**The Mathematics Education into the 21 ^{st}
Century Project**

** **

**Universiti Teknologi **

Reform, Revolution and Paradigm Shifts in Mathematics Education

**Editor**

**Alan Rogerson**

**Hotel**** Eden Garden, **

**Nov 25th – Dec 1 ^{st} 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 21 ^{st}
Century Project wishes to thank for their support**

**Autograph**

**RIC
Publications**

CASIO

**Statworks
(M) Sdn Bhd**

**Texas**** Instruments**

**VSG
Enrichment**

**Wholemovement**

**Greygum
Software**

**The
Third World Forum**

**The
Hong Kong Institute of Education**

**ALMA
(Teacher Training **

*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,

Professor Roberto Baldino, UNESP (Brazil).

Dr. Andy Begg , Senior Lecturer in Mathematics Education,

Dr. Donna F. Berlin, Mathematics, Science & Technology Education,

Prof. Dr. Werner Blum,

Professor Ubiratan D'Ambrosio, Emeritus Professor of Mathematics,
Campinas/UNICAMP, (

Professor Bruno D'Amore,

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,

Professor Paul Ernest,

Prof. Dr.

Dr. Madeleine J. Long, Program
Director, American Association for the Advancement of Science

Prof Dr Fayez Mina, Faculty of Education,

Prof Nicolina Malara, University of Modena (Italy)

Prof Dr M. Ali M. Nassar, Director of Planning Center,

Professor Lionel Pereira Mendoza, Associate Professor, National
Institute of Education (

Professor Angela Pesci,

Prof. Medhat Rahim,

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,

Professor. Wacek Zawadowski,

**Local
Organizing Committee**

**Chairman**:

Prof. Dr. Noor Azlan Ahmad Zanzali, Faculty
of Education, Universiti Teknologi

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

This volume contains the papers presented at the International
Conference on ** Reform, Revolution and Paradigm Shifts in
Mathematics Education **held from November 25 to December 1

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.

http://math.unipa.it/~grim/21_malasya_2005.doc - Malaysia 2005 Conference

http://math.unipa.it/~grim/21project.htm - Our Project Home Page

http://math.unipa.it/~grim/egypt.pdf -
Egypt Conference site

http://math.unipa.it/~grim/jourdain -

http://math.unipa.it/~grim/cairms -

http://math.unipa.it/~grim/palermo2002 -
Sicily Conference site

http://dipmat.math.unipa.it/~grim/21_project/21_brno_03.htm - Brno Conference site

http://math.unipa.it/~grim/21_project/21_ciechocinek_04.htm - Ciechocinek Conference site

Filippo Spagnolo, of

Krys Bestry is webmaster for our Polish Superkurs Home Page at http://superkurs.republika.pl/ (in Polish -
but with pictures!) See also:
http://www.vsg.edu.au/egypt99/ 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 arogerson@vsg.edu.au

Dr. Alan Rogerson

Chaiman of the Programme Committee

*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 **Presentation with Power Point*

*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 *

*Jaguthsing Dindyal .....70*

*Early School Leavers Experiences
Of Learning Mathematics: The Discourses *

*Bronwyn Ewing **.....75*

*The Two Fundamental Learning Games We Play: A Framework For *

*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 *

*Amal *

*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*

*Iris Johnson ...124*

*Kwan Shi-pui & Sze Chong-lap **...129*

*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*

*Nancy Nui Wambui **...214*

*“Masifunde Nosapho” (“Let us learn with our families”)*

*Lise Westaway & Carol
Carter **...218*

*Paul Ernest*

*Longitudinal assessment of
problems solving and mathematical competences*

*Verónica
Díaz &. Alvaro Poblete*

*Improving the professional competence of mathematics
teachers*

*Verónica
Díaz &. Alvaro Poblete*

*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*

*Carol Bier **...224*

*George Booker ...227*

*Teacher-student
cooperation
*

*Liv Sissel Grønmo ...227*

*Jean Michel Hanna ...228*

*Wholemovement of Folding Circles*

*Bradford** Hansen-Smith ...230*

*Mathematical Experiences in a Technology Integration Research
Study Presentation with power point*

*Mhairi (Vi) Maeers ...230*

*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*

*Kerry J Thomas ...237*

*Rüdiger Vernay ...237*

*Integrating
Constructivist approaches in e-learning to enhance mathematical self-study*

*Ya
Ling Lee ...238 *