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The Masterclass on Fundamentals of Singapore Math was well attended by close to 150 educators.
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Welkom Master Class
Singapore Math
Dr.Yeap Ban Har Marshall Cavendish Institute
2011alt/ HCO R MAP101 Fundamentals in SingaporeMathematics
Dr Yeap Ban [email protected]
Marshall Cavendish Institute Singapore
Presentation slides are available at www.banhar.blogspot.com
MasterclassSingapore RekenenRotterdam Utrecht
is singaporewhat
mathematics
Singapore Mathematics: Focus on Thinking
excellentvehicle
an
for the development&improvement ofa person’s intellectual
competenciesMinistry of Education Singapore 2006
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.
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?
Singapore Math
Patterns & Generalization
Singapore Mathematics: Focus on Problem Solving
CPA Approach based onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.
Singapore Math
Learn New Concept Through
Problem Solving
Singapore Math
Drill-and-Practice Through
Problem Solving
Singapore Math
Applying Knowledge in
Problem Solving
Learning Theories
How many 4s are there in 12? 12 ÷ 4 = 3