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This course was for about 80 teachers in the island of Maui in Hawaii, USA.
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MAP101 Fundamentals of Singapore Math M a u i , H a w a i i
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
General Overview of Singapore and its
Education System
General Overview of Singapore and its
Education System
Students 500 000
Teachers 30 000
Principals & Vice-Principals 900
Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
Canossa Convent Primary School, Singapore
High achievement was not a given. In 1960,
among 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)
All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table.
1992 Introduction of Problem-
Solving Curriculum
1997 Thinking Schools Learning Nation
1982 Introduction of Singapore mathematics
textbooks as they are known today. 2001 Introduction of textbooks published by
private publishers and approved by Ministry of Education.
2007 New 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
Page 1
2013 New editions of textbooks are
published with the revision of the curriculum.
Page 4
The brown sugar problem
demonstrates the importance of
visualization.
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 g Bella puts 270 g sugar on the dish.
Professional Development in London, UK
Escuela de Guetamala, Chile
x + 2x = 12
Fundamentals of Singapore Math Initial Concrete Experiences & Building Conceptual Understanding
Yeap Ban Har
Marshall Cavendish Institute Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
Relational Understanding
R Skemp
Concrete Introduction J Bruner
Junyuan Secondary School, Singapore
what & how
Page 08
Page 13
Page 5
3 fourths 4 = 12 sixteenths 4 = 3 sixteenths
3 fourths 4 = 1
4×
3
4
Share 3 fourths equally among 3.
3 fourths 3 = 1 fourth
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
Fundamentals of Singapore Math Emphasis on Number Sense & Visualization
Yeap Ban Har Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
Student in The Philippines doing long division using number bonds.
Students’ work from Maui, Hawaii
King Solomon Academy, London
King Solomon Academy, London
King Solomon Academy, London
Globe Academy, London
Globe Academy, London
Globe Academy, London
Allfarthing Primary School, London
Teaching Multiplication Facts
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.
Primary Mathematics (Third Edition)
Visuals are used to teach
concepts – distributive
property of multiplication
– without using formal
terms.
Primary Mathematics (Third Edition)
emphasis visualization
Math in Focus
Math in Focus
Math in Focus
Math in Focus
Math in Focus
Da Qiao Primary School, Singapore
Page 15
3 units = 18 1 units = 18 3 = 6
6 x 8 = 48 There were 48 coins at first.
If can learn our students must
too.
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