The Mathematics Education into the 21st Century Project




 University of Applied Sciences, Dresden


  Proceedings of the 10th International    Conference


  “Models in Developing Mathematics Education”

September 11-17, 2009

Dresden, Saxony, Germany

Editors: Ludwig Paditz & Alan Rogerson



Major Sponsors

CASIO Autograph



 Printing supported by the Dresden University of Applied Sciences


ISBN Number 83-919465-9-2

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 21st Century Project wishes to thank for their support:


Saxony Ministry of Education

Saxony Ministry of Science and the Arts

Dresden University of Applied Sciences (HTW)

The Institute for Educational Progress (IQB) Berlin

Dresden University of Technology (TU)

Gesellschaft für Didaktik der Mathematik (GDM)

MUED, DQME II, MAV, MERGA, Wholemovement

The Hong Kong Institute of Education

ALMA Teacher Training Centre, Poland


Major Sponsors




International Program Committee



Dr. Alan Rogerson, Coordinator of the Mathematics in Society Project (Poland).

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


Prof. Khaled Abuloum, University of Jordan (Jordan).

Prof. Roberto Baldino, UNESP (Brazil).

Dr. Andy Begg, Auckland University of Technology (New Zealand).

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

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

Prof. Ubiratan D'Ambrosio, Campinas/UNICAMP (Brazil).

Prof. Bruno D'Amore, University of Bologna (Italy).

Prof. Dr. Tilak de Alwis, Southeastern Louisiana University (USA).
Prof. Dr. William Ebeid, Emeritus Professor, Ain Shams University (Egypt).

Prof. Paul Ernest, University of Exeter (UK).

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

Dr. Madeleine J.  Long, Hunter College, City University of New York (USA).

Prof. Nicolina Malara, University of Modena (Italy).

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

Prof. Lionel Pereira Mendoza, Educational Consultant (Canada).

Prof. Angela Pesci, University of Pavia (Italy).

Prof. Medhat Rahim, Lakehead University, Faculty of Education (Canada).

Prof. Filippo Spagnolo, University of Palermo, Sicily (Italy).

Prof. Dr. Alicia Villar Icasuriaga, IPA, Montevideo (Uruguay).

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

Prof. Wacek Zawadowski, Siedlce University (Poland).




Local Organizing Committee

Prof. Dr. Ludwig Paditz, Dresden University of Applied Sciences.

Dr. Rainer Heinrich, Ministry of Education of Saxony.

Prof. Dr. Stefan Deschauer, Dresden University of Technology.
Prof. Dr. Michael Jung, Dresden University of Applied Sciences.
Prof. Dr. Claus Lange, Dresden University of Applied Sciences.
Prof. Dr. Klaus Neumann, Dresden University of Applied Sciences.
Prof. Dr. Wolfgang Preuß,  Dresden University of Applied Sciences.
Prof. Dr. Matthias Richter, Dresden University of Applied Sciences.
Prof. Dr. Margit Voigt, Dresden University of Applied Sciences.
Prof. Dr. Matthias Weber, Dresden University of Applied Sciences.
Dr. Hans-Dieter Dahlke, Dresden University of Applied Sciences.
Dr. Martina Timmler, Dresden University of Applied Sciences.




This volume contains the papers presented at the International Conference on “Models in Developing Mathematics Education” held from September 11-17, 2009 at The University of Applied Sciences, Dresden, Germany.  The Conference was organized jointly by The University of Applied Sciences and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on Our Project Home Page

It has been our pleasure to edit all of the papers 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 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 a Plenary Paper and then the contributions of the Principal Authors in alphabetical name order. We 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. For further information about the work of our Project, please email

We wish to thank especially Fayez Mina and Rainer Heinrich for all their support and hard work without which this conference, and these Proceedings, would not have been possible. A special thanks are also due to all our very generous major sponsors, the Saxony Ministries of Education and Science & the Arts and the City of Dresden.





Presented Papers


Keynote Plenary Address


Language and Mathematics: A Model for Mathematics in the 21st Century


David K. Pugalee (IQB Visiting Professor)                                                   1



Proofs and "Puzzles"

Buma Abramovitz, Miryam Berezina, Abraham Berman & Ludmila Shvartsman    5


Some Initiatives in Calculus Teaching

Buma Abramovitz, Miryam Berezina, Abraham Berman & Ludmila Shvartsman  10


A Study On Problem Posing-Solving in the Taxicab Geometry and Applying Simcity Computer Game

Tuba Ada & Aytaç Kurtuluş                                                                            15


An innovative model for developing critical thinking skills through mathematical education

Einav Aizikovitsh & Miriam Amit                                                                      19


The “Kidumatica” project - for the promotion of talented students from underprivileged backgrounds

Miriam Amit                                                                                                    23


How do rabbits help to integrate teaching of mathematics and informatics?

Agnis Andžāns & Laila Rācene                                                                        28


Conjecturing (and Proving) in Dynamic Geometry after an Introduction of the Dragging Schemes

Anna Baccaglini-Frank                                                                                     31


Workshop Summary

Mathematics brought to life by the Millennium Mathematics Project

Nadia Baker                                                                                                    37


Pre-service teachers’ mathematics profiles and the influence thereof on their instructional behaviour

Hayley Barnes                                                                                                 39

The Relationship between Didactics and Classroom Management:  Towards New Tools for the Training of Math Teachers

Michel Beaudoin & Catherine Lanaris                                                             43

Learning Mathematics through Scientific Contents and Methods

Astrid Beckmann                                                                                             47


Rescuing Statistics from the Mathematicians

Mike Bedwell                                                                                                  52


Presentation of the Digital School Journal Revista Escolar de la Olimpiada Iberoamericana de Matemática, Sponsored by the O.E.I. Organización de Estados Iberoamericanos para la Educación, la Ciencia y la Cultura

Francisco Bellot-Rosado                                                                                  56


In what case is it possible to speak about Mathematical capability among pre-school children?

Anna V. Beloshistaya                                                                                       57


Possibilities and Challenges of Mathematical Modeling in Teacher’s Formation

Maria Salett Biembengut                                                                                  60


How to increase the understanding of differentials by using the Casio-calculator model 9860 G I/II  to solve differential equations

Bjřrn Bjřrneng                                                                                                64


Origami-Mathematics Lessons: Researching its Impact and Influence on Mathematical Knowledge and Spatial Ability of Students

Norma Boakes                                                                                                            69


Linking Geometry, Algebra and Calculus with GeoGebra

Josef Böhm                                                                                                      74


Innovations in Educational Research and Teaching of Experimental Calculus

Horacio E. Bosch, Claudia Guzner, Mercedes S. Bergero,

Mario A. Di Blasi, Adriana Schilardi & Leonor Carvajal                                   78


The Best of Both Worlds:  Teaching Middle School and College Mathematics

Daniel J. Brahier                                                                                              83


Language and Number Values: The Influence of the Explicitness of Number Names on Children’s Understanding of Place Value

Sandra Browning                                                                                             86


Integrating Technology into the Mathematics Classroom: Instructional Design and Lesson Conversion

Marcia M. Burrell & Clayton Cohn                                                                  90


The Role of Dynamic Interactive Technology in Teaching and Learning Statistics

Gail Burrill                                                                                                       95


Presentations Using Autograph

Douglas Butler                                                                                   100


Elementary Teacher Candidates’ Understanding of Rational Numbers:  An International Perspective

Rose Elaine Carbone                                                                                     101

Text Box: 
Knon confounders

Dealing with confounding is relatively easy if, as in this case, you 
know what the likely confounders are. You could stratify your results- 
i.e. analyse smokers and non smokers separately, or you could use 
statistical techniques to adjust for confounding.

Unknown confounders

Dealing with unknown confounders is obviously much trickier. There is 
always a risk that an apparent association between a risk factor, or an 
intervention, and an outcome is being mediated by an unknown confounder.
 This is particularly true of observational studies where patients may 
be selected to one treatment group or another, not according to any 
explicit criteria, but by some unknown process, such as a care providers
 'gut feeling'. The best defence against unknown confounders is 
randomisation. This ensures that both known and unknown confounders are 
randomly distributed between treatment groups.Use and misuse of quantitative and graphical Information in Statistics. An Approach in Teaching

Lucette Carter & Cécile Hardouin                                                                  106


Basic knowledge and Basic Ability: A Model in Mathematics Teaching in China

Cheng Chun Chor-Litwin                                                                               111


How Involving Secondary Students in the Assessment Process Transforms a Culture of Failure in Mathematics to a Culture of Accountability, Self-Efficacy and Success in Mathematics Student Action Plans, Assessment, and Cultural Shift

Katharine W. Clemmer                                                                                  116


An Alternate Route to Urban Mathematics Teaching: The NYC Teaching Fellows Program

Laurel A. Cooley                                                                                           120


Analyzing the effects of a linguistic approach to the teaching of algebra: students tell “stories of development” revealing new competencies and conceptions

Annalisa Cusi                                                                                                 124


Localization of Learning Objects in Mathematics

Valentina Dagiene &  Inga Zilinskiene                                                 129


Large-Scale Assessment as a Tool for Monitoring Learning and Teaching: The Case of Flanders, Belgium

Erik De Corte, Rianne Janssen & Lieven Verschaffel                          134


Connections between Mathematics and Arts & Culture: An exploratory Study with Teachers in a South African school

Joseph Dhlamini                                                                                             139


Mathematical Competitions for University Students

Alexander Domoshnitsky & Roman Yavich                                                    143


Internet Mathematical Olympiads

Alexander Domoshnitsky & Roman Yavich                                                    146


Essential Ingredients that form the basis for Mathematical Learning: What has 20 years of teaching mathematics to teenagers taught me?

Ruth J. Duffield                                                                                              149


Exploring mathematical identity as a tool for self-reflection amongst pre-service primary school teachers: “I think you have to be able to explain something in about 100 different ways”

Patricia Eaton & Maurice OReilly                                                                   153


Recognising Torres Strait Islander Women’s Knowledges in their Children’s Mathematics Education

Bronwyn Ewing                                                                                             157


Proportional Reasoning Models in Developing Mathematics Education Curricula for Prospective Elementary School Teachers

Beverly J. Ferrucci & Jack Carter                                                                  162


Modelling in Mathematics and Informatics: How Should the Elevators Travel so that Chaos Will Stop?

Andreas Filler                                                                                                166


Matrices and Routing

Ajda Fošner                                                                                                  172


Mathematics Professional Learning Communities:  Opportunities and Challenges in an Elementary School Context

Douglas Franks                                                                                              176


Impact on Student Achievement of Teacher Participation in K-8 Mathematics Professional Development

Todd Frauenholtz & Derek F. Webb                                                             180


One mathematical formula in the science textbook: looking into innovative potential of interdisciplinary mathematics teaching

Viktor Freiman                                                                                              184


The Role of the Music to Learn Geometrical Transformations

Daniela Galante                                                                                              189


A Cross-Cultural Comparison of Algebra 1 Students’ Achievement

Sofokli Garo                                                                                                  195


Can Early Algebra lead non-proficient students to a better arithmetical understanding?

Sandra Gerhard                                                                                             199


Problems to put students in a role close to a mathematical researcher

Nicolas Giroud                                                                                               202


Toward Calculus via Real-time Measurements

Tine Golež                                                                                                     204


Problem Fields in Elementary Arithmetic

Günter Graumann                                                                                           209


Disrupting linear models of mathematics teaching|learning

Barbara Graves & Christine Suurtamm                                                           215


Modelling tasks for learning, teaching, testing and researching

Gilbert Greefrath                                                                                            219


Transcribing an Animation: The case of the Riemann Sums

May Hamdan                                                                                                 223

Each and Every Student: The Stamford, Connecticut Model for Change in Mathematics

Mona Hanna, Carrie Chiappetta                                                                     227


Folding the circle in half is a text book of information

Bradford Hansen-Smith                                                                                 231


CAS and calculation competence of students

Dr. Rainer Heinrich                                                                                        235


Using Data Modeling at the Elementary Level to Make Sense of Doing Mathematics and Science

Marjorie Henningsen & Nisreen Ibrahim                                                         239


The use of notebooks in mathematics instruction: What is manageable? What should be avoided?  A field report after 10 years of CAS-application.

Peter Hofbauer                                                                                              242


Community Engagement: Home School Partnership

Marilyn Holmes                                                                                              246


Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives

Ye Yoon Hong, Suzanne Kerr, Sergiy Klymchuk, Johanna McHardy,

Priscilla Murphy, Sue Spencer, Mike Thomas & Peter Watson                       250


Linking Teachers and Mathematicians: The AWM Teacher Partnership Program

Pao-sheng Hsu, Suzanne Lenhart & Erica Voolich                                          255


Project work Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization?

Darka Hvastija & Jasna Kos                                                                          259


A Model to Develop Mathematics Education: Modify the Public Traditional Perceptions of Mathematics-Case of UAE Schools’ Principals

Hanan Innabi                                                                                                 262


A Four Phase Model for Predicting the Probabilistic Situation of Compound Events

Irma Jan & Miriam Amit                                                                                267


From a textbook to an e-learning course (E-learning or e-book?)

Antonín Jančařík & Jarmila Novotná                                                              272


Reflections on an Initiative to Improve Junior Secondary School Pupils’ Understanding of Number

Noel Johnston                                                                                                277

Preventing ‘Pushing for Privileged Passage’: A study of a charter school working to step back from tracking
            Tina Louise Johnston                                                                                      282


Creating and Utilizing Online Assignments in a Calculus Class

Veselin Jungic, Deborah Kent & Petra Menz                                                  287


Understanding Quadratic Functions Using Real World Problems and IT

Nakhshin A. Karim                                                                                        291


Individual Approaches in Rich Learning Situations Material-based Learning with Pinboards

Michael Katzenbach                                                                                      296


Does the parameter represent a fundamental concept of linear algebra?

Stefan-Harald Kaufmann                                                                                300


Using the Media as a Means to Develop Students’ Statistical Concepts
            Marian Kemp                                                                                                302


A program for reducing teacher's resistance to changes in curriculum in centralized education systems. An experience on changes of mathematics text books in Iran based on distinction results

Zohreh Ketabdar                                                                                           307


Professional Development for Mathematics Teachers Through Lesson Study

Azimeh Sadat Khakbaz                                                                                  312


An Apt Perspective of Analysis

Nanad Kishore & Ramesh Chandra                                                               317


Models for harnessing the Internet in mathematics education
Barry Kissane                                                                                                319

Cryptography and number theory in the classroom -- Contribution of cryptography to mathematics teaching
            Katharina Klembalski                                                                                    323

Using History to Teach Mathematics

            Jacqui Klowss                                                                                               328


The use of technology to motivate, to present and to deepen the comprehension of math

            Damjan Kobal                                                                                               331


Experience with solving real-life math problems in DQME II project

            Koreňová L., Dillingerová M., Vankúš P., Židová D                                       333



Workshop: Some interesting math problems for high school students solved by graphic calculators CASIO

            Koreňová L., Židová D                                                                                  335


Accompanying “in-service teaching” internships of prospective mathematics teachers – a model for encouraging exchange between theory and practice using the triple coaching approach
            Sebastian Kuntze, Anke Wagner & Claudia Wörn                                          336

The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects: Two assessment results

            Li Tsung Wen Kuo, Wei-Hao Cheng & Chih-Chen Kao                                341


Interactive PDF Documents in Math Education. Focused on Tests for Differential Equations

            Silvie Kuráňová                                                                                             347


Helping a Young Child Connect Fact Family Addition and Subtraction using Tools

            Terri L. Kurz, H. Bahadir Yanik & Jorge Garcia                                             353


The van Hiele Phases of Learning in studying Cube Dissection

            Shi-Pui Kwan & Ka-Luen Cheung                                                                 358


Elementary Students’ Construction of Proportional Reasoning Problems: Using Writing to Generalize Conceptual Understanding in Mathematics

            Millard Lamm & David K. Pugalee                                                                364


How to teach modeling in mathematics classrooms? The implementation of modeling tasks. Comparing learning arrangements and teacher methods with respect to student’s activities

            Céline Liedmann                                                                                            368


A Collaborative Model for Calculus Reform—A Preliminary Report

            Po-Hung Liu, Ching-Ching Lin, Tung-Shyan Chen, Yen-Tung Chung,

            Chiu-Hsiung Liao, Pi-Chuan Lin, Hwai-En Tseng & Ruey-Maw Chen            372


Changes in the North Carolina Mathematics Curriculum: A Comparative Study, 1920s, 1930’s with 2003
            Corey Lock & David Pugalee                                                            376


Bridging the gap between technology design and school practice: a specific experiment within the ReMath Project

            Laura Maffei                                                                                      378


The Effect of Rephrasing Word Problems on the Achievements of Arab Students in Mathematics

            Asad Mahajne & Miriam Amit                                                                       383


Open-Ended Approach To Teaching And Learning Of High School Mathematics

            Radley Kebarapetse Mahlobo                                                                        386


Mathematics and Mathematics Education Development in Finland: the impact of curriculum changes on IEA, IMO and PISA results 

            George Malaty                                                                                              390


A class practice to improve student’s attitude towards mathematics
            Maria Flavia Mammana & Mario Pennisi                                                        395


Identifying Modelling Tasks

            Stefanie Meier                                                                                               399


Paper&Pencil Skills in the 21st Century, a Dichotomy?

            Hartwig Meissner & Annabella Diephaus                                                        404


How to Solve It

            Luigi Menna                                                                                                   409


Tasks for tests and A-levels using CAS
            Heidi Metzger-Schuhäker                                                                              413


Models of Mathematics Curriculum Development in Egypt

            Fayez M. Mina                                                                                              417


To Teach Combinatirics, Using Selected Problems

            Laurenţiu Modan                                                                                           420


Modelling Geometric Concepts Via Pop-Up Engineering

            Vivekanand Mohan-Ram                                                                               423


Exploring the mathematics that children read in the world: A case study of Grade 8 learners in a South African School

            Lesego Brenda Mokotedi                                                                              427


On Teaching Quality Improvement of a Mathematical Topic Using Artificial Neural Networks Modeling (With a Case Study)

            Hassan. M. Mustafa  & Ayoub Al-Hamadi                         431


New Forms of Assessment in the South African Curriculum Assessment Guidelines: What Powers do Teachers Hold?

            Willy Mwakapenda                                                                                        436


Investigating Elementary Teachers’ Mathematical Knowledge for Teaching Geometry: The Case of Classification of Quadrilaterals

            Dicky Ng                                                                                                      440


Mathematics Teacher TPACK Standards and Revising Teacher Preparation

            Margaret Niess                                                                                              445


Balancing the Use of Technology and Traditional Approaches in Teaching Mathematics within Business Courses

            Mehryar Nooriafshar                                                                                      450


Chapter-spanning Review: Teaching Method for Networking in Math Lessons

            Swetlana Nordheimer                                                                                    454


Students’ knowledge of Application of Mathematics – From Diagnostics to Innovations
            Reinhard Oldenburg                                                                                       459


From Physical Model To Proof For Understanding Via DGS: Interplay Among Environments

            Iman M. Osta                                                                                                464


Using ClassPad-technology in the education of students of electrical engineering (Fourier- and Laplace-Transformation)

            Ludwig Paditz                                                                                                469


Reflective practices – a means to instil a deep learning approach to mathematics or another time consuming fad? Work-in-progress.

            Mandy Parnell                                                                                               475


A Discussion of different teaching strategies adopted during a Statistics tutorial
            Vasos Pavlika                                                                                                477


The Learning of Mathematics for Limited English Proficient Learners: Preparation of Doctoral Level Candidates

            Theresa Perez & David K. Pugalee                                                                481


Cooperative Learning and Peer Tutoring to Promote Students’ Mathematics Education

            Angela Pesci                                                                                                  486


Building leadership capacity in the development and sharing of mathematics learning resources, across disciplines, across universities

            Anne L. Porter                                                                                               491


The use of visualization for learning and teaching mathematics 

             Medhat H. Rahim & Radcliffe Siddo                                                            496


Clearness as a Principle of  the Teaching of Mathematics 

            Ildar S. Safuanov & Irina G. Shamsutdinova                                                  501


Creative mathematical activity of the students in the Model of Differentiated Teaching in Russian Federation

            Ildar S. Safuanov & Valery A. Gusev                                                           505



Innovations in Podcasting and Screencasting Course Materials To Bring Mathematics to Life

            Paula Savich & Sandra Pierce                                                                        509


Concept Literacy in Mathematics and Science:  experiences with the development and use of a multilingual resource book in Xhosa, Zulu, English and Afrikaans in South Africa

Marc Schäfer                                                                                                 512


Single Sex Mathematics Classes: A Critical Analysis of the Impact at a Secondary School

Angelique Seifert & David K. Pugalee                                                            517


Visual Modeling of Integrated Constructs in Mathematics As the Base of Future Teacher Creativity

Eugeny Smirnov, Sergei Burukhin & Irina Smirnova                                        520


Using Technology to Discover and Explore Linear Functions and Encourage Linear Modeling

Tanja Soucie, Nikol Radović , Renata Svedrec & Helena Car                         524


Virtual Manipulatives: Design-based Countermeasures to Selected Potential Hazards

William R. Speer                                                                                            526


Teaching for the objectification of the Pythagorean Theorem

Panagiotis Spyrou                                                                                          530


Mathematics education reform: The role of coherence within the complexity of change
            Christine Suurtamm & Barbara Graves                                                           535


Mathematics games: Time wasters or time well spent? 

Paul Swan and Linda Marshall                                                                       540


On Evaluation Problem of the Quality of Educational Models

Vladimir A. Testov                                                                                         545


How Can a System with no Public Exams be Fair?

Kerry J Thomas                                                                                             548


Teaching Mathematics in Eniaio Lykeio (Unified Upper-Secondary Education) with the use of New Technologies

Eleni Tsami                                                                                                    554


Math lessons for the thinking classrooms

Ariana-Stanca Văcăreţu                                                                                 559


Good classroom practice – how a new journal supports this

            Rüdiger Vernay                                                          Please Note Page      335

A Stochastic Model for the Process of Learning

Michael Gr. Voskoglou                                                                                  565


Developing explanatory competencies in teacher education

Anke Wagner, Claudia Wörn & Sebastian Kuntze                                          570


Improving Student Interest, Mathematical Skills, and Future Success through Implementation of Novel Mathematics Bridge Course for High School Seniors and Post-secondary Students
           Derek Webb, Glen Richgels, Marty J. Wolf, Todd Frauenholtz &

           Ann Hougen                                                                                                   575


Family Maths and Complexity Theory

Paul Webb & Pam Austin                                                                              579


Elementary Mathematics from an Advanced Standpoint and Elementary Views on Advanced Mathematics
           Ysette Weiss-Pidstrygach                                                                               584


DeltaTick: Applying Calculus to the Real World through Behavioral Modeling

Michelle H. Wilkerson-Jerde & Uri Wilensky                                                 587


Algebraic Thinking- More to Do with Why, Than X and Y

Windsor W.J.J                                                                                               592


A New Pedagogical Model for Teaching Arithmetic.

David Womack                                                                                             596


Solids of Revolution – from the Integration of a given Function to the Modelling of a Problem with the help of CAS and GeoGebra
           Otto Wurnig                                                                                                   600


A way of computer use in mathematics teaching -The effectiveness that visualization brings-

Shuichi Yamamoto & Naonori Ishii                                                                606


Using physical experiments in mathematics lessons to introduce mathematical concepts
           Simon Zell                                                                                                      611





Papers Accepted for the Proceedings but not Presented at the Conference


Hypothesis Aided Approach to the Instruction of the Limit of a Function          

Ivan Mezník                                                                                                               615


Using Digital Video to Strengthen Student Learning of Mathematics
Virginia (Ginny) Keen



Photos of the participants in Dresden


Working Group Reports


1. Technology: A summary of themes and key ideas discussed*

Barry Kissane, Mehryar Noorisfshar & Naikshin Karim

2. Comparative Education

George Malaty, Miriam Amit, Filippo Spagnolo And Franco Favilli

3.  Innovation Working Group

Willy Mwakpenda, Bronwyn Ewing, Ariana Vacaretu

4. Teacher Education and Development

Marjorie Henningsen, Arjorie Henningsen, Beverly Ferrucci, Angela Pesci

5. „Problem Solving“

Günter Graumann

6. Applications and Statistics

Members: Ivan Meznik, Gail Burrill  & Viktor Freiman