The Mathematics Education into the 21st Century Project
The Future of Mathematics Education
Editor
Alan Rogerson
Pod Tezniami, Ciechocinek, Poland
June 26th July 1st, 2004
Major Sponsors
CASIO & AUTOGRAPH
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
The Hong Kong Institute of Education
The Third World Forum
CASIO
Autograph
Greygum Software
ALMA (Teacher Training Centre, Poland)
SNM (Polish Association of Teachers of Mathematics)
VSG Enrichment
Wholemovement
ISBN Number 83-919465-4-1
International Program Committee
Chairman Dr. Alan Rogerson, Coordinator of the Mathematics in Society Project (Poland).
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, Math, Science, and Technology Education, The Ohio State University (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).
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, Professor of Philosophy of Mathematics Education, University of Exeter (UK).
Prof. Dr. Gabriele Kaiser, Hamburg University (Germany).
Dr. Madeleine J. Long, Program Director, American Assn. for the Advancement of Science (USA).
Prof Dr Fayez Mina, Dept. of Curriculum & Instruction, Faculty of Education, Ain Shams University (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, Lakehead University, Faculty of Education (Canada).
Professor Filippo Spagnolo, University of Palermo, Sicily, (Italy).
Professor Dr. Alicia Villar Icasuriaga, Instituto de Profesores "Artigas"(IPA), Montevideo, (Uruguay)
Dr. Arthur L. White, Math, Science, and Technology Education, The Ohio State University (USA)
Professor. Wacek Zawadowski, Warsaw University (Poland).
Local Organizing Committee
Chairperson: Margaret Fryska, Centrum Doskonalenia Nauczycieli ALMA, Poznań
Alan Rogerson, Chairman of the International Program Committee.
Krzysztof Nowakowski, University of Poznań
Marek Pisarski, University of Białystok
Alicja Radek, SNM
Dorota Kraska, SNM
Justyna & Ania Fryska, (Conference Secretaries)
This volume contains the papers presented at the International Conference on The Future of Mathematics Education held from June 26th to July 1st at the Hotel Pod Tezniami, Ciechocinek, Poland. It also contains papers submitted in Polish for the parallel National Polish Superkurs meeting held in the same venue from June 26-29. This Conference was organized by The 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. Previous Conferences have been held in Cairo, Egypt (1999), Amman, Jordan (2000), Zajaczkowo Poland & Palm Cove, Australia (2001), Sicily, Italy (2002) and in Brno, Czech Republik in 2003.
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 of them report on innovative experiences in the classroom and new technology or ideas." 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 a Plenary Paper and otherwise contain contributions mostly in alphabetical order of the Principal Presenters. At the end are contributions in Polish to the National Superkurs Meeting which was held from June 26-29th in parallel and in cooperation with our international conference. 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. They will also serve as a stepping stone for the new and exciting International Initiative, SuperCourse, which features strongly throughout the conference programme. For further information about this initiative and the work of our Project, please email arogerson@vsg.edu.au.
The Proceedings for all our conferences
can be found online at the following sites. Egypt :
egypt.pdf , Jordan:
jourdain
Australia :
cairms, Sicily:
palermo2002 Brno:
http://dipmat.sites.unipa.it/grim/21_project/21_brno_03.htm Ciechocinek:
21_project/21_ciechocinek_04.htm . Our Project Home Page is: 21project.htm. Warm thanks to Dr. Filippo Spagnolo of the University of Palermo, Sicily, Italy, who is webmaster for the above sites. Information about our project can also be found on the following sites: www.cdnalma.poznan.pl, http://superkurs.republika.pl/ (in Polish) and http://www.vsg.edu.au/egypt99/ .
Dr. Alan Rogerson
Chairman of the Programme Committee
Presented Papers
Plenary Lecture: Common - Sense Logic for Managing Uncertainty
Ivan Mezník .. 1
Disadvantages of Multiple Choice Tests and Possible Ways of Overcoming Them
B. Abramovitz, M. Berezina & A. Berman . 7
Graphic calculator in education at schools and in the educational training of future teachers
Helena Bereková .. 12
Playing to win: using games for motivation and the development of mathematical thinking
George Booker . 16
Modern mathematics schoolbook in Poland in 21st century what should it be like?
Krystyna Dałek .. 21
Sabita M. DSouza & Leigh N. Wood .. 24
Improving mathematics written tests: Impact of research on student teachers conceptions
Rosa Antónia Tomás Ferreira .. 29
Dynamic Representations and Prospective Teachers Understanding of Functions
Beverly J. Ferrucci & Jack Carter .. 35
3D Computer Graphics and Analytic Geometry in Mathematics Education in Grammar Schools
A. Filler & F. Rieper .. 39
Exemplary Practices in the Primary Mathematics Curriculum - The Singapore Experience
Foong Pui Yee .. 45
Douglas Franks & Murat Tuncali, .. 50
Rich learning tasks occupies the body, feeds the mind, touches the spirit
Bradford Hansen-Smith .. 55
An Effective Identification and Response to Childrens Learning Needs in Number.
Marilyn Holmes & Lynn Tozer .. 60
E-learning in teaching of mathematics using computer Algebra system Maple
Jiří Hřebíček, Jana Hřebíčková, Ivan Mezník & Zuzana Chvátalová .. 66
Pre-service Teachers Beliefs Regarding Inquiry Learning and the Use of Graphing Calculators
Iris DeLoach Johnson .. 71
On Improving School Maths Curriculum through Fashionable Maths
Nazla H.A. Khedre .. 77
Some models of using ClassPad in teaching mathematics for secondary students
Lilla Korenova .. 81
An exponential function: is its description not problematic?
Mahlobo Radley .. 86
Some Remarks On The Future of Mathematics Education
Fayez M. Mina .. 93
Laurenţiu Modan .. 98
Word Problems Can the Model Method Help?
Ng Swee Fong & Kerry Lee .. 104
Kathleen Nolan .. 109
On symbolic calculation with the ClassPad300
Ludwig Paditz .. 114
Anna Gallo Selva, & Angela Pesci .. 119
Didactics Varieties in Geometry
Alvaro Poblete & Verónica Díaz .. 123
Mathematical Competences and Types of Problems
Alvaro Poblete & Verónica Díaz .. 124
Bizhan Shabankhani .. 125
Lesson Study: A Student-Centered Professional Development for Teachers
Agnes Tuska .. 128
Mathematics A Fresh Approach
Ariana-Stanca Văcăreţu .. 131
New Models in Assessment in Computer integrated Mathematical Instruction -
Experiences in the Austrian CA Projects
Otto Wurnig .. 137
Binary decimal numbers and decimal numbers other than base ten
Thomas Kim-wai Yeung & Eric Kin-keung Poon .. 142
Graphs and systems of equations with a real parameter solved by a graphic calculator
Helena Bereková
Using games to develop meaning and proficiency with fraction concepts and processes
George Booker
How to solve geometrical problems with Class Pad
Monika Dillingerová
Investigating geometry on ClassPad 300. Introductory workshop.
Number theory on ClassPad 300.
Using the ClassPad 300 spreadsheet.
Gunnar Gjone
Using Technology to Support Inquiry Learning in Mathematics
Iris DeLoach Johnson
Some models of using ClassPad in teaching mathematics for secondary students
Lilla Korenova
Several aspects of 2D-graphic with the ClassPad300
Several aspects of 3D-graphic with the ClassPad300
Ludwig Paditz
Analytic Geometry with 3D Computer Graphics in Maths Education
Felix Rieper & Dr Andreas Filler
Presentation of the educational software program VUStat for learning and teaching of statistics and probability.
Anna Rybak
The website with the pictures from conference in Ciechocinek:
Polish Contributions 149 - 171
Working groups
WG1:
TECHNOLOGY IN THE CLASSROOM
Ivan Meznik, Jirí Hrebícek & Anna Rybak
WG2:
INNOVATIONS IN MATHEMATICS AND STATISTICS EDUCATION#
Maher Shawer, Iris Johnson, Otto Wurnig
WG3: EQUITY,
ETHNOMATHEMATICS, AND CLASSROOM CULTURE
Krystyna Dalek, Beverly Ferrucci, John Bibby
WG4:
TEACHER EDUCATION & DEVELOPMENT
Angela Pesci, Jaromir Vosmansky & Agnes Tuska