News: Photos of Meeting

Palm Cove 19-24 August 2001 - Australia


The Mathematics Education into the 21st Century Project

Proceedings of the International Conference

New Ideas in Mathematics Education


Alan Rogerson

All Rights Reserved. 

Presented Papers

Teaching and Learning Mathematics in the 21st Century (Plenary Paper)

Gail Burrilli

Effectiveness of Problem Posing Strategies on Prospective Mathematics Teachers' Problem Solving Performance

Reda Abu-Elwan El Sayed1

Modeling in the Real World: Teaching Students Cost Estimation Methodologies

Joni de Almeida Amorim, Carlos Machado & Rosana G. S. Miskulin7

Linguistic Relativity and Place Value Concept: The Case of Arabic

Othman N. Alsawaie12

Interweaving Mathematics and Indigenous Cultures 

Karen Arnason, Judith J. McDonald, Mhairi (Vi) Maeers, and J. Harley Weston17

Integration of CAS in the Didactics of Differential Equations

Angel Balderas Puga22

One Geometrical Situation and Three Competitions

Francisco Bellot Rosado30

Researching Teaching: Telling the holeâd truth and nothing but my truth?

Chris Breen33

The Net Concept on Mathematics Education

Roberto Cassibba& Jorge Poliszuk38

Coaxing unwilling learners into Statistics

Indira Chacko43

Classroom Focused Research: Teachers Understanding, Assessing and DevelopingYoung Childrenâs Mathematical Thinking (Plenary Paper)

Doug Clarke      47

Changes of teaching methods and mathematical content caused by new technologies. Changes of methods, objectives and content.Traps and threats.


Rich Learning Tasks: Changing the Culture of the Mathematics Classroom

Gary Flewelling59

Communication in the Secondary Mathematics Classroom: Exploring New Ideas

Douglas Franks & Daniel Jarvis                                                                                 62

Using Web Sources to Promote Critical Thinking in High School Mathematics

Evan Glazer67

InterMath-Professional and Cognitive Development through Problem Solving with Technology 

Evan Glazer72

Problem Fields in Geometry Teaching

Günter Graumann76

Symmetry teaching in heterogeneous classes - Common learning with handicapped and Gifted children in regular classes

Olga & Günter Graumann80

Synergetic Environments for Mathematical Development: Fact or Fiction ö Myth or Reality?

Pamela Hagen85

The Problem Solving Cognitive Strategies Used by High Achievers of the Hashemite University

Hind Hammouri91

On the use of handheld technology in Math instruction

Lars Jakobsson                                                                                               96

Using Problem-Based Learning (PBL) to Address the Needs of Teaching and Learning Mathematics for Students in the Non-dominant Cultures of our Society

Iris DeLoach Johnson102

Teachers = Interpretations of Effective Whole Class Interactive Teaching

Sonia Jones & Howard Tanner109

Algebra in the head, on paper and on the screen

Dr. Steve Kennewell115

Construction of knowledge about measurement of area within Integrated Learning System (ILS) environments

Gillian Kidman &Rod Nason121

The Algebra Curriculum and Personal Technology: Exploring the Links

Barry Kissane127

New ideas in teaching the Multiplication Table in Primary Mathematics Education

Yeung Kim Wai Thomas & Leung Hing Keung 133

Structural equation modelling of affects and learning approach in mathematics education

Samuel Hing Keung Leung278

Evaluation of Numerous Groups of Students in mathematics

G. Leví & E. Ramos141

Periodic Functions - A unit for Year 11 Mathematics B students

Ian Luxton145

Design and Implementation of Vocational Education at Brisbane Boys' College

Shane MacDonald148

Integrating Technology into Mathematics Teaching and Learning

Mhairi (Vi) Maeers152

An Aspect of a Didactical path for Approoaching the Concept of Function: The Qualitative Interpretation of the Graph

Nicolina A. Malara & Rosa Iaderosa156

The behaviour of Furure Teachers Dealing with proof problems in arithmetic

Nicolina A. Malara162

On Structural Features of Modelling

Ivan Meznik167

Modelling with Economics

Ivan Meznik & Miloslav Kerkovsky171

Prospective Scenarios for Mathematics Education Around the Year 2020

Fayez M.Mina176

Finding out of the Incommensurability in the Technological Context

Rosana Giaretta Sguerra Miskulin & Fernando Massucheto Jorge180

Virtual Manipulatives in the K-12 Classroom

Patricia S. Moyer, Johnna J. Bolyard & Mark A. Spikell184

Mathematics Education into the 21st Century: Improving the Curriculum of Future Teachers

Rosana Giaretta Sguerra Miskulin & Joni de Almeida Amorim 188

Does The Learning Equation Have a Role in Australian Mathematics Education?Possibly Yes!

Stephen J Norton & Tom J Cooper193

Students' Perceptions of the Importance of Closure in Arithmetic: Implications for Algebra

Stephen J. Norton & Tom J. Cooper198

The Investigation of Relation between Attitude toward Mathematics and Attitude toward Science of 9th Grade Students in Eski?ehir Science High School According to Some Variables

Nevin Orhun &Önder Orhun203

Studentâs Mistakes and Misconceptions on Teaching of Trigonometry

Nevin Orhun208

The Mathematics Teacherâs Judgment on Înon traditionalâ Lessons: The Results of anInvestigation

Angela Pesci212

New Research Findings, Ideas and techniques In Teaching and Learning Mathematics

Medhat Rahim (Plenary Paper) 217

World View Theory and the Conceptualization of Space and Shape in Mathematics Education

Marc SchSfer223

Understanding Statistics Through Probability

Maher Shawer 229

Some Valuable and Applicable Mathematics.

Anthony Sofo 234

Semiotic and hermeneutic can help us to interpret teaching/learning? 

Filippo Spagnolo 240

Assessing Children's Mathematical Thinking in Practical Modelling Activities

Howard Tanner & Sonia Jones, 245

A Picture is Worth a Thousand Words

Steve Thornton 251

A Graphic Probability Calculator

Ricardo V*lez257

Teaching application-orientated mathematics and developing didactics from the bottom up

Regina Puscher and Rüdiger Vernay (Plenary Paper)261

Quandaries and Queries: A mathematics question and answer service

J. Harley Weston267

Counting mental strategies as new mathematical operations

David Womack271

The New Reform of the Mathematics Curriculum on Basic Education in China

Ma Yunpeng275


Structural equation modelling of affects and learning approach in mathematics education

Samuel Hing Keung Leung278

Using Games to promote Multicultural Mathematics

Nkopodi Nkopodi283

Problems of Teaching Mathematics in a developing country, Papua New Guinea University of Technology, a case study                                                                                               288

Jimmy Keake &John Wamil 

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Sponsored by Autograph

Making mathematics more fun to learn and more fun to teach

Making mathematics easier to learn and much easier to teach

in cooperation with

The Third World Forum,

The Hong Kong Institute of Education

The Australian Association of Mathematics Teachers,

The Virtual School for the Gifted


Ansett Australia


Greygum Software


Mimosa Shortland 

Hearne Scientific Software

Texas Instruments

International Program Committee

ChairmanDr. Alan Rogerson, Mathematics in Society Project (Poland/Australia).

Prof Khaled Abuloum, University of Jordan (Jordan).

Professor Roberto Baldino, UNESP (Brazil).

Dr. Andy Begg , University of Waikato (New Zealand).

Dr. Donna F. Berlin, The Ohio State University (USA)

Prof. Dr. Werner Blum, University of Kassel (Germany).

Professor Ubiratan D'Ambrosio, UNICAMP, (Brazil).

Professor Bruno D'Amore, University of Bolgna (Italy).

Prof Dr William Ebeid, Ain Shams University (Egypt).

Prof. Omar Hassan El Sheikh, University of Jordan (Jordan).

Professor Paul Ernest, University of Exeter (UK).

Dr Hanan Innabi, University of UAE (UAE)

Prof. Dr. Gabriele Kaiser, Hamburg University (Germany).

Dr. Madeleine J.Long, American Association for the Advancement of Science (USA).

Prof Dr Fayez Mina, Ain Shams University (Egypt).

Prof Nicolina Malara, University of Modena (Italy)

Prof Dr M. Ali M. Nassar, Institute of National Planning (Egypt).

Professor Lionel Pereira Mendoza, National Institute of Education (Singapore). 

Prof. Angela Pesci, University of Pavia (Italy)

Prof. Medhat Rahim, Lakehead University (Canada).

Professor Filippo Spagnolo, University of Palermo (Italy).

Professor Dr. Alicia Villar Icasuriaga, Instituto deProfesores"Artigas" (IPA) (Uruguay)

Dr. Arthur L. White,The Ohio State University ( USA)

Professor. Wacek Zawadowski, Warsaw University (Poland). 

Local Organizing Committee

Margaret Lupi, Cairns State High School, Queensland.

Ian Luxton, Head of Mathematics, The Southport School, Southport, Queensland.

Rob Money, Past President of the Mathematical Association of Victoria. 

Ken Payne, QAMT Cairns Branch, Queensland.

Dr. Anthony Sofo, Victoria University, Melbourne, Victoria.

Kathryn Weldon, Treasurer, QAMT Cairns Branch, Queensland.


This volume contains papers presented at the International Conference on New Ideas in Mathematics Education held in Palm Cove, Australia from August 19-24, 2001. This Conference arose out of the work of the Mathematics Education into the 21st Century Project - a non-commercial international educational initiative founded in 1986. The Project is dedicated to the improvement of mathematics education worldwide through the publication and dissemination of innovative ideas. Previous successful Conferences have been held in Cairo, Egypt (1999) and in Amman, Jordan (2000) and future conferences are planned for Sicily, Finland, Mexico and Canada.

The Mathematics Education into the 21st Century Project is fortunate in having AUTOGRAPH as our Major Sponsor for the conference. We are also grateful for the support and cooperation of The Third World Forum, The Hong Kong Institute of Education, The Australian Association of Mathematics Teachers, The Cairns Branch of QAMT, The Virtual School for the Gifted and all our other numerous sponsors.

It has been my pleasure to read all of these contributions and to edit them for the Proceedings. The overall purpose of the editing was, as far as possible, to retain the individual styles, in line with our minimal instructions for the preparation of papers. These Proceedings contain contributions mostly in alphabetical order of the Presenter(s). Plenary papers at the conference were given by Gail Burrill, Doug Clarke, Medhat Rahim and by Rudiger Vernay and Regina Puscher. Please note that some diagrams and illustrations have had to be converted to black and white but were clearer in their original full colour. 

I sincerely thank all of the contributors for their time and effort. It should be clear from the variety and quality of the papers in these Proceedings that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will be a useful step 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, The Super Course of the Future, which held its first planning meeting in Poland in June, 2001. For further information about this initiative and the work of our Project, please email

Dr. Alan Rogerson

Chaiman of the Programme Committee