**MATHEMATICS
EDUCATION INTO THE 21 ^{ST} CENTURY PROJECT **

*Palm Cove 19-24 August 2001 - Australia*

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

**Proceedings
of the International Conference**

*New
Ideas in Mathematics Education*

**Editor**

**Alan
Rogerson**

**All
Rights Reserved. **

**Presented
Papers**

**Teaching
and Learning Mathematics in the 21 ^{st} Century (Plenary Paper)**

Gail
Burrill**i**

Reda
Abu-Elwan El Sayed**1**

**Modeling
in the Real World: Teaching Students Cost Estimation Methodologies**

Joni
de Almeida Amorim, Carlos Machado & Rosana G. S. Miskulin**7**

**Linguistic
Relativity and Place Value Concept: The Case of Arabic**

Othman
N. Alsawaie**12**

**Interweaving
Mathematics and Indigenous Cultures**

Karen
Arnason, Judith J. McDonald, Mhairi (Vi) Maeers, and J. Harley Weston**17**

**Integration
of CAS in the Didactics of Differential Equations**

Angel
Balderas Puga**22**

**One
Geometrical Situation and Three Competitions**

Francisco
Bellot Rosado**30**

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

Chris
Breen**33**

**The
Net Concept on Mathematics Education**

Roberto
Cassibba& Jorge Poliszuk**38**

**Coaxing
unwilling learners into Statistics**

Indira
Chacko**43**

Doug
Clarke **47**

KrystynaDa?ek**56**

**Rich
Learning Tasks: Changing the Culture of the Mathematics Classroom**

Gary
Flewelling**59**

**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
Glazer**67**

**InterMath-Professional
and Cognitive Development through Problem Solving with Technology **

Evan
Glazer**72**

**Problem
Fields in Geometry Teaching**

Günter
Graumann**76**

Olga
& Günter
Graumann**80**

**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
Hammouri**91**

**On
the use of handheld technology in Math instruction**

Lars
Jakobsson **96**

Iris
DeLoach Johnson**102**

**Teachers
= Interpretations of Effective Whole Class Interactive Teaching**

Sonia
Jones & Howard Tanner**109**

**Algebra
in the head, on paper and on the screen**

Dr.
Steve Kennewell**115**

Gillian
Kidman &Rod Nason**121**

**The
Algebra Curriculum and Personal Technology: Exploring the Links**

Barry
Kissane**127**

**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 Leung**278**

**Evaluation
of Numerous Groups of Students in mathematics**

G.
Leví & E. Ramos**141**

**Periodic
Functions - A unit for Year 11 Mathematics B students**

Ian
Luxton**145**

**Design
and Implementation of Vocational Education at Brisbane Boys' College**

Shane
MacDonald**148**

**Integrating
Technology into Mathematics Teaching and Learning**

Mhairi
(Vi) Maeers**152**

Nicolina
A. Malara & Rosa Iaderosa**156**

**The
behaviour of Furure Teachers Dealing with proof problems in arithmetic**

Nicolina
A. Malara**162**

**On
Structural Features of Modelling**

Ivan
Meznik**167**

Ivan
Meznik & Miloslav Kerkovsky**171**

**Prospective
Scenarios for Mathematics Education Around the Year 2020**

Fayez
M.Mina**176**

**Finding
out of the Incommensurability in the Technological Context**

Rosana
Giaretta Sguerra Miskulin & Fernando Massucheto Jorge**180**

**Virtual
Manipulatives in the K-12 Classroom**

Patricia
S. Moyer, Johnna J. Bolyard & Mark A. Spikell**184**

**Mathematics
Education into the 21 ^{st} 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 Cooper**193**

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

Stephen
J. Norton & Tom J. Cooper**198**

Nevin
Orhun &Önder Orhun**203**

**Studentâs
Mistakes and Misconceptions on Teaching of Trigonometry**

Nevin
Orhun**208**

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

Angela
Pesci**212**

**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
SchSfer**223**

**Understanding
Statistics Through Probability**

Maher
Shawer** 229**

**Some
Valuable and Applicable Mathematics.**

Anthony
Sofo** 234**

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*lez**257**

**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 Weston**267**

**Counting
mental strategies as new mathematical operations**

David
Womack**271**

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

Ma
Yunpeng**275**

********************************************************************************

**Structural
equation modelling of affects and learning approach in mathematics education**

Samuel
Hing Keung Leung**278**

**Using
Games to promote Multicultural Mathematics**

Nkopodi
Nkopodi**283**

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

Jimmy Keake &John Wamil

**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.**

**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**

**Autograph**

**Ansett
Australia**

**Casio-Shriro**

**Greygum
Software**

**QED/MatheMagic**

**Mimosa
Shortland **

**Hearne
Scientific Software**

**Texas
Instruments**

**International
Program Committee**

**Chairman****Dr.
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.

**Foreword**

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 21 ^{st} 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 21^{st} 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 arogerson@vsg.edu.au

Dr.
Alan Rogerson

Chaiman
of the Programme Committee