nctm2011 morning session

Making Mathematics

Accessible The Singapore Method

Dr Yeap Ban HarMarshall 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.

The CPA ApproachFocus on Thinking

makes abstract concepts accessible to learners who are not yet ready for abstraction

builds fundamental intellectual competencies required for learners to handle abstraction

ExampleSingapore

Grade 2Multiplication

Woodlands Primary School, Singapore

Grade 2Multiplication

Concrete to Pictorial

Pictorialto

Symbolic

Symbolic

Reference: Primary Mathematics

Reference: Math in Focus

Reference: Math in Focus

ExamplePhilippines

Grade 4Division of Large

Numbers

Keys Grade School, Manila, The Philippines

ExampleIndonesia

Grade 8Volume of Pyramid

Bina Bangsa School, Semarang, Indonesia

ExampleFlorida

Grade 2Fractions

St Edward’s School, Vero Beach, Florida

Initial Concrete

Experience

Subsequent Pictorial

Representation

Eventual Symbolic

Representation

ExampleSingapore

Primary 6Circumference

of Circles

Fuchun Primary School, Singapore

Ratio 2.8 3.0 3.1 3.2 3.3 3.5 3.8Frequency 1 3 5 7 18 4 1

Fuchun Primary School, Singapore

ExampleMalaysia

KindergartenSubtraction

bruner’s theoryconcrete

mathz4kidz Learning Centre, Penang, Malaysia

concreteexperiences

mathz4kidz Learning Centre, Penang, Malaysia

pictorialconcreteto

from

Reference: Earlybird Kindergarten Mathematics

abstractpictorialto

from

Reference: All Kids Are Intelligent Series

symbols

mathz4kidz Learning Centre, Penang, Malaysia

ExampleSingapore

Primary 1Division

Reference: My Pals Are Here! Maths

Reference: Primary Mathematics (Standards Edition)

Reference: Primary Mathematics (Standards Edition)

Scarsdale Middle School, New York

ExampleSingapore

Primary 5Multiplication

of Fractions

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.

4 x $18 = $72

$72 ÷ 3 = $24 Allan’s allowance = 4 x $24 = $96

Student’s Initial Solution

Student’s Alternate Solution

The Curriculum (Ministry of Education 2006)

The Curriculum (Ministry of Education 2006)

The Curriculum (Ministry of Education 2006)

The CPA ApproachFocus on Thinking

makes abstract concepts accessible to learners who are not yet ready for abstraction

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.