NCTM2011 Morning Session

Making Mathematics Accessible
The Singapore Method
DrYeap Ban Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
Slides are available at www.banhar.blogspot.com

MCI-WSU Singapore Math Summer Institute 6 – 8 July 2011
Comprehensive program taught collaboratively by Singapore mathematics educators and WSU’s professors.

makes abstract concepts accessible to learners who are not yet ready for abstraction
The CPA Approach
Focus on Thinking
builds fundamental intellectual competencies required for learners to handle abstraction

Grade 2
Multiplication
Example
Singapore

Woodlands Primary School, Singapore
Grade 2
Multiplication

Pictorial
to
Symbolic
Concrete to Pictorial
Symbolic
Reference: Primary Mathematics

Reference: Math in Focus

Grade 4
Division of Large Numbers
Example
Philippines

Keys Grade School, Manila, The Philippines

Grade 8
Volume of Pyramid
Example
Indonesia

BinaBangsa School, Semarang, Indonesia

Grade 2
Fractions
Example
Florida

St Edward’s School, Vero Beach, Florida

Initial Concrete Experience
Subsequent Pictorial Representation

Eventual Symbolic Representation

Primary 6
Circumference of Circles
Example
Singapore

Fuchun Primary School, Singapore

Kindergarten
Subtraction
Example
Malaysia

mathz4kidz Learning Centre, Penang, Malaysia
bruner’s theory
concrete

concrete
experiences

from
concrete
to
pictorial
Reference: Earlybird Kindergarten Mathematics

from
pictorial
to
abstract
Reference: All Kids Are Intelligent Series

symbols

Primary 1
Division
Example
Singapore

Reference: My Pals Are Here! Maths

Reference: Primary Mathematics (Standards Edition)

Scarsdale Middle School, New York

Primary 5
Multiplication of Fractions
Example
Singapore

Da Qiao Primary School, Singapore

Allan spent ¼ of his allowance on a gift and ¼ of the remainder on a book. The book cost $18. Find the amount of Allan’s allowance.
Allan’s allowance = 4 x $24 = $96
$72 ÷ 3 = $24
4 x $18 = $72

Student’s Initial Solution
Student’s Alternate Solution

The Curriculum (Ministry of Education 2006)

makes abstract concepts accessible to learners who are not yet ready for abstraction
The CPA Approach
Focus on Thinking
builds fundamental intellectual competencies required for learners to handle abstraction

MCI-WSU Singapore Math Summer Institute 6 – 8 July 2011
Comprehensive program taught collaboratively by Singapore mathematics educators and WSU’s professors.

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NCTM2011 Morning Session

by Jimmy Keng on Apr 14, 2011

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NCTM2011 Morning Session — Presentation Transcript