map202a teaching of fractions 1
DESCRIPTION
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.TRANSCRIPT
F R A CT I O N in singapore
m a t hDr Yeap Ban Har
Marshall Cavendish Institute Singapore
[email protected] 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
[email protected] 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.