The Mathematics Education into the 21st Century Project



 

 

Proceedings of the International Conference

 

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)

 

 

Foreword

 

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 : http://math.unipa.it/~grim/egypt.pdf , Jordan: http://math.unipa.it/~grim/jourdain
Australia : http://math.unipa.it/~grim/cairms, Sicily: http://math.unipa.it/~grim/palermo2002 Brno: http://dipmat.math.unipa.it/~grim/21_project/21_brno_03.htm Ciechocinek:

http://math.unipa.it/~grim/21_project/21_ciechocinek_04.htm . Our Project Home Page is: http://math.unipa.it/~grim/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 Meznνk                                                                            ………………………..       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 Berekovα                                                                      ………………………..      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

The need for higher education reform – Problems faced with assessing collaborative team based work: Implications for changes in assessment procedures

Sabita M. D’Souza & Leigh N. Wood                                        ………………………..      24

Improving mathematics written tests: Impact of research on student teachers’ conceptions

Rosa Antσnia Tomαs 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

Building a Relationship Between Undergraduate Mathematics and Mathematics Teacher Education: Innovation in Teacher Education

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 Children’s Learning Needs in Number.

Marilyn Holmes & Lynn Tozer                                                 ………………………..     60

E-learning in teaching of mathematics using computer Algebra system Maple

Jiřν Hřebνček, Jana Hřebνčkovα, Ivan Meznνk & Zuzana Chvαtalovα  …………………..      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

Games and Probabilities

Laurenţiu Modan                                                                     ………………………..     98

Word Problems – Can the Model Method Help?

Ng Swee Fong & Kerry Lee                                                      ………………………..   104

In Teacher Education, The Future Is Now: The Importance of Modelling Effective Technology Integration in Mathematics Education Classes

Kathleen Nolan                                                                      ………………………..      109

On symbolic calculation with the ClassPad300

Ludwig Paditz                                                                        ………………………..      114

taking into account metaphors, autobiographies and non verbal languages in the professional training of mathematics teachers

Anna Gallo Selva, & Angela Pesci                                           ………………………..      119

Didactics Varieties in Geometry     

Alvaro Poblete & Verσnica Dνaz                                                ………………………..     123

Mathematical Competences and Types of Problems

Alvaro Poblete & Verσnica Dνaz                                    ………………………..     124

The survey of environmental health indexes of schools (educational places) in the villages of Mazandaran province

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

 

Workshop Summaries  145- 147

Graphs and systems of equations with a real parameter solved by a graphic calculator

Helena Berekovα

Using games to develop meaning and proficiency with fraction concepts and processes

George Booker

How to solve geometrical problems with Class Pad

Monika Dillingerovα

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:

http://www.ph-heidelberg.de/wp/filler/ciecho04/index.htm

 

 

Polish Contributions 149 - 171

 

Working groups

  1. WG1: TECHNOLOGY IN THE CLASSROOM
    Ivan Meznik, Jirν Hrebνcek & Anna Rybak

  2. WG2: INNOVATIONS IN MATHEMATICS  AND STATISTICS EDUCATION#
    Maher Shawer, Iris Johnson, Otto Wurnig

  3. WG3: EQUITY, ETHNOMATHEMATICS, AND CLASSROOM CULTURE
    Krystyna Dalek, Beverly Ferrucci, John Bibby

  4. WG4: TEACHER EDUCATION & DEVELOPMENT
    Angela Pesci, Jaromir Vosmansky & Agnes Tuska