nctm2011 morning session
DESCRIPTION
This was presented at the NCTM Annual Meeting and Exposition. It provides participants with features of math program that make mathematics accessible to average and struggling learners.TRANSCRIPT
Making Mathematics
Accessible The Singapore Method
Dr Yeap Ban HarMarshall Cavendish Institute
Singapore
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.