The Mathematics Education into the 21st Century Project
Universiti Teknologi Malaysia
Proceedings of the Eighth International Conference
Reform, Revolution and Paradigm Shifts in Mathematics Education
Editor
Alan Rogerson
HotelEdenGarden, Johor Bahru, Malaysia
Nov 25th – Dec 1st 2005
Major Sponsors
AUTOGRAPH, RIC PUBLICATIONS & CASIO
All Rights Reserved.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright holder.
The Mathematics Education into the 21st Century Project wishes to thank for their support
Autograph
RIC Publications
CASIO
QED Education Scientific Pte Ltd
Statworks (M) Sdn Bhd
Texas Instruments
VSG Enrichment
Wholemovement
Greygum Software
The Third World Forum
The Hong Kong Institute of Education
ALMA (Teacher Training Centre, Poland)
ISBN Number 83-919465-7-6
Conference Committees
International Program Committee
Chairman
Dr. Alan Rogerson, International Coordinator of the Mathematics in Society Project
Prof Khaled Abuloum, University of Jordan (Jordan).
Professor Roberto Baldino, UNESP (Brazil).
Dr. Andy Begg , Senior Lecturer in Mathematics Education, University of Waikato (New Zealand).
Dr. Donna F. Berlin, Mathematics, Science & Technology Education, OhioStateUniversity (USA)
Prof. Dr. Werner Blum, University of Kassel (Germany).
Professor Ubiratan D'Ambrosio, Emeritus Professor of Mathematics, Campinas/UNICAMP, (Brazil).
Professor Bruno D'Amore, University of Bolgna (Italy).
Professor Dr. Tilak de Alwis, Southeastern Louisiana University (USA)
Prof Dr William Ebeid, Emeritus Professor, Faculty of Education, Ain Shams University (Egypt).
Prof. Omar Hassan El Sheikh, University of Jordan (Jordan).
Professor Paul Ernest, University of Exeter (UK).
Prof. Dr. Gabriele Kaiser, Hamburg University (Germany).
Dr. Madeleine J. Long, Program Director, American Association for the Advancement of Science
Prof Dr Fayez Mina, Faculty of Education, AinShamsUniversity (Egypt).
Prof Nicolina Malara, University of Modena (Italy)
Prof Dr M. Ali M. Nassar, Director of Planning Center, Institute of National Planning (Egypt).
Professor Lionel Pereira Mendoza, Associate Professor, National Institute of Education (Singapore).
Professor Angela Pesci, University of Pavia (Italy)
Prof. Medhat Rahim, LakeheadUniversity, Faculty of Education (Canada).
Professor Filippo Spagnolo, University of Palermo, Sicily, (Italy).
Professor Dr. Alicia Villar Icasuriaga, Instituto de Profesores "Artigas", Montevideo, (Uruguay)
Dr. Arthur L. White, Mathematics, Science, and Technology Education, OhioStateUniversity (USA)
Professor. Wacek Zawadowski, WarsawUniversity (Poland).
Local Organizing Committee
Chairman:
Prof. Dr. Noor Azlan Ahmad Zanzali, Faculty of Education, Universiti Teknologi Malaysia
Associate Prof. Dr. Md. Nor Bakar
Associate Prof. Dr. Zaleha Ismail
Associate Prof. Dr. Mohini Mohamed
Associate Professor Aziz Nordin
Dr. Zaidatun Tasir
Secretariat:
En. Asram Sulaiman @ Saim
Puan Sumi Hj. Isman
En. Bahrim Kasim
Foreword
This volume contains the papers presented at the International Conference on Reform, Revolution and Paradigm Shifts in Mathematics Educationheld from November 25 to December 1st, 2005 at the HotelEdenGarden, Johor Bahru, Malaysia. This Conference was organized jointly by Universiti Teknologi Malaysia andThe Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. Our Project is dedicated to the improvement of mathematics education worldwide through the publication and dissemination of innovative materials and ideas.
The title Reform, Revolution and Paradigm Shifts in Mathematics Education derives from Kuhn's seminal work on "The Structure of Scientific Revolutions" which made popular the concept of "paradigm shift", and the work of Lakatos which revealed the essentially creative and human nature of progress in science and mathematics. We hope these powerful ideas will help to inspire our conference.
The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on the following webpages.
- Malaysia 2005 Conference
- Our Project Home Page
- Egypt Conference site
- Jordan conference site
- Australia conference site
- Sicily Conference site
- Brno Conference site
- Ciechocinek Conference site
Filippo Spagnolo, of PalermoUniversity, is webmaster for the above sites. Felix Rieper has some photos of the Ciechocinek Conference:
Krys Bestry is webmaster for our Polish Superkurs Home Page at (in Polish - but with pictures!) See also: and for more information about our project and its work.
It has been my pleasure to read all of the papers and to edit them for these Proceedings. Not all papers are about research in mathematics education, a number report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and so in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators .
These Proceedings begin with two commissioned papers and otherwise contain contributions mostly in alphabetical order of the Principal Presenters. I sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future. For further information about the work of our Project, please email
Dr. Alan Rogerson
Chaiman of the Programme Committee
Presented Papers
Comparing mathematics education traditions in four European countries: The
case of the teaching of percentages in the primary school
Erik De Corte, Fien Depaepe, Peter Op ’T Eynde & Lieven Verschaffel...... 1
Cultural differences in scholastic and non-scholastic environments: reasoning
patterns and logical-linguistic questions in European and Chinese cultures
Maria Ajello, Filippo Spagnolo, Zhang Xiaogui.....12
Learning with Examples and Students’ Understanding of Integration
Shafia Abdul-Rahman.....24
Share the Experience! Problem-Solving is No Longer a Problem.
Fadia Abou Najem .....29
Teachers’ competency in the teaching of mathematics in English in Malaysian
secondary schools
Hamidah Ab Rahman, Aziz Nordin, Mukheta Isa, Fatimah Puteh, et al. .....31
Students Problem Solving Processes in LOGO Programming Environment Pengaturcaran LOGO
Suguna Appalanayudu, Zaleha Ismail.....37
Dynamic Worksheets – a Tool for Individual and Cooperative Learning
Peter Baptist .....41
Mathematics education in Finland – what makes it work?
Ole Bjorkqvist.....45
Thinking mathematically – making sense and solving problems
George Booker.....49
Enhancement of Teaching Policy by means of Technology
Hennie Boshoff.....54
Curriculum Issues in Statistics Education
Gail Burrill.....59
The mathematics allergy: Is Drama in Education the much-needed antidote?
Carol Carter and Lise Westaway.....65
Emphasis on Problem Solving in Mathematics Textbooks from Two Different
Reform Movements
Jaguthsing Dindyal.....70
Early School Leavers Experiences Of Learning Mathematics: The Discourses
Of Mathematics Classrooms
Bronwyn Ewing.....75
The Two Fundamental Learning Games We Play: A Framework For
Discussion And Reflection
Gary Flewelling.....81
Introducing the Least Squares Regression Principle with Computer Technologies
Patricia A Forster.....87
SEARCHING for control in a post-modern mathematics classroom.
Noel Geoghegan.....92
Dominant Representation In The Understanding Of Basic Integrals Among Post Secondary Students
Munirah Ghazali, Siti Aishah Sheikh Abdullah, Zurida Ismail, Mohd Irwan Idris.....97
The Role of Professional Development Networks in Reforming Mathematics
Education in Egypt
Amal Gouda & Frank Banks...101
Elementary Mathematics Pre-Service Teachers’ Learning from Cases
Marjorie Henningsen...106
Conceptests: Active Learning In Calculus
Deborah Hughes Hallett, Maria Robinson, David Lomen...112
The Mathematics Carnival: A Platform to Appreciate Mathematics
Zaleha Ismail, Mohd Khalid Kasmin & Norma Alias...115
Mathematics textbooks – the link between the intended and the implemented curriculum?
Monica Johansson...119
Inservice and Preservice Teachers’ Attitudes Regarding the Use of Graphing Calculators to Support Inquiry Learning in Mathematics
Iris Johnson...124
Paper Folding Squares
Kwan Shi-pui & Sze Chong-lap...129
Promoting MathematicsTeacher Collaboration through Lesson Study:What Can We Learn from Two Countries’Experience?
Lim Chap Sam, Allan Leslie White & Chiew Chin Mon...135
Recruiting, Educating, and Retaining Teachers of Mathematics
Madeleine J. Long...140
Developing mathematical thinking with the assistance of manipulatives
Linda Marshall & Paul Swan...144
Using Autobiography To Change Preservice Teachers’ Attitudes Towards Mathematics
Keith McNaught...148
Reform, Revolution and Paradigm Shifts in Mathematics Education. Some
Examples and Applicable Strategies
Fayez M. Mina...154
The Use Of Metacognitive Process In Learning Mathematics
Mohini Mohamed & Tan Ten Nai...159
An Evaluative Study to Pre-service Primary Teachers in Mathematics in Egypt
Ayman Moustafa Moustafa ...163
Enriching math teaching by computers
Marjatta Näätänen...169
Innovative and Technology Based Methods of Teaching Statistics Concepts
Mehryar Nooriafshar...172
Teaching Mathematics: Tablet PC Technology adds a new dimension
Werner Olivier...176
New Possibilities in Analysis using the ClassPad300Plus
Ludwig Paditz...182
Identifying mentoring practices for developing effective primary mathematics teaching
Peter Hudson and Robert Peard...189
Math Anxiety in Junior/Intermediate Pre-Service Teachers
Medhat H. Rahim & Matthew Koeslag...194
Making the most of games: Lesson learned from playing Numero
Paul Swan & Linda Marshall....199
Preparing Teachers to Teach Mathematics to Students with Learning Disabilities
Tony Thompson...204
Misconceptions And Difficulties With The Chain Rule
Tangül Uygur & Aynur Özdaş...209
Paradigm Shift in Mathematics Education from 'Traditional’ Learning Method to Modified Climbing Learning Method: Its Applicability and Effectiveness in KenyanSecondary School
Nancy Nui Wambui...214
“Masifunde Nosapho” (“Let us learn with our families”)
Lise Westaway & Carol Carter...218
Workshop Presentations & Short Abstracts
Mathematica© As a Tool For Exploring Mathematics
Mohamad Faisal Abdul Karim...223
Secondary Students Scheme of Composite Functions
Siti Aishah Sh.Abdullah & Fatimah Saleh ...224
Teaching about Islamic Art/Learning Geometry, Teaching Geometry/Learning
about Islamic Art
Carol Bier...224
Using games to develop conceptual understanding in order to analyse problem meanings and devise problem solutions
George Booker...227
Teacher-student cooperation
Josephine Buskes...227
Pure and applied mathematics –what is the driving force in curriculum in different countries – and what about the interaction between pure and applied mathematics?
Liv Sissel Grønmo...227
Doing mathematics is not only solving set problems given by others, but also (and especially) creating new problems and asking good questions
Jean Michel Hanna...228
Wholemovement of Folding Circles
Bradford Hansen-Smith...230
Mathematical Experiences in a Technology Integration Research Study
Mhairi (Vi) Maeers...230
Using An Interactive Whiteboard In The Mathematics Classroom. A workshop for practitioners and educators
Dave Miller and Doug Averis...231
Being Mathematical: New Questions for Old
Yudariah Mohd. Yusof and Roselainy Abdul Rahman...231
Invoking Students’ Use of their Own Powers of Mathematical Thinking Workshop
Yudariah Mohd. Yusof & Roselainy Abdul Rahman....232
An Introduction to Dynamic Programming - The Two Hour Challenge
Mehryar Nooriafshar...232
Stochastics/Simulation and Exploration with the new ClassPad300plus
Ludwig Paditz...233
Autograph is a dynamic software which is effective, efficient and FUN for both teacher and student.
Cecily Peters...236
Visualizing Algebra Using Dynamic Geometry® Software
Steve Rasmussen...236
What Happens When…
Kerry J Thomas...237
Images with maths
Rüdiger Vernay...237
Integrating Constructivist approaches in e-learning to enhance mathematical self-study
Ya Ling Lee...238