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

**Proceedings
of the International Conference **

*The
Humanistic Renaissance in Mathematics Education*

**Editor**

**Alan Rogerson**

**Hotel Città
del Mare, Terrasini, Palermo, Italy**

**September
20-252002**

**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.**

**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**

**CDNALMA**

**Greygum**

**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 (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**

**Chairman**Dr. 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**

**Welcome, Good
morning and thanks to all participants of the fourth meeting of our international group
“21 ^{st} 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:**

**The “Circolo Matematico di Palermo” (1884) and the review “Rendiconti del Circolo Matematico di Palermo” with contributions of Poincaré, etc.,****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:**

**the teachers association “Mathesis” (1895),****the relevant contributions of Enriques (1871-1946),****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?**

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

**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**

**Challenging curriculum: process and product**

**A Mathematica Notebook about Ancient Greek Music
and Mathematics**

**Luigi
Borzacchini & Domenico Minunni56**

**PaceXL: Statistics Add-in for Excel**

**Teaching Algebra Concepts in the Early Grades**

**Mathematics and Technologies: Bridging Diverse
Languages**

**Forming Partnerships to Improve Mathematics Teaching**

**Multiple factor interactions. Role of effect modifier
factors.**

**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**

**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**

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

**Predicting the Future – Training Teachers for
Tomorrow**

**Matching Unusual Word Problems with Given Answers**

**Iliada Elia
& Athanasios Gagatsis116**

**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**

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

**Learning Mathematics: a SEARCH for meaning.**

**Claudia
Giacalone & Filippo Spagnolo145**

**General Aims of Mathematics Education Explained with
Examples in Geometry Teaching**

**General Education in Mathematics Lessons An
Introduction to Humanistic Holistic Education**

**It's not surprising that Euclid got excited about
Geometry**

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

**An application of concepts from statics to geometrical
proofs**

**Gila Hanna,
Ysbrand DeBruyn, Nathan Sidoli & Dennis Lomas166**

**Computer Simulations and Modelling in Mathematics
Education**

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

**Nazla H.A.Khedre188**

**Three roles for technology: Towards a
humanistic renaissance in mathematics education**

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

**Libby
Krussel****196**

**Shi-Pui Kwan200**

**Mathematics Education Reform in Hong Kong**

**Louisa Lam204**

**Sally I. Lipsey
& Bernard S. Pasternack209**

__Concentrated Reinforcement Lessons (CoReL)__

__Madeleine J.
Long__**213**

**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**

**The Notion of variable in Semiotic Contexts
Different**

**Representations and Learning of Fractions**

**Andry Marcou & Athanasios
Gagatsis250**

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

**Bob Mathews254**

**Alexandre S.
Mendes, Joni A. Amorim, Rosana G. S. Miskulin, 258**

**Mathematics Towards Perception of the World**

**Ivan Meznik263**

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

**Christina Misailidou &
Julian Williams269**

**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**

**On computer education in Japan**

**Mathematical Mistakes of Solving Physics Problems**

**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)**

**Creating a Constructivist Mathematics Department from
a Traditional Setting**

**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**

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

**Anna Rybak317**

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

**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**

**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**

**Developing mental abilities through structured
teaching methodology**

**Maryt? Stri?kien? & Elmundas
Žalys 358**

**Valeria Facchini, Francesca Gialanella, Maria Talamo, Annalaura
Trampetti361**

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

**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__

*
Working Group 2 : Statistics
and Probability, Gail Burrill*

*
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 for Teacher Education and Development,
Marjorie Henningsen
**