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This course is offered in Chile as part of a Certificate in Mathematics Teaching programme. This presentation is for MAP101 Fundamentals of Singapore Mathematics Curriculum. It is a study of the problem solving approach and an emphasis on thinking - visualization, generalization and number sense. Plus learning theories such as Dienes and Bruner.

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Dr Yeap Ban Har banhar.@sg.marshallcavendish.com

Marshall Cavendish Institute Singapore

Day

MAP 101 Fundamentals in Singapore Mathematics Curriculum

Dr Yeap Ban Har banhar.@sg.marshallcavendish.com

Marshall Cavendish Institute Singapore

Singapore Mathematics: Focus on Thinking

excellentvehicleanforthe

development&improvement of

a 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 Mathematics focuses on the ability to visualize. For example, bar models are used extensively.

Singapore MathVisualization

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.

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.

In December 2010, another group of teachers in Chile who did this course also came up with a similar method.

Another MethodIn a course done in December 2010 with another 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 MathPatterns & Generalization

Singapore Mathematics: Focus on Problem Solving

CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.

Singapore MathLearn New Concept Through

Problem Solving

Singapore MathDrill-and-Practice Through

Problem Solving

Singapore MathApplying Knowledge in

Problem Solving

Learning Theories

How many 4s are there in 12? 12 ÷ 4 = 3

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