map202a teaching of fractions 1

F R A CT I O N in singapore

m a t hDr Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.comSlides are available at

www.banhar.blogspot.comHawa

ii

F R A CT I O N in singapore

m a t h

This course is in two parts. Today

we focus on pre-fraction ideas

i.e. ideas learnt in the early

grades which are important in

the learning of fraction as well as

basic concept of fractions. We

will also examine fraction topics

typically taught in lower primary

levels i.e. grades one to three.

Slides are available at

www.banhar.blogspot.comHawa

ii

MAP202 TEACHING OF FRACTIONSreviewing fundamentals of singapore math

F R A CT I O N in singapore

m a t h

Slides are available at

www.banhar.blogspot.comHawa

ii

General Overview of Singapore and its Education System

Land 700 sq km

People 4.7 million

General Overview of Singapore and its Education System

GDP per capita in current U.S. dollars1965 $510 2010 $43 300

General Overview of Singapore and its Education System

Students 500 000

Teachers 30 000

Principals & Vice-Principals 900

Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools

The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.

Canossa Convent Primary School Singapore

Universities

PolytechnicsJunior

Colleges

Integrated Programmes

National Examination

Secondary Schools

National Examination

Institutes of Technical Education

Primary Schools

National Examination

A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest http://www.moe.gov.sg/education/education-statistics-digest/

Singapore Ministry of Education 1997

THINKING SCHOOLSLEARNING NATION

Singapore Ministry of Education 2006

“Mathematics is an excellent vehicle for the development

and improvement of a person’s intellectual competencies”

21st Century Competencies FrameworkSingapore Ministry of Education 2011

F R A CT I O N in singapore

m a t h

Slides are available at

www.banhar.blogspot.comHawa

ii

MAP202 TEACHING OF FRACTIONS

pre-numeracy skills

Pre-Numeracy Skills

Matching

Sorting / Classifying

1

counting same units

Earlybird Kindergarten Mathematics

number bonds

Photo: PCF Telok Blangah Kindergarten

adding same units

tens ones

1 3renaming

1

1

1

1

1

renaming

adding same units

x + 2y 3x

x + 2y 3y

x + 2y 3xy

F R A CT I O N in singapore

m a t hDr Yeap Ban Har

Marshall Cavendish Institute Singapore

yeapbanhar@gmail.comSlides are available at

www.banhar.blogspot.comHawa

ii

BASIC IDEAS OF FRACTIONS

F R A CT I O N the C P Aapproach

F R A CT I O N the C P Aapproach

F R A CT I O N mathematical

variability

F R A CT I O N conceptualapproach

F R A CT I O N teaching for

meaning3 fourths 3

4

St Edward’s School, Florida

St Edward’s School, Florida

Grade 2concrete pictorial abstract

It does not show half. What does it

show then?

It does not show fourth. What does it

show then?

F R A CT I O N opportunities for differentiation

My Pals Are Here! Mathematics (Second Edition)

Initial Concrete

Experience

Subsequent Pictorial

RepresentationMy Pals Are Here! Mathematics (Second Edition)

St Edward School, Florida

Eventual Symbolic

Representation

My Pals Are Here! Mathematics (Second Edition)

Singapore Examination & Assessment BoardPrimary School Leaving Examination

1 fourth

4 eighteenths

+ 8 36

9 36

F R A CT I O N spiralapproach

3 fourths3 pieces3 pencils

3 fifths + 1 fifth

3 fifths + 1 tenth

3 fifths + 9 tenths

3 fifths + 1 half

Primary 2

Primary 3

Primary 4

Primary 5

COMPARING FRACTIONS

EQUIVALENT FRACTIONS

Lim Siong GuanHead, Civil Service

Singapore

We discussed teaching mathematics versus

teaching the ability to learn mathematics and

developing the belief that one can figure things out by oneself.

We discussed visualization and looking for patterns. Also we discussed generic competencies including

metacognition and collaboration.