Electronic Proceedings of the
August, 69, 2001 — University of Klagenfurt, Austria
Proceedings in book version
At the Viennese publishing house öbv & hpt, two volumes have been published in 2002. The books contain a sometimes shorter version of the contribution but cover the main ideas of the authors.
Technology in Mathematics Teaching
Plenary Lectures and Strands
(ed. by Manfred Borovcnik – Hermann Kautschitsch)
Vol 25 of Schriftenreihe Didaktik der Mathematik — ISBN 3209038473
Technology in Mathematics Teaching
Special groups and working groups
(ed. by Manfred Borovcnik – Hermann Kautschitsch)
Vol 26 of Schriftenreihe Didaktik der Mathematik — ISBN 3209038481
Link to the publishing house
Book 1 on Plenary lectures and strands (vol 25)
Book 2 on Special groups and working groups (vol 26)
In August 2001, the University of Klagenfurt hosted the Fifth International Conference on Technology in Mathematics Teaching – the ICTMT 5. Situated at the junction of three grand European cultures, the German, the Slavic, and the Roman culture, Carinthia has always been a transit region for Europe, important paths through the Alps are crossing the country. This has welcome symbolic implications for a conference like the ICTMT 5 to serve also as junction; as junction of – at least – three grand cultures of mathematics and mathematics teaching, i.e. Anschauliche Mathematik, experimental mathematics, and computer aided mathematics.
The University of Klagenfurt is the youngest institution of tertiary education in Austria, established in 1972, an offspring of a personal idea and vision of the former vice mayor of Klagenfurt, Hofrat Hans Romauch which was later supported by the central government, by the federal state of Carinthia, and by the city of Klagenfurt. „Bildungswissenschaften“ in the Humboldtean sense was the principal idea behind the foundation of the Klagenfurt University – a radical new approach to science focussing on „Didaktik“ and teaching – a teaching research institute of European rank was the desired goal. Whilst developments took a different turn, the concept and educational philosophy of „Bildungswissenschaften“ are still much alive at our university. Consistent with this idea, the university hosted an institute for teaching technology and several professors for didactics at the mathematics department right from the beginning.
In 1981, we organised a workshop on visualisation in mathematics teaching in cooperation with the visualisation groups at Kassel and Koblenz. And 15 more workshops were to follow over the years. Our equipment in those times looks outdated from today’s perspective, we did not even have a suitable computer for teaching. We worked with a simple video camera and a trick table. Our ideas in those times, however, are still relevant, as a whole series of films prove. The Fifth ICTMT, thus, coincides with our 20^{th} anniversary of this first workshop.
Anschauung and Experimental mathematics, our mottos from the beginning, once meant a cut compared to the then prevailing New Math, which was heavily theory, loaded. In general, such cuts lead to crises, which in the Greek origin means „danger and potential at the same time“. A parallel cut is forced by the use of technology in teaching that leads to great changes. History tells us that it is of no use to defend stubbornly the old; see e.g. the controversy abacus – Adam Riese in the 16^{th} century. Thus, we have to take up the challenge of the new; the challenge of the New Technologies. We should focus on maximising the potential, minimising the dangers – these proceedings should contribute to that process.
The single sessions of the conference were attributed to strands, special groups, and working groups. It was the plan of the organisers and an international board preparing the conference to structure the presentations into strands each devoted to an important topic. Each strand should have a renowned plenary speaker as a leading figure. Moreover, to offer a plenty of discussion and group work, there are a number of special groups and working groups organised. Working groups were intended to focus around a common theme, while special groups should be working groups signified by a common tool. Presentations in special and working groups were much shorter and allowed for intense discussions and group work.
The strands were:
Integration of IC technologies into learning processes – chaired by J.B. Lagrange, with the focus on the change of cognitive notions by new contents and new tools.
Technologically presented learning material  chaired by Bernard Winkelmann; devoted to questions like: Criteria for the use of technologically presented material for the teaching of mathematics and how to implement these.
Technology in teacher education  chaired by J. Carvalho e Silva; with the accent on teachers and how they are going to change their practice and how they may be influenced by teacher inservice.
Changes in Geometry and Algebra via DGS and CAS  chaired by H.G. Weigand; covering questions like the change of mathematics, change of curricula, change of presentation, change of concepts to acquire, and change of assessment.
Cooperation between DGS and CAS  chaired by M. Garbayo Moreno; devoted to an aspect as far highly neglected; how to link these tools boosting thus the benefit of technologies.
Mathematical modelling with technology  chaired by J. Sharp; devoted to new opportunities of working with concrete situations, simplifying the calculations, and giving insight with simulations.
The global perspective of information technology  chaired by P. Bender; informing about the potential but also about dangers and limitations of the New Technologies.
This volume is devoted to the plenary sessions and presentations of all these strands. The results of the efforts in the special and working groups will be published in the next volume (volume 26). Moreover, in accordance with the interactive character of many presentations, there will be a CDROM with all the contributions in a much longer version with many valuable links to sources all over the Internet.
This conference could only be carried through by the combined effort of many. We had an excellent technical support from our computer centre, especially from Peter König there who also guided us through the cliffs of the proceedings. Our Internet specialist was Heinz Pozewaunig.
We express our gratitude and thanks to the delegates who contributed so many challenging ideas so that we will have a long time to digest them. A great thank you also to the persons chairing the various sessions; they, too, gave a lot of effort in preparing the conference and the proceedings. Last but not least, we thank Prof. A. Oldknow, honorary president of this conference.
The local organisers tried to offer a platform for the exchange of ideas. We hope you can use it to improve the benefit of the New Technologies in teaching for those whom we teach. We wish you challenging days in reading this and the following book with the results of ICTMT 5 in the interest of our science.
Finally, two photos as a memory to our landscape and nature we missed now for more than one year in preparing the conference and the proceedings.
Hermann Kautschitsch
Goto 



In August 2001, the University of Klagenfurt hosted the Fifth International Conference on Technology in Mathematics Teaching – the ICTMT 5. Situated at the junction of three grand European cultures, the German, the Slavic, and the Roman culture, Carinthia has always been a transit region for Europe, important paths through the Alps are crossing the country. This has welcome symbolic implications for a conference like the ICTMT 5 to serve also as junction; as junction of – at least – three grand cultures of mathematics and mathematics teaching, i.e. Anschauliche Mathematik, experimental mathematics, and computer aided mathematics.
The University of Klagenfurt is the youngest institution of tertiary education in Austria, established in 1972, an offspring of a personal idea and vision of the former vice mayor of Klagenfurt, Hofrat Hans Romauch which was later supported by the central government, by the federal state of Carinthia, and by the city of Klagenfurt. „Bildungswissenschaften“ in the Humboldtean sense was the principal idea behind the foundation of the Klagenfurt University – a radical new approach to science focussing on „Didaktik“ and teaching – a teaching research institute of European rank was the desired goal. Whilst developments took a different turn, the concept and educational philosophy of „Bildungswissenschaften“ are still much alive at our university. Consistent with this idea, the university hosted an institute for teaching technology and several professors for didactics at the mathematics department right from the beginning.
In 1981, we organised a workshop on visualisation in mathematics teaching in cooperation with the visualisation groups at Kassel and Koblenz. And 15 more workshops were to follow over the years. Our equipment in those times looks outdated from today’s perspective, we did not even have a suitable computer for teaching. We worked with a simple video camera and a trick table. Our ideas in those times, however, are still relevant, as a whole series of films prove. The Fifth ICTMT, thus, coincides with our 20^{th} anniversary of this first workshop.
Anschauung and Experimental mathematics, our mottos from the beginning, once meant a cut compared to the then prevailing New Math, which was heavily theory, loaded. In general, such cuts lead to crises, which in the Greek origin means „danger and potential at the same time“. A parallel cut is forced by the use of technology in teaching that leads to great changes. History tells us that it is of no use to defend stubbornly the old; see e.g. the controversy abacus – Adam Riese in the 16^{th} century. Thus, we have to take up the challenge of the new; the challenge of the New Technologies. We should focus on maximising the potential, minimising the dangers – these proceedings should contribute to that process.
The single sessions of the conference were attributed to strands, special groups, and working groups. It was the plan of the organisers and an international board preparing the conference to structure the presentations into strands each devoted to an important topic. Each strand should have a renowned plenary speaker as a leading figure. Moreover, to offer a plenty of discussion and group work, there are a number of special groups and working groups organised. Working groups were intended to focus around a common theme, while special groups should be working groups signified by a common tool. Presentations in special and working groups were much shorter and allowed for intense discussions and group work.
The five special groups comprised:
Derive, TI89/92 and other CAS — organised by Josef Böhm, Bernhard Kutzler, Marlene TorresSkoumal; contributions were based on teaching experience of presenters focusing on Computer Algebra Systems exploiting their advantages.
DGS — Dynamic Geometry Software — organised by Adrian Oldknow; with the accent on illustrating the potential of wellknown software of this type but also introducing some new, nationally created packages.
Handheld technology — organised by Jan Kaspar and Alison ClarkJeavons; the presentations centred on the graphing calculator TI83 illustrating its capacity and reflecting the overlap and borderline to PCs.
Spreadsheets — organised by Erich Neuwirth; showing the wide range of possibilities of this type of software focusing also on questions of efficiency of input and output in availability and easiness of usage in comparison to CAS.
Traditional programming — In the age of CAS — organised by Karl Josef Fuchs; pleading for traditional programming as a basis to create a special type of thinking, which is highly valuable even if we are in the age of CAS.
The six working groups comprised:
Computer animation, visualization and experimental mathematics — organised by Gert Kadunz; covering issues from mathematics education including questions like how to establish learning processes by discovery activities on the computer or in specially designed learning environments.
System dynamics and systems thinking — organised by Günther Ossimitz; focusing on the special kind of thinking in systems and the open modelling approach from system dynamics ranging from a crash course in that field up to presenting teaching experience.
Continued professional development — organised by Edward Laughbaum; reporting about various programs to integrate technology use into teacher inservice training putting the accent on establishing teacher networks to exchange their ideas and problems.
Probability simulators and data analysis programs — organised by Manfred Borovcnik; dealing with difficult curricular topics by special educational software, forming intuitive ideas by training programs, supporting understanding by the simulation technique, or backing the whole course by a suitable programming language.
Computer technology in mathematics teaching: Dangers and limitations — organised by Hartmut Köhler; facing problems that may arise from an alltoo naïve approach, e.g. with the formation of adequate concepts and the danger of technologically caused new misconceptions; or the widespread overrating of executing actions as opposed to understanding actions.
Curricular questions — organised by Rolf Neveling; discussing new aspects of learning with technologies and the necessary curricular change including a revision of the teacher’s role.
This volume contains the keynote papers and results of discussions of the special and working groups. The reader might also be interested in the plenary sessions and contributed papers of the conference. These are contained in the first volume (volume 25) of the proceedings. We summarise the strands and their goals briefly in what follows. Moreover, in accordance with the interactive character of many presentations, there will be a CDROM with all the contributions in a much longer version with many valuable links to sources all over the Internet. The strands were:
Integration of IC technologies into learning processes – chaired by J.B. Lagrange, with the focus on the change of cognitive notions by new contents and new tools.
Technologically presented learning material  chaired by Bernard Winkelmann; devoted to questions like: Criteria for the use of technologically presented material for the teaching of mathematics and how to implement these.
Technology in teacher education  chaired by J. Carvalho e Silva; with the accent on teachers and how they are going to change their practice and how they may be influenced by teacher inservice.
Changes in Geometry and Algebra via DGS and CAS  chaired by H.G. Weigand; covering questions like the change of mathematics, change of curricula, change of presentation, change of concepts to acquire, and change of assessment.
Cooperation between DGS and CAS  chaired by M. Garbayo Moreno; devoted to an aspect as far highly neglected; how to link these tools boosting thus the benefit of technologies.
Mathematical modelling with technology  chaired by J. Sharp; devoted to new opportunities of working with concrete situations, simplifying the calculations, and giving insight with simulations.
The global perspective of information technology  chaired by P. Bender; informing about the potential but also about dangers and limitations of the New Technologies.
The contributions and the discussions at the conference clearly showed that these New Technologies offer new possibilities with reference to elementary mathematics and school mathematics on the one hand and to applications of mathematics on the other hand. With respect to school mathematics, we get new approaches based on technology for understanding elementary concepts including new ways to establish understanding numbers and understanding geometric space for our students. Furthermore, an algorithmic understanding of mathematical concepts opens up completely new ways of thinking. With the focus on applications of mathematics, we come up with more flexible concepts and modelling techniques by the help of special software – be it realized on the PC or on handheld technology. The experimental face of the concepts extends mathematics, its understanding, and its applicability. This helps to solve problems closer to reality than without technology. Moreover, this leads to new answers to problems in the form of algorithmic descriptions instead of mere numbers or formulae.
The potential of the New Technologies will not be realized per se but only by specific efforts. This necessitates more and more qualified mathematicians and, one level below, or better, before, more qualified teachers of mathematics. There is an increasing demand for persons who are really capable to exploit the New Technologies, which gives a challenge and a chance to our youth.
The contributions of the delegates of ICTMT 5 are very close to teaching in class, to applications of mathematics, or to establish new networks of continued professional development of teachers. There is a wide range of new ideas and activities on new contents, new teaching approaches, and a new role for teachers in class, and new efforts to cope with problems on the side of teachers in the two volumes of the proceedings.
This conference could only be carried through by the combined effort of many. We had an excellent technical support from our computer centre, especially from Peter König there who also guided us through the cliffs of the proceedings. Our Internet specialist was Heinz Pozewaunig. We express our gratitude and thanks to the delegates who contributed so many challenging ideas so that we will have a long time to digest them. A great thank you also to the persons chairing the various sessions; they, too, gave a lot of effort in preparing the conference and the proceedings. Last but not least, we thank Prof. A. Oldknow, honorary president of this conference.
The local organisers tried to offer a platform for the exchange of ideas. We hope you can use it to improve the benefit of the New Technologies in teaching for those whom we teach. We wish you challenging days in reading this and the preceding book with ICTMT 5’s results in the interest of our science.
Schriftenreihe Didaktik der Mathematik, vol. 25. öbv & hpt, Vienna 2002.
ISBN 3209038473
Strand 1: Integration of IC technologies into learning processes Chair: JeanBaptiste Lagrange 


Plenary: Tommy Dreyfus 
Computerrich learning environments and the construction of abstract algebraic concepts 

Mara Alagic Rebecca Langrall 
Differentiating mathematics instruction through technology: Deliberations about mapping personalized learning 

Mária Bakó 
Mathematical software in the educational process of the French and Hungarian teachers 

John Berry Andy Smith 
Observing student working styles when using graphic calculators 

Neil Challis, H. Gretton M. Robinson, St. Wan 
Diagnosing mathematical needs and following them up 

Roger Fentem Jenny Sharp 
The impact of training for students on their learning of mathematics with a graphical calculator 

Ruth Forrester 
Data collection and manipulation using graphic calculators with 1014 year olds 

Jenny Gage 
The role of the graphic calculator in early algebra lessons 

Samer Habre 
The ODE curriculum: traditional vs. nontraditional. The case of one student 

Christian Thune Jacobsen 
Experimental mathematics 

Gisèle Lemoyne François Brouillet Sophie René de Cotret 
Cognitive and didactic ideas designed in TIC environments for the learning and teaching of arithmetic and prealgebra knowledge and concepts 

MarieThérèse Loeman 
To learn from and make history of maths with the help of ICT 

Claus MeyerBothling 
Thinking the unthinkable — Understanding 4 dimensions 

Hitoshi Nishizawa Y. Kajiwara T. Yoshioka 
Remedial education of quadratic functions using a webbased online exercise system 

John Pappas, E. Koleza J. Rizos, C. Skordoulis 
Integrating mathematics, physics and Interactive Digital Video 

Neil Pitcher 
How to use computerbased learning effectively in mathematics 

Carel van de Giessen 
The visualisation of parameters 

Henk van der Kooij 
Functional algebra with the use of the graphing calculator 

Strand 2: Technologically presented learning material Chair: Bernard Winkelmann 


Plenary: Alison ClarkJeavons Rosalyn Hyde 
Developing a technologically rich scheme of work for 11 – 12 year olds in mathematics for electronic delivery 

May C. Abboud 
Animation — A tool for understanding polar coordinates 

Douglas Butler 
Adding a sparkle to classroom teaching — Using Word, the Internet, and objectoriented software 

Peter Cooper B. Magan, K. M. Dilks 
Design of content independent instructional systems 

Timo Ehmke 
Geometria: A tool for the production of interactive worksheets on the Web 

Mary Susan Hall 
Creating and teaching online mathematics courses 

Judith H. Hector 
Teaching probability and statistics via the Internet 

Duncan A. Lawson J. Reed, S. Tyrrell 
A Website for a mathematics support centre 

Pavel Leischner Karel Kabelka 
The collection of interactive solids figures and spatial situations in the Cabri  geometry 

Michael McCabe Ann Heal Alison White 
Computer assisted assessment of proof = Proof of CAA — New approaches to computer assisted assessment for higher level learning 

Vladimir Nodelman 
Parametric nature of mathematics’ objects and computer environment 

Nancy J. Priselac Stephen M. Priselac 
The Communiversity Project delivers a restructured precalculus distance learning course 

Alfred Schreiber 
Project Zero: Developing online material for mathematics teacher education 

Peter van Wijk Hans Stam 
Mathematics and the Internet 

A. Waterson E.R. Smith 
Online mathematics teaching: The development of student instructor interaction 

Strand 3: Technology in teacher educationChair: Jaime Carvalho e Silva 


Plenary: Branca Silveira 
Teacher training: The role of technology 

George Adie Bogdan Zoltowski 
Practical aspects of CAS using sinusoidal functions 

Adnan Baki 
Investigating teachers’ perceptions on their preparation to use IT in classroom instruction 

Elizabeth Belfort Luiz C. Guimarães Rafael Barbastefano 
Using computers in mathematics teacher training programs: A reflection upon an experiment 

Primo Brandi Anna Salvadori 
A modern approach to limit processes 

Jaime Carvalho e Silva José Carlos Balsa Maria José Ramos 
Internet as a tool in the preparation of future mathematics teachers 

Isabel Fevereiro Maria C. Belchior 
Changing the classroom practices — The use of technology in mathematics teaching 

Henryk Kakol 
Integrated teaching mathematics with elements of computer science 

Konrad Krainer 
Innovations in mathematics, science and technology teaching — IMST² — Initial outcome of a nationwide initiative for upper secondary schools in Austria 

Auxencia A. Limjap 
Current educational theories and New Technologies: Development of a training program for mathematics teachers in the Philippines 

Eva Milková Milan Turčáni 
Integrating ICT into the teaching and learning of discrete mathematics 

Walther A. Neuper 
What teachers can request from CASdesigners 

Rein Prank Eno Tonisson 
Computers in school mathematics — A pilot course for school teachers of mathematics in Estonia 

Ana Isabel Rosendo Jaime Carvalho e Silva 
Computers in mathematics education — An ongoing experience 

Nelson Urrego P. 
Using Derive for beginner courses of recursion theory 

Maria Zajac 
Internet materials in mathematics teaching 

Zulkardi Nienke Nieveen 
CASCADEIMEI: Web site support for student teachers learning — Realistic mathematics education in Indonesia 

Strand 4: Changes in geometry and algebra via DGS and CAS Chair: HansGeorg Weigand 


Plenary: Jean Flower 
Fitting from function families with CAS and DGS 

Denis Bouhineau J. –F. Nicaud, X. Pavard E. Sander 
A microworld for helping students to learn algebra 

HansJürgen Elschenbroich 
Teaching and learning geometry: Dynamic and visual 

Thomas Gawlick 
Dynamic notions for Dynamic Geometry 

Michalis Kourkoulos M.A. Keyling 
Selfcorrection in algebraic algorithms with the use of educational software: An experimental work with 1315 years old pupils 

Eoghan MacAogáin 
A CASindex applied to engineering mathematics papers 

Tom Macintyre 
Improving maths skills with CAS technology: A CAS project carried out in Scotland with 1617 year olds using TI92s 

Miroslaw L. Majewski M. E. Fred Szabo 
Integrating MuPAD into the teaching of mathematics 

Robert Mayes 
Absolute geometry: Discovering common truths 

Bronisław Pabich 
Magic polyhedrons 

Pavel Pech Jaroslav Hora 
Cubics and quartics on computer 

Expression equivalence checking in Computer Algebra Systems 

Strand 5: Cooperation between DGS and CAS Chair: Martín Garbayo Moreno 


Plenary: Eugenio RoanesLozano 
Boosting the geometrical possibilities of Dynamic Geometry Systems and Computer Algebra Systems through cooperation 

Yuriko Yamamoto Baldin Yolanda K. S. Furuya 
A study of conics with Maple V and CabriGéomètre II 

Francisco Botana José L. Valcarce 
The three and four bar linkages revisited: Graphs and equations 

Wolfgang Fraunholz 
A computer aided learning environment of linear algebra using the computer algebra system MuPAD 

Bridging the gap between dynamic geometry and computer algebra: The case of loci discovery 

Strand 6: Mathematical modelling with technology Chair: Jenny Sharp 


Plenary: John Berry 
The use of technology in developing mathematical modelling skills 

George Adie Bengt Löfstrand Bogdan Zoltowski 
Differential equations instead of analytical methods 

G. Albano C. D’Apice M. Desiderio 
Laplace Transform and electrical circuits: An interdisciplinary learning tool 

Burkhard Alpers 
Mathematical application projects for mechanical engineers — Concept, guidelines and examples 

Brigitta Aspetsberger Klaus Aspetsberger 
Cross curriculum teaching and experimenting in math & science courses using New Technology 

Per Broman 
Mathematical modelling with use of Cabri 

André Heck André Holleman 
Modelling human growth 

André Heck André Holleman 
Investigating bridges and hanging chains 

Iavor V. Hristov 
Model of deformations of fluid particles due to electric field 

Duncan A. Lawson J. H. Tabor 
Introducing models and modelling through spreadsheets 

Pavel Prazak Antonin Slaby 
Software Maple in the teaching of ODE’s 

Mazen Shahin 
Discrete delayed population models with Derive 

Strand 7: The global perspective of Information Technology Chair: Peter Bender 


Plenary: Walter Oberschelp 
Chances and limits for teaching in the information age — Human mind models and society demands 

John Berry Roger Fentem 
Investigation into student attitudes to using calculators with CAS in learning mathematics 

Stefanie Krivsky 
The potential of the Internet for innovations in didactics of mathematics 

Ewa Lakoma 
On the impact of handheld technology on mathematics learning — From the epistemological point of view 

Tatyana Oleinik 
A project on the development of critical thinking by using technology 

Tadeusz Ratusinski 
The role of the computer in discovering mathematical theorems 

Monika Schwarze 
Selfguided learning — Scenarios and materials from a German pilot project 

Angela Schwenk Manfred Berger 
Mathematical abilities of university entrants and the adapted use of computers in engineering education 

John Searl 
Of Babies and Bath Water 

Schriftenreihe Didaktik der Mathematik, vol. 26. öbv & hpt, Vienna 2002.
ISBN 3209038481
Special group 1: Derive, TI89/92 and other CASOrganisers: Josef Böhm, Bernhard Kutzler, Marlene TorresSkoumal 


How to make tests for students that are using a CAS tool (TI89) 


Halil Ardahan Yaşar Ersoy 
Issues on integrating CAS in teaching mathematics: A functional and programming approach 

Detlef Berntzen 
Animiertes GrafikenZusammenspiel von PC und TC in der Mathematik 

Josef Böhm 
From pole to pole — A numerical journey to an analytical destination 

John Cosgrave 
Fermat’s Little Theorem: A thing of beauty is a joy for ever 

Guido Herweyers Dirk Janssens 
Elimination of parameters and substitution with computer algebra 

Theoremabased TI92 simulator for exploratory learning 


KarlHeinz Keunecke 
Krümmung als Grenzwert — Curvature as limit 

Heiko Knechtel 
Mathematics with graphic and symbolic calculators — Teacher training in Lower Saxony 

Josef Lechner 
Standardizing the normal probability distribution — An anachronism?! 

Carl Leinbach 
Using a CAS to teach algebra — Going beyond the manipulations 

Alex J. Lobregt 
Introducing Fourier Series with Derive 

Wolfgang Pröpper 
The TI89/92 as a tool for analytic geometry 

Karsten Schmidt 
The use of CAS in the Thuringian school system: Present and future 

Rolf Wasén 
Computers and Computer Algebra Systems in engineering education 

Wilhelm Weiskirch 
Ortskurven — Loci 

Otto Wurnig 
Advantages and dangers in the teaching of stochastics by using CAS 

Special group 2: DGS — Dynamic Geometry Software Organiser: Adrian Oldknow 


Alison ClarkJeavons 
Why dynamic geometry software is such an effective tool in mathematics education 

Björn Felsager 
Through the looking glass: Euclid’s twin — The Minkowski Geometry 

Chantal GabrielRandour Jean Drabbe 
Cabri and anamorphoses 

Luiz Carlos Guimarães Rafael Barbastefano Elizabeth Belfort 
Tabulæ and Mangaba: Dynamical geometry with a distance twist 

Victor Lysytsya 
Computer experiments in the lecture of analytical geometry 

Valentyna Pikalova 
Learning explorations and its DG support in the geometry course for secondary schools 

Harry Silfverberg 
Voronoi diagrams produced by DGS as a tool in an educational study 

Herrmann Vogel 
Use of Cinderella in higher elementary geometry 

Special group 3: Handheld technologyOrganisers: Jan Kaspar and Alison ClarkJeavons 


Piotr Bialas 
Anova with the TI83 graphing calculator 

Piotr Bialas 
Linking graphing calculators to the Internet 

Jan Kaspar 
Programming as a tool for the precision 

Regis Ockerman 
Probability simulations with TI 83(p) 

Jarmila Robová 
Graphic solutions of equations and their systems 

Special group 4: SpreadsheetsOrganiser: Erich Neuwirth 


Deane Arganbright 
Creative spreadsheet graphics in mathematics teaching and modeling 

Piotr Bialas 
Spreadsheet uses in elementary statistics course 

Douglas Butler 
Why are spreadsheets so unfriendly? 

Kent M. Neuerburg 
Elementary statistics with spreadsheets 

Erich Neuwirth 
The spreadsheet paradigm as a new mathematical notation 

Robert S. Smith 
Spreadsheets across the curriculum 

Special group 5: Traditional programming — In the age of CAS Organiser: Karl Josef Fuchs 


Alfred Dominik 
Taylor Series and finding zeros with Mathematica and Derive 

Karl Josef Fuchs 
Programming in the age of CAS 

Karl Josef Fuchs Eva Vasarhélyi 
Problem—Analysis—Encoding—Testing About program and data structures 

Judith H. Hector 
Programming principles for mathematics and engineering students 

Wolfgang Lindner 
The digraphCASenvironment and corresponding elementary programming concepts 

Csaba Sárvári M. Klincsik, I. Hámori 
Combining CAS with authoring systems to create flexible learning environments 

Working
group 1: Computer animation,
visualization



Adding a sparkle to classroom teaching — Introducing Autograph 


Kate Mackrell 
The role of dynamic geometry packages in visualization and animation 

Susanne Saminger 
MeetMATH — Visualizations and animations in a didactic framework 

Ralf Schaper 
Mathematica graphics in the Internet: Additional lighting and clipping in LiveGraphics3D 

Grosio Stanilov Lidia Stanilova 
Mittels Computer zu mathematischen Entdeckungen 

Yulian Tsankov 
Cubic section by moving plane 

Working group 2: System dynamics and systems thinking Organiser: Günther Ossimitz 


Ernst Gebetsroither 
Modelling carbon dioxide pollution — The Austrian carbon balance model 

Stefan Gueldenberg Werner H. Hoffmann 
Leadership, management and management control — A system dynamics approach 

Guenther Ossimitz 
Systems thinking and system dynamics: A new perspective for math classes? 

Franz Schlöglhofer 
Teaching system dynamics modelling in secondary schools 

Working group 3: Continued professional development Organiser: Edward Laughbaum 


Gregory D. Foley 
Mathematics teacher development that works 

Rosalyn Hyde 
Creating a professional development network 

Mark L. Klespis 
An ongoing program of professional development in handheld technology for instructors of prospective teachers 

Technology as a vehicle for updating middle grades content and pedagogy 

Working group 4: Probability simulators and data analysis programs Organiser: Manfred Borovcnik 


Joachim Engel Marcus Otto 
Simulation and modelling with LispStat 

Giora Mann Nurit Zehavi 
Virtual experiments and probability 

Let the spreadsheet throw the dice—Spreadsheets as Monte Carlo simulation engines 


Marcus Otto Joachim Engel 
Design and use of a computer language for teaching mathematics — Some examples from statistics 

Peter Sedlmeier 
Improving statistical reasoning: A computer program for highschool students 

Piet van Blokland 
A sample of ideas in teaching statistics 

Working group 5: Computer technology in mathematics teaching: Dangers and limitationsOrganiser: Hartmut Köhler 

Working group 6: Curricular questions Organiser: Rolf Neveling 


Nils Fruensgaard 
Danish experiences with technology in mathematics teaching in upper secondary schools 

Addresses of authors 


Delegates of ICTMT 5 


Contents of volume 1 
Plenary Lectures and Strands 
