The Mathematics Education into the 21st Century Project

Proceedings of the International Conference 

The Humanistic Renaissance in Mathematics Education


Alan Rogerson

Hotel Città del Mare, Terrasini, Palermo, Italy

September 20-252002


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.

Wishes to thank the following for their support:

Facoltà di Scienze della Formazione dell'Università di Palermo

Dipartimento di Matematica dell'Università di Palermo

G.R.I.M. (Gruppo di Ricerca Insegnamento Matematica)

Dipartimento di Matematica dell'Università di Pavia
L'Università degli Studi di Palermo

Provincia Regionale di Palermo

IRRSAE- Sicilia

Regione Siciliana

The Hong Kong Institute of Education 

The Virtual School for the Gifted

The Third World Forum

SNM (Poland)

Design Science




International Program Committee

ChairmanDr. 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 (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, State University of 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 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, Division of Mathematics, 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 deProfesores"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

ChairmanDr. Filippo Spagnolo, University of Palermo, Sicily, Italy.

Prof.ssa Rosa Maria Sperandeo, Direttore della S.I.S.S.I.S. (Scuola Interuniversitaria Siciliana per la Specializzazione e l'Insegnamento Secondario) 

Prof.ssa Patrizia Lendinara, Preside della Facoltà di Scienze della Formazione Università di Palermo 

Prof. Aurelio Rigoli, Presidente del Consiglio di Corso di Laurea in Scienze della Formazione Primaria Università di Palermo 

Prof. Pasquale Vetro, Direttore del Dipartimento di Matematica e Applicazioni dell'Università di Palermo. 

Prof. Pietro Nastasi, Dipartimento di Matematica Università di Palermo 

Prof. Aldo Brigaglia, Dipartimento di Matematica Università di Palermo 

Prof.ssa Grazia Indovina, Dipartimento di Matematica Università di Palermo 

Prof.ssa Teresa Marino, Dipartimento di Matematica Università di Palermo 

Prof.ssa Maria Vittoria Di Leonardo, Dipartimento di Matematica Università di Palermo 

Prof. Umberto Bottazzini, Dipartimento di Matematica Università di Palermo.

Alan Rogerson

Chaiman of the Programme Committee


Introduction 21 September 2002

Welcome, Good morning and thanks to all participants of the fourth meeting of our international group “21st Century for Mathematics Education” (with symbol MEC21).

I’m very pleased to meet in Palermo the olds friends of Cairo (1999), Amman (2000) and Cairns (2001) (Australia).

I hope that your permanence in “Città del Mare” and Palermo will be very comfortable and agreeable.

The organisation of the conference program guaranties a variety of approaches following different schools of thoughts, different cultures, and different cognitive styles, in perfect accord with constitutive international group MEC21. The Mathematics Education will be able to assure a Renaissance if we will link, in other words throw a bridge, with other sciences: art, linguistic, anthropology, philosophy, neuroscience, sociology and … mathematics, history of mathematics, logic, fundamentals of mathematics, application of mathematics, experimental sciences, etc… In this way we will be able among other things to exchange methods and contents. 

The understanding of phenomena of learning/teaching is complex, it needs many tools. The semiotic approach to mathematics and to mathematics education is one possibility. 

For this purpose it is very important to have suggestions by teachers and by researchers in mathematics education. An example is the “Super Course”, which will be shown today in the plenary session by Alan Rogerson & Fayez Mina.

Palermo has a tradition in research in Mathematics and in Mathematics Education:

  1. The “Circolo Matematico di Palermo” (1884) and the review “Rendiconti del Circolo Matematico di Palermo” with contributions of Poincaré, etc.,
  2. The review “Il Pitagora” (1895-1919) (Liceo “Umberto”, Palermo) with contributions of pupils and teachers from all schools of Italy.

All these activity are well connected with researches in Mathematics Education in Italy.

For example we cite:

  1. the teachers association “Mathesis” (1895), 
  2. the relevant contributions of Enriques (1871-1946),
  3. The “Enciclopedia delle Matematiche Elementari” (1929-1949).

It is custom in all meetings to have a presentation with formal many thanks. In this occasion they are not formal because the collaboration in organisation of meeting has been constructive and efficient by many people.

Many thanks to the President of Sicily Region on. Salvatore Cuffaro.

Many thanks to the President of Province Regional of Palermo on. Francesco Musotto.

Many thanks to the Prof.ssa Patrizia Lendinara Dean of “Science of Education Faculty” and in this occasion delegate by the Rector of Palermo University. I should like remember the important role of Science of Education Faculty in organise this meeting.

Many thanks to the Dean of course of degree in “Scienze della Formazione Primaria” (formation of future teacher in elementary and maternal school), prof. Aurelio Rigoli.

Many thanks to the Dean of SISSIS (post degree master for future teachers in middle and secondary school of Sicily) and Vice-President of GIREP (International Group of Physics Education)Prof.ssa Rosa Maria Sperandeo.

Many thanks to the Head of Mathematics DepartmentProf. Pasquale Vetro.

Many thanks to PhD students in Mathematics Education, to graduate students of “Primary Education Science”, to people which just have the degree in “Primary Education Science”.

Many thanks to components of GRIM (Research Group on Learning/Teaching of Mathematics), to components of Palermo’s teacher association AICM, to components of the Local Organizing Committee. 

Many thanks to Publischer Center ofScience of Education Faculty.

And finally, many tanks to Alan Rogerson & Fayez Mina, the heart of international group !!!

Filippo Spagnolo

Local Chaiman of the Programme Committee

Article of Regional Journal of Sicily "Giornale di Sicilia"

Presented Papers

Can Technology Save Classroom Mathematics 

Douglas Butler (Plenary Lecture)1

Mathematics Teachers and Students: How can we improve the human side of their relationship?

Angela Pesci (Plenary Lecture)11

Bi-laterality in mathematics

Mahdi Abdeljaouad20

Student's Constructivist Paradigm in a Spatial Problem Solving Inquiry-Based Mathematics Classroom

Medhat H. Rahim - Thunder Bay

Pedagogical Issues in WebMathematica Applications in Distance Learning Mathematics

M.F. Abdul Karim & U. Ufuktepe25

Humanitarian role of mathematics in training of a teacher

V.V. Afanasiev & E.I. Smirnov30

Some experimental observations on common sense and fuzzy logic

Maria Ajello & Filippo Spagnolo35

Pre-service Mathematics Teachers Conducting Research to Enhance Their Knowledge of Children’s Thinking

Othman Nayef Alsawaie40

Effectively using new paradigms in the teaching and learning of mathematics: Action research in a multicultural South African classroom

Hayley Barnes44

Challenging curriculum: process and product

Andy Begg50

A Mathematica Notebook about Ancient Greek Music and Mathematics

Luigi Borzacchini & Domenico Minunni56

PaceXL: Statistics Add-in for Excel

Robin Boyle60

Teaching Algebra Concepts in the Early Grades

Jack Burrill64

Making Decisions with Data

Gail Burrill67

Mathematics and Technologies: Bridging Diverse Languages

Isabel Cabrita72

Forming Partnerships to Improve Mathematics Teaching

Rose Elaine Carbone76

Multiple factor interactions. Role of effect modifier factors.

Lucette Carter79

The Use of Hand-held Technology in the Learning and Teaching of Secondary School Mathematics. The functionality of CABRI and DERIVE in a graphic calculator.

Ercole Castagnola80

The Image of Rational Numbers in Students

N. Çetin87

Misconceptions about triangle in Elementary School

Palmina Cutugno & Filippo Spagnolo89

Reasoning, Modelling and Communication in Classroom Mathematics

Krystyna Dalek                                94

Unraveling students’ belief systems relating to mathematics learning and problem solving

Erik De Corte & Peter Op ’t Eynde96

Using XML to Share Statistics Education Materials in PAPIRIS

H. Edward Donley102

Investigating the Effectiveness of Mental Imagery Strategies in a Constructivist Approach to Mathematics Instruction

Patricia Douville, David K. Pugalee, Josephine Wallace, Corey R. Lock107

Predicting the Future – Training Teachers for Tomorrow

Patricia T. Eaton112

Matching Unusual Word Problems with Given Answers

Iliada Elia & Athanasios Gagatsis116

Mathematical Representation of Real Systems: Two Modelling Environments Involving Different Learning Strategies

C. Fazio, R. M. Sperandeo-Mineo, G. Tarantino121

Humanistic Influences in Mathematics Achievement: Department Heads’ Perceptions of Their Role

Beverly J. Ferrucci & Jack A. Carter126

We Need Learning Tasks That Support Sense Making

Gary Flewelling130

Using Short Open-ended Mathematics Questions to Promote Thinking and Understanding.

Foong Pui Yee134

Learning Mathematics: a SEARCH for meaning.

Noel Geoghegan141

The Systemic Thinking in the passage from the arithmetic language to the algebraic language with use of mediator software Excel (in the children of 9-10 years)

Claudia Giacalone & Filippo Spagnolo145

General Aims of Mathematics Education Explained with Examples in Geometry Teaching

Günter Graumann150

General Education in Mathematics Lessons An Introduction to Humanistic Holistic Education

Günter Graumann153

It's not surprising that Euclid got excited about Geometry

Thomas Hagspihl158

Why is the teaching of Mathematics in such a crisis - a perspective from the tip of Africa.

Thomas Hagspihl163

An application of concepts from statics to geometrical proofs

Gila Hanna, Ysbrand DeBruyn, Nathan Sidoli & Dennis Lomas166

Wholemovement of the circle

Bradford Hansen-Smith171

Computer Simulations and Modelling in Mathematics Education

Michael Hardiker176

Using Narrative Classroom Cases to Promote Inquiry and Reflection on Mathematics, Teaching, and Learning

Marjorie Henningsen181

How one can use “The Super Farmer” game in teaching mathematical modelling and problem solving.

Agata Hoffmann186

On Humaninizing Mathematics

Nazla H.A.Khedre188
Three roles for technology: Towards a humanistic renaissance in mathematics education

Barry Kissane191

What's the Difference? Teaching Mathematics to Standards in a Distance Learning Environment
Libby Krussel

Farey Series and Ford Circles

Shi-Pui Kwan200

Mathematics Education Reform in Hong Kong

Louisa Lam204

Mathematics in Literature

Sally I. Lipsey & Bernard S. Pasternack209

Concentrated Reinforcement Lessons (CoReL)
Madeleine J. Long

Investigation and Alleviation Concerning the Reasons for poor Performance in Introductory Mathematics at Technikon Northern Gauteng (SA)

CJ (Ina) Louw217

A comparison of strategies adopted by primary students in four cities of China in solving mathematical problems

Luk Hok Wing221

The Lack of Geometric Comprehension in Integral Instruction

N. Mahir226

ArAl: a Project for an Early Approach to Algebraic Thinking

Nicolina A. Malara & Giancarlo Navarra228

Future middle school teachers’ beliefs about Algebra: incidence of the cultural background

Nicolina A. Malara   234

School Mathematics Geometric Problems: Past, Present and future

George Malaty240

The Notion of variable in Semiotic Contexts Different

Elsa Malisani245

Representations and Learning of Fractions

Andry Marcou & Athanasios Gagatsis250

Publishing math on the Web - What are the Best Solutions?

Bob Mathews254

Connecting Mathematics and Biology in the Information Society Schools: A Brazilian Perspective on Technology Usage

Alexandre S. Mendes, Joni A. Amorim, Rosana G. S. Miskulin258

Mathematics Towards Perception of the World

Ivan Meznik263

The Role of the Systemic Approach in the Humanistic Renaissance in Mathematics Education

Fayez M. Mina267

Facilitating Problem Solving: Children Argue their way to a Multiplicative Structure with the aid of Selected Cultural Tools

Christina Misailidou & Julian Williams269

Interactivity in Mathematics Education: Collaborative Knowledge Generation in Internet Based Sharing Environments

Rosana GiarettaSguerra Miskulin, Joni de Almeida Amorim, Fernando Massucheto Jorge273

Web-Based Learning: Using Telecollaboration Modelsto Enhance Mathematics Instruction

Monique C. Lynch, Patricia S. Moyer, Denise Frye, Jennifer M. Suh279

Five years experiences with the Finnish mathematics web magazine Solmu

Marjatta Näätänen283

On computer education in Japan

Yoko Ono and Yumi Asahi285

Mathematical Mistakes of Solving Physics Problems

Nevin Orhun & Önder Orhun288

Solution of verbal problems Using Concept of Least Common Multiplier (LCM) and Greatest Common Divisor (GCD) in Primary School Mathematics and Misconceptions

Nevin Orhun290

Simulation and Statistical Exploration of Data (e.g. Fair Die or Unfair Die) 

Test of Hypothesis on Fair Die (Simulation of Chi Square Tests)

Ludwig Paditz293

Creating a Constructivist Mathematics Department from a Traditional Setting

Bevan Penrose299

Authentic Tasks and Mathematical Problem Solving

David K. Pugalee, Patricia Douville, Corey R. Lock, Josephine Wallace303

Students’ Constructivist Paradigm in a Spatial Problem-Solving Inquiry-Based Mathematics Classroom

Medhat Rahim307

Arithmetic, algebra and technology: a study on beginner pupils

Maria Reggiani312

Why and How I use Computer programs during the Lessons of mathematics

Anna Rybak317

Art, Mathematics and Architecture for Humanistic Renaissance: the Platonic Solids

Nicoletta Sala321

Applications of Mathematics in the Real World: Territory and Landscape

Nicoletta Sala, Silvia Metzeltin, Massimo Sala326

Rabbit Ears to Slope to Derivatives: Longitudinal Development of an Algebraic Concept

Lynnea C. Salvo, Lorraine Smith, Vickie Inge, John Staley, Johnna J. Bolyard, Patricia S. Moyer334

Following Goldbach’s tracks

Aldo Scimone339

Simple Linear Regression: A PAPIRIS Example

Maher Y. Shawer, Michael J. Bossé, Frederick W. Morgan, John D. Baker343

The Solution is Just the Beginning: Using Rich Learning Tasks to Develop Mathematical Creativity

Linda Jensen Sheffield349

Developing mental abilities through structured teaching methodology

Mihaela Singer353

The Local "Super Course" and the National Experiment in the Humanization of Mathematical Education (Lithuanian Case)

Maryt? Stri?kien? & Elmundas Žalys 358

Drawing by Equations

Valeria Facchini, Francesca Gialanella, Maria Talamo, Annalaura Trampetti361

Wrappings, carpentersand symmetries ineverydaylife – making flexible use of knowledge and supportingindependentlearning

Rüdiger Vernay365

The spatial consciousness of the blind: a contribution to the research

Giovanna Virga366

Understanding of three dimensional arrays of cubes - Children in transition

 Stamatis Voulgaris & Anastasia Evangelidou                                                            377


Aboutthe success of integration of information technology in math education



Final Discussion

Working Group 1: Powerful learning environments for mathematics problem solving, Erik De Corte (Belgium) and George Malaty (Finland)

Working Group 2 : Statistics and Probability, Gail Burrill


Working Group 3: Rich Learning Tasks: Position Paper, Gary Flewelling & Rudiger Vernay

Working Group 3: Rich Learning Tasks , Summary

Working Group 4: Technology in the Classroom, Angel Balderas, Maria Reggiani & Medhat Rahim

Working Group 5: Real world Applications of Mathematics, Ivan Meznik, Agata Hoffman & Aldo Scimone


Working Group 6: Classroom focussed research, how do kids learn?, Angela Pesci, Anastasia Evangelidou & Gianna Manno


Working Group 7:  “Equity and Ethnomathematics”, Gila Hanna, Liv Sissel Grønmo & Franco Favilli

Working group 7:Classroom Focussed Research, How do Kids Learn?


Working Group 8: Classroom Focussed Research, How do Kids Learn?, Angela Pesci, Krysia Dalek


Working Group 9: Teacher Education, Wacek Zawadowski


Working Group 9 for Teacher Education and Development, Marjorie Henningsen


Report of the SuperCourse Workshop „Mathematics and Society, Values and Feelings“ on Monday 23rd September 2002 in Sicily (conducted by Günter Graumann)