The Philippines
Indonesia The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
By 1990’s, Singapore has
buckled the trend …
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 The Philippines
Indonesia 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.
Singapore
Taiwan
Japan
Hong Kong
Att
itu
de
Ac
hie
ve
me
nt
71 41
67 40
50 24
62 23
Gra
de
4
Kazakhstan
Russia
International
England
89 19
62 16
80 16
72 5
TIMSS Boston College
Taiwan
Singapore
Hong Kong
S Korea
Att
itu
de
Ac
hie
ve
me
nt
37 45
33 40
60 40
47 31
Gra
de
8
Japan
England
International
Hungary
30 26
30 10
40 8
54 2
TIMSS Boston College
Shanghai
Hong Kong
S Korea
Singapore
Me
an
600
562
555
546
15
ye
ar-
old
s
Taiwan
Liechtenstein
International
Finland
543
541
536
496
PISA OECD
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 =
4
13
4
3
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
28
62
4
3
Let the piece of paper
represents a cake.
3 fourths 2 =
8
32
8
62
4
3
Let the piece of paper
represents a cake.
3 fourths 2 =
4
3
2
12
4
3
Let the piece of paper
represents a cake.
3 fourths 2 =
8
3
4
3
2
12
4
3
Let the piece of paper
represents a cake.
3 fourths 2 =
8
3
8
1
4
12
4
3
2 fourths 2 =
1 fourths 2 =
Archipel Basisschool Tweemaster-Kameleon, The Netherlands
King Solomon Academy, London UK
A number (x) is of a second number (y).
The sum of the two numbers (x and y) is 120. 5
3
A number is of a second number.
The sum of the two numbers is 120. 5
3
8 units = 120
1 units = 120 8
1 units = 15
120
80 40
One of the numbers is 3 x 15 = 45.
The greater number is 5 x 15 = 75.
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 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.
20 Box C
Box A
Box B
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.
x
x x
x 20 Box C
Box A
Box B
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.
20 Box C
Box A
Box B
116 – 20 = 116 – 16 – 4 = 96
4 units = 96
4 units = 80 + 16
1 units = 96 4 =
24
24 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
x x
x 20 Box C
Box A
Box B
x + 20 + x + 2x = 116
4x + 20 = 116
4x = 116 – 20 = 96
x = 96 4 = 24
Box A …
Box B …
Box C …
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