map101 hilo, hawai'i
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Dr Yeap Ban Haryeapbanhar@gmail.com
Marshall Cavendish Institute Singapore
Presentation slides are available at www.banhar.blogspot.com
Professional DevelopmentSingapore Mathematics
Big Island of Hawai’i 5 – 9 June 2012
www.mcinstitute.com.sgwww.facebook.com/MCISingapore
Day 1
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
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General Overview of Singapore and its Education System
Land 700 sq km
People 4.7 million
General Overview of Singapore and its Education System
GDP per capita in current U.S. dollars
1965 $510 2010 $43 300
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 educationsystem. The data excludes post-secondary education system which includes institutesof technical education, polytechnics and universities.
Canossa Convent Primary School
Singapore
Universities
Polytechnics
Junior Colleges
Integrated Programmes
National Examination
Secondary Schools
National Examination
Institutes of Technical Education
Primary Schools
National Examination
A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest
http://www.moe.gov.sg/education/education-statistics-digest/
Singapore Ministry of Education 1997
THINKING SCHOOLS
LEARNING NATION
Singapore Ministry of Education 2006
“Mathematics is an excellent vehicle for the development
and improvement of a person’s intellectual competencies”
21st Century Competencies FrameworkSingapore Ministry of Education 2011
is singaporewhat
mathematics
Singapore Mathematics: Focus on Thinking
excellentvehicle
an
for the development&improvement ofa person’s intellectual
competenciesMinistry of Education Singapore 2006
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Ma
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110 g
290 g
110 g180 g
Bella puts 180 g brown sugar on the dish.
110 g
290 g
110 g180 g
2 units = 180 g
1 unit = 90 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
on an identical dish
Singapore Mathematicsfocuses on the ability tovisualize. For example,bar models are usedextensively.
Bar models were introduced to overcome thepervasive problems students had with word problems– even the basic ones.
Such word problems are used to
help students
Deal with information
Handle and clarify ambiguity –
one dish or two
Develop visualization – bar
models are used extensively
Practice mental strategies –
numbers used are not difficult to
compute
Singapore Math
Visualization
C H E R Y L
C H E R Y L1
C H E R Y L2
C H E R Y L3
C H E R Y L4
C H E R Y L5
C H E R Y L6
C H E R Y L7
C H E R Y L8
C H E R Y L9
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
Which letter is 99?
Method 1The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.
Method 2The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.
Method 3Numbers ending with 9 are at E. So, 99 is at E too.
Method 4The position for 99 can be found by writing out all the numbers but this is not efficient method.
D A V I D
Method 1The letters under A and I are even. So 99 cannot be there.
Method 2The positions of numbers ending with 9 form a diagonal pattern.
Method 3The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.
Method 4The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out.
Method 5Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.
Method 2The positions of numbers ending with 9 form a diagonal pattern.
The methods were the ones that participants in Chile came up with.
Another MethodIn a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 : 10.
For David, it was 99 : 8. Are you able to figure out that method?
We did this version in Big Island of Hawai’i.
Kamehameha Schools, Hawaii
Singapore Math at Kamehameha Schools, Hawai’i USA
Singapore Math
Patterns & Generalization
Singapore Mathematics: Focus on Problem Solving
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Ma
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CPA Approach based onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.
Singapore Mathematics: Focus on Conceptual Understanding
Kamehameha Schools, Hawaii
Singapore Math at Kamehameha Schools, Hawai’i USA
Kamehameha Schools, Hawaii
Singapore Math at Kamehameha Schools, Hawai’i USA
Singapore Math
Learn New Concept Through
Problem Solving
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
Ma
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Kamehameha Schools, Hawaii
Singapore Math at Kamehameha Schools, Hawai’i USA
Singapore Math
Drill-and-Practice Through
Problem Solving
Singapore Math
Problem Solving Lesson
Anchorvale Primary School,
Singapore
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
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Further Examples
Singapore Math
Applying Knowledge in
Problem Solving
FUNDAMENTALS
of singapore
m a t h
Slides are available at
www.banhar.blogspot.com
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Learning Theories
How many 4s are there in 12? 12 ÷ 4 = 3
Marcus gave ¼ of his coin collection to his
sister and ½ of the remainder to his
brother.
As a result, Marcus had 18 coins.
Find the number of coins in his collection
at first.
3 units = 18
8 units = ???
Marcus had 48 coins at first.
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