1. Day 5 | June 2014
Singapore
Mathematics Institute
with Dr. Yeap Ban Har
coursebook
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Contact Information
yeapbanhar@gmail.com
www.banhar.blogspot.com
about yeap ban har
Dr Yeap Ban Har spent ten years at Singapore's National Institute
of Education training pre-service and in-service teachers and
graduate students. Ban Har has authored dozens of textbooks,
math readers and assorted titles for teachers. He has been a
keynote speaker at international conferences, and is currently
the Principal of a professional development institute for
teachers based in Singapore. He is also Director of Curriculum
and Professional Development at Pathlight School, a primary
and secondary school in Singapore for students with autism. In
the last month, he was a keynote speaker at World Bank’s READ
Conference in St Petersburg, Russia where policy makers from
eight countries met to discuss classroom assessment. He was
also a visiting professor at Khon Kaen University, Thailand. He
was also in Brunei to work with the Ministry of Education Brunei
on a long-term project to provide comprehensive professional
development for all teachers in the country.
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introduction
The Singapore approach to teaching and learning mathematics was the result of
trying to find a way to help Singapore students who were mostly not performing
well in the 1970’s.
The CPA Approach as well as the Spiral Approach are fundamental to teaching
mathematics in Singapore schools. The national standards, called syllabus in
Singapore, is designed based on Bruner’s idea of spiral curriculum. Textbooks are
written based on and teachers are trained to use the CPA Approach, based on
Bruner’s ideas of representations.
“A curriculum as it develops should revisit this basic ideas repeatedly,
building upon them until the student has grasped the full formal
apparatus that goes with them”.
| Bruner 1960
“I was struck by the fact that successful efforts to teach highly structured bodies
of knowledge like mathematics, physical sciences, and even the field of history
often took the form of metaphoric spiral in which at some simple level a set of
ideas or operations were introduced in a rather intuitive way and, once
mastered in that spirit, were then revisited and reconstrued in a more
formal or operational way, then being connected with other knowledge, the
mastery at this stage then being carried one step higher to a new level of formal
or operational rigour and to a broader level of abstraction and
comprehensiveness. The end stage of this process was eventual mastery of the
connexity and structure of a large body of knowledge.”
| Bruner 1975
Bruner's constructivist theory suggests it is effective when faced with new material
to follow a progression from enactive to iconic to symbolic representation;
this holds true even for adult learners.
| Bruner 1966
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Fractions, Fractions, Fractions!
an in-depth study of the teaching of fractions
Two Fundamentals |Session 1
Idea of ‘Nouns’
Idea of Equal Parts
Case Study 1 |
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Show 2 equal parts.
What do you mean by equal parts?
Show 4 equal parts.
In lesson study, we might discuss why use squares. Why not circles? Why not
rectangles?
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Case Study 2 |
5
2
5
1
5
1
5
3
Equivalent Fractions |Session 2
Case Study 3 |
8
?
4
1
?
9
4
3
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A cake is cut into 6 equal slices.
Aaron and Ben share four slices.
Case Study 4 |
What fraction of the rectangle is shaded?
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Open Lesson for Rising Seventh Graders |Session 3
What do we want the students to learn?
Lesson Segment Observation / Question
How can we tell if students are
learning?
What help students who
struggle?
What are for students who
already know what we want
them to learn?
Summary
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Basic Operations |Session 4
Case Study 5 |
Mary has a blue ribbon that is
3
2
1 m long. She has a red ribbon that is
4
3
1 m long.
Source | Primary Mathematics (Standards Edition) 6A
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Case Study 6 |
There are 12 cupcakes left over. Alex takes
4
3
of them home.
How many cupcakes does Alex take?
There are
2
1
3 pies left over. Ali takes
4
3
of them home.
How many pies does Ali take?
Source | Primary Mathematics (Standards Edition) 6A
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Case Study 7 |
The longest side of a triangle is
4
3
2 times as long as the shortest side. The
shortest side is
3
2
in. Find the length of the longest side.
Source | Primary Mathematics (Standards Edition) 6A
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Practice and Problem Solving |Session 5
Instructional Models
o Teaching through Problem Solving
o Teaching for Problem Solving
o Teaching of Problem Solving
Case Study 8 |
A total of 325 boys and girls attended a performance in the school hall.
5
4
of the
boys and
4
3
of the girls left the hall after the performance ended. There were 29
more boys than girls who remained in the hall. How many girls attended the
performace?
Source | Catholic High School (Primary) Primary 6 Examination
