The Mathematics Education into the 21^st Century Project

 

 

Proceedings of the International Conference

 

The Decidable and the Undecidable in Mathematics Education

 

 

Editor

Alan Rogerson

 

  

Hotel Continental, Brno, Czech Republic

September 19-25  2003

 

 

 

 

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 21^st Century Project wishes to thank

 

Brno University of Technology

Statutory City of Brno

Masaryk University, Brno

The Union of Czech Mathematicians and Physicists

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

Veletrhy Brno a.s.

Starobrno a.s.

Znovín Znojmo a.s

  

 

ISBN Number 83-919465-1-7

 

 

International Program Committee

Chairman  Dr. Alan Rogerson, International 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 (OU/New Zealand).

Dr. Donna F. Berlin, Mathematics, 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).

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, University of Jordan (Jordan).

Professor Paul Ernest, Professor of the Philosophy of Mathematics Education, University of Exeter (UK).

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

Dr. Madeleine J.  Long, Program Director, American Association 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, Mathematics, Science, and Technology Education, The Ohio State University ( USA)

Professor. Wacek Zawadowski, Warsaw University (Poland).

 

Local Organizing Committee

Chairman : 

Prof.Dr. Ivan Mezník, Pro Dean, Faculty of Business and Management, Brno University of Technology

Local Conference Secretary:

Dr. Zuzana Chvátalová, Faculty of Business and Management, Brno University of Technology

Members :

Prof. Dr. Jan Chvalina, Head, Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology

Prof. Ing. Jiří Dvořák, Faculty of Business and Management, Brno University of Technology

Prof.dr.Jiří Hřebíček, Faculty of Informatics, Masaryk University Brno

Assoc.Prof. Ing. Miloš Koch, Dean, Faculty of Business and Management, Brno University of Technology

Assoc.Prof.Dr.Václav Viktora, Head, Department of Mathematics, Faculty of Education, Masaryk University Brno

Assoc.Prof. Dr. Jaromír Vosmanský, Faculty of Science, Masaryk University Brno

 

 

Foreword

 

This volume contains the papers presented at the International Conference on The Decidable and the Undecidable in Mathematics Education held from September 19-25, 2003 at the Hotel Continental, Brno, Czech Republic. This Conference was organized by The Mathematics Education into the 21^st 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 successful Conferences have been held in Cairo, Egypt (1999), Amman, Jordan (2000), Zajaczkowo Poland, Palm Cove, Australia (2001) and Sicily, Italy (2002).

 

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 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 the Plenary 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. They will also serve as a stepping stone for the new and exciting International Initiative, SuperCourse, which will feature strongly throughout the conference programme. For further information about this initiative and the work of our Project, please email arogerson@vsg.edu.au

 

Finally a word about our conference theme - The Decidable and the Undecidable - a tribute of course to Kurt Godel, who was born and educated in Brno before moving to Vienna and the United States. The importance of his work, in freeing mathematics from the alluring but simplistic idea that all mathematics can be deduced from a few logical axioms, cannot be overestimated. Mathematics, like art, like music and literature, and like life itself, has the power to make us happy by means of our personal creativity and openness, and through our own personal resolution of what is decidable, and what is undecidable, not only in mathematics and not only in mathematics education, but in life itself.

Dr. Alan Rogerson

Chaiman of the Programme Committee

 

 

Presented Papers

• Mathematical principles of graphic systems, Dalibor Martisek, Miloslav Druckmuller     1

• Promoting Teachers’ Changes: Examples from an Educative Process in Early Algebra, Nicolina A. Malara       5 

• Fuzzy Logic, Fuzzy Thinking and the teaching/learning of mathematics in multicultural situations. Filippo Spagnolo        17

• INTEGRATING ICT IN MATHEMATICS TEACHING METHODS COURSE: HOW HAS ICT CHANGED STUDENT TEACHERS’ PERCEPTION ABOUT PROBLEM SOLVING, Shafia Abdul Rahman, Munirah Ghazali, Zurida Ismail        29

• Implementing the intended mathematics curriculum: Teachers’ beliefs about the meaning and relevance of problem solving, Noor Azlan Ahmad Zanzali       34

• WHAT ROLES DO MATHEMATICS TEACHERS PLAY WHEN THEIR STUDENTS SOLVE PROBEMS?, Othman N. Alsawaie        38

• Java Applets in Education, Andrea BULNOVÁ           42

• INTERVENTION RESEARCH: A TOOL FOR BRIDGING THE  THEORY-PRACTICE GAP IN MATHEMATICS EDUCATION?, Erik DE CORTE    45

• PRINCIPIA PROGRAM: TEACHING MATHEMATICS  TO ENGINEERS WITH INTEGRATED CURRICULUM, TEAMWORK ENVIRONMENT AND USE OF TECHNOLOGY., Francisco Delgado, Rubén D. Santiago          56

• SOLVING OF CONTEXT TYPE MATHEMATICAL PROBLEMS, Veronica Diaz Q. & Alvaro Poblete L.       61

• Investigating the Relationship between Mental Imaging and Mathematical Problem Solving, Patricia Douville and David K. Pugalee       62

• Does a proof render the truth of a claim decidable?, Nella Yollesh and Tommy Dreyfus         68

• MENDEL: BIOLOGY, MATHEMATICS AND HISTORY OF SCIENCE, Soledad ESTEBAN, María P. GONZÁLEZ and Luis TEJERO       72

• Deciding Optimal Experiences in Coordinate Geometry for Pre-Service Elementary School Teachers, Jack A. Carter, Beverly J. Ferrucci    75

• MOM, TUT, SENSE MAKING and RICH LEARNING TASKS, Gary Flewelling         79

• Development of a framework to assess primary students’ number sense in Malaysia, Munirah Ghazali, Shafia Abdul Rahman, Zurida Ismail Sharifah Norhaidah Idros, & Fatimah Salleh       83

• AN INVESTIGATION INTO THE MATHEMATICAL KNOWLEDGE OF PRE-SERVICE PRIMARY  TEACHERS., Maria Goulding    87

• Assessment of General Aims like Ordering, Structuring and Analogising – a decidable task?, Günter Graumann,     91

• Assessment of a Comprehensive, School-wide Intervention: The CAMMP Experience, Michael Green & John A. Piel      94

• Linking procedural and conceptual mathematical knowledge in technology-based learning, Lenni Haapasalo   98

• The Experience of the Arab Supercourse, Jean Michel Hanna      102

• PRACTICAL APPLICATION OF THE ETHICS IN GEOMETRY, Bradford Hansen-Smith         105

• Intertwining Research and Teacher Development in Lebanese Elementary Mathematics Classrooms:  The MARAL Project, Marjorie Henningsen     110

• The Internet as Instructional Tool: A Consideration of Its Potential Role in the Elementary Mathematics Classroom, Terese A. Herrera    114

• Using Symbolic Computation Systems in Applications, Jiří Hřebíček, Jan Pešl, Jaroslav Ráček    116

• An investigation into the modelling of word problems leading to algebraic equations, Ruth Hubbard       119

• Aspects of Critical Thinking in Classroom Instruction of Secondary School Mathematics Teachers in Jordan, Hanan Innabi    124

• USE OF IT & MAPLE IN TEACHING PRE-CALCULUS, Nakhshin Karim,  130

• TEACHING STOCHASTIC CONCEPTS AT THE BUT FACULTY OF MECHANICAL ENGINEERING, Zdenek Karpisek – Pavel Popela – Josef Bednar     135

• Empowerment of Teachers as Learners: Active Learning in the College Mathematics Classroom, Ada Katsap    140

• Critical numeracy: helping people to decide, Marian Kemp      144

• Towards convergence of mathematics and computer science education, Alexander Khait     149

• A model for professional development for graphics calculator use, Barry Kissane    153

• Heron triangles and Heron´s Formula, Mgr. Daniela Křížová     158

• Differential Calculus  Maxima and Minima, RADLEY MAHLOBO   162

• Mathematical Problems and Mathematical Structures, George Malaty     166

• A didactical proposal: perpendicular and vertical straight lines, Gianna Manno – Palmina Cutugno   172

• Banach Fixed Point Theorem and the Stability of the Market, Ivan Mezník   177

• The impact of interactive whiteboards on classroom practice: examples drawn from the teaching of mathematics in secondary schools in England., Derek Glover, David Miller and Doug Averis    181

• The Decidable and the Undecidable in Mathematics Education “Going Beyond The Paradox”, Fayez M. Mina   186

• ON THE NEGATION OF THE PREDICATES WITH APPLICATIONS IN COMBINATORIAL PROBABILITIES, LAURENŢIU MODAN    189

• A “Big Problem” as a Motivator and Backbone For Mathematics Learning, Dan Fendel, Nitsa Movshovitz-Hadar, Diane Resek,  193

• Concept mapping and context in mathematics education, Dr. Willy Mwakapenda  198

• Embedding, reorganization and construction of mathematical and didactical contents as an objective in teachers education, Engelbert Niehaus  204

• Effects of Some Properties 5. Grade Students on the Performance of Mathematical Problem Solving, Nevin ORHUN    209

• The Investigation of Usage-Proficiency of Length, Area, Volume Units of 8^th Grade Students According to Some Variables, Nevin ORHUN, Onder ORHUN     213

• Simulation and Statistical Exploration of Data (Let’s Make a Deal – The Monty Hall Problem), using the new ClassPad300-technology, Ludwig Paditz     217

• Could metaphorical discourse be useful for analysing and transforming individuals’ relationship with mathematics?, Angela Pesci   224

• EVALUATION OF THE PROFESSIONAL COMPETENCES OF THE MATHEMATICS TEACHER, Alvaro Poblete & Verónica Díaz  231

• Exercises of division theory leading to brand new results, Zdeněk Polický   232

• Improving Statistical Education: Developing a CDRom orientation and training program for casual tutors., Dr Anne Porter and Dr Carolyn McPhail   235

• The Treatment of Mathematical Communication in Mainstream Algebra Texts, David K. Pugalee, Barbara Bissell, Corey Lock, Patricia Douville    238

• NOVICES’ CHOICE OF EXAMPLES IN THE TEACHING OF ELEMENTARY MATHEMATICS, Tim Rowland, Anne Thwaites and Peter Huckstep    242

• Applying the Graphic Calculus for Differentiation in Secondary School., Anna Rybak     246

• STATISTICS TEACHING WITH AN EXAMPLE, BIZHAN  SHABANKHANI, M.A.QAJAR KOOHESTANI    250

• Perception of infinity: does it really help in problem solving?, Mihaela Singer, Cristian Voica   252

• Fibonacci and Some of His Relations, Anthony Sofo,   257

• The comic of Clamat’:  the use of a comic as a linguistic mediator, Claudia Sortino   262

• The introduction of the symbolic language in secondary school: experimental analysis of a-didactic situation by Vigotskij semiotic tools, Claudia Sortino -  Filippo Spagnolo       267

• ON-LINE LEARNING FOR BRIDGING MATHEMATICS STUDENTS, GEERT MARIUS SPYKER   284

• Attempts to Improve the Problem Solving Abilities of Practicing Teachers, Agnes Tuska     288

• Politics in maths lessons? – Why not? Paper recycling and demographic developments as topics, Regina Puscher and Rüdiger Vernay    293

• Application of mathematical concepts across disciplines: an example, Stamatis Voulgaris & Anastasia Evangelidou    294

• Using PC and TI-92 in teaching Binomial and Normal Distribution in the final Grades of Austrian Grammar Schools, Otto WURNIG      298

• Two-Way Tables: Introducing Probability Using Real Data, Gail Burrill     304

• INTEGRATING ICT IN MATHEMATICS TEACHING METHODS COURSE: HOW HAS ICT CHANGED STUDENT TEACHERS’ PERCEPTION ABOUT PROBLEM SOLVING, Shafia Abdul Rahman, Munirah Ghazali, Zurida Ismail

   

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