LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

LEAP Educators’ Conference 2011
Developing Thinking
Through High School Mathematics
Yeap Ban Har
Marshall Cavendish Institute
Singapore
banhar@sg.marshallcavendish.com
Presentation is available on www.banhar.blogspot.com

Link to Keynote Lectures
First lecture raised the question: “Why is the achievement level eroded when students progress from elementary to high school?”. The second lecture calls for changing mindset.
This lecture attempts to answer the question and suggest an alternate way of looking at school mathematics.

Introduction
Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence…
Ministry of Education 2006

Problem Solving
National Test

National Test Grade 10 (Secondary 4)
A fly, F, starts at a point with position vector (i + 12j) cm and crawls across the surface with a velocity of (3i + 2j) cm s-1. At the instant the fly starts crawling, a spider, S, at the point with position vector (85i + 5j) cm, sets off across the surface with a velocity of (-5i + kj) cm s-1, where k is a constant. Given that the spider catches the fly, calculate the value of k.

Problem Solving
Textbook

Draw a 4-sided polygon.
Cut it into triangles.
How many triangles can you get?

Example: Algebra
Factoring a quadratic expression.

Algebra Tiles

Example: Algebra
Completing the square.

Example: Algebra
Solve .

Solve .

Example: Coordinate Geometry
Find the distance between two points.

Problem: Find the distance between points A (2, 3) and B (10, 9).
Students working collaboratively on a problem to learn the coordinate geometry topic on distance between points. Traditionally, students were given a formulae to do this. Instead students had to conduct a mini-inquiry to use what they had previously learned.
BinaBangsa School, Indonesia

Every group was able to use their previous learning (Pythagoras Theorem) to solve the main problem.

Later they were also asked to find points where the distance is a whole number.

Example: Circles
Learning definition and making sense of formulae.

Example
To engage pupils in the learning of mathematics.
Fuchun Primary School

Task 1 Find the longest distance between two points on a circle.
Fuchun Primary School, Singapore

Task 2 Measure circumference and diameter of four circles.

Task 3 Draw a circle given that its circumference is 6 metres.

Example: Circles
Learning definition and making sense of formulae.

Area > 2r2

Area < 4r2

2r2 < Area < 4r2

Conclusion
Mathematics is not just for its content but also for the opportunities to develop generic thinking skills.

Example: Trapezium
a
c
b
h
d

Example: Trapezium
a
d
c
b
h
d
a

International Benchmarks

TIMSS 2007 Achievement
Singapore
International
USA
Grade 8
Advanced
40
6
2
High
70
31
15
Intermediate
88
67
46
Low
97
92
55
Photo: Catholic High School (Primary)

TIMSS 2007 Affect
PATM
SVM
SCM
Grade 8
High
60
41
77
Medium
20
34
19
Low
20
25
4
Photo: Catholic High School (Primary)

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LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

by Jimmy Keng on Feb 14, 2011

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LEAP Educators’ Conference 2011, Manila, The Philippines, 11 - 12 February 2011 — Presentation Transcript