Special group 2:

DGS - Dynamic Geometry Software

ICTMT 5, Klagenfurt, 6-9 August 2001

(Schedule, tentative as of 28/6/2001)

Chair: Adrian Oldknow

Tuesday 8:30 - 9:15 Chair: Adrian Oldknow

Cinderella

Herrmann Vogel (Germany, vogel@mathematik.tu-muenchen.de)

Tuesday 9:30 - 10:15 Chair: Adrian Oldknow

Why DGS is such an effective tool in math education

Alison Clark-Jeavons (UK, aclarkjeavons@hotmail.com)

Tuesday 10:30 - 11:15 Chair: Adrian Oldknow

Through the Looking Glass: A glimpse of the Minkowski Geometry

Bjørn Felsager (Denmark, Bjoern.Felsager@Skolekom.dk)

Tuesday 16:15 - 17:00 Chair: Valentine Pikalova

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

Harry Silfverberg (Finland, tnhasi@uta.fi)

Tuesday 17:00 - 17:45 Chair: Bjørn Felsager

Functions as First-Class Dynamic Geometry Objects

Nicholas Jackiw (USA, njackiw@keypress.com)

Wednesday 9:30 - 10:15 Chair: Luiz Carlos Guimaraes

Cabri and Amorphoses

Chantal Randour (Belgium, randour-c@ibelgique.com)

Wednesday 10:30 - 11:15 Chair: Luiz Carlos Guimaraes

Cabri Java: A new communication and pedagogical tool

Jean-Jacques Dahan (France, jjdahan@wanadoo.fr)

Thursday 10:30 - 11:15 Chair: Harry Silfverberg

Tabulae and Mangaba: Dynamical Geometry with a Distance Twist

Luiz Carlos Guimaraes (Brazil, lcg@centroin.com.br)

Thursday 15:15 - 16:00 Chair: Nicholas Jackiw

University level Geometry Course and DG

Victor Lysytsya (Ukraine, lisitsa@univer.kharkov.ua)

Thursday 16:15 - 17:00 Chair: Nicholas Jackiw

Learning Explorations and its DG Support in Geometry Course for Secondary School

Valentine Pikalova (Ukraine, vpikalova@hotmail.com)

Abstracts:

Alison Clark-Jeavons, UK:

Why DGS is such an effective tool in math education

Many school curricula are advocating the use of dynamic gemoetry software. This presentation will outline why DGS is such an effective tool in the maths classroom, relating current views on how we learn in an ICT environment. The presenter will suggest generic ways in which the software can be used to enhance learning for understanding.

Jean Jaques Dahan, France:

Cabri Java: A new communication and pedagogical tool

1. Presentation of the software "Cabriweb": I will show how to create a Cabrijava applet (internet file) starting from a Cabri file and what it is possible to do with this applet (automatic animations and manipulation of the figure on the Web). 2. Exemples of problems under cabrijava: like "inversed problems" that can be shared with different persons in different countries (black boxes are particular "inversed problems" but I will present others of different levels). 3. How to write an article using this tool in order to get a dynamic communication between us.

Björn Felsager, Denmark:

Through the Looking Glass: A glimpse of the Minkowski Geometry

The Minkowski geometry offers the possibility of seeing well-known concepts from high school mathematics in a new perspective. The investigation of Minkowski Geometry requires the use of a Hyberbolic compass. This is introduced using Cabrii, which supports conic sections as a primitive geometric object. Thus the use of modern technology makes it feasible to investigate Minkowski Geometry in almost the same elementary way as Euclidean Geometry.

Luiz Carlos Guimarães, Brazil:

Tabulae and Mangaba: Dynamical Geometry with a Distance Twist

We report on the ongoing development of two complementary DGS, for plane and space geometry. The design briefs of both softwares were tailored bearing in mind the needs of distance teaching and Web communication. The current implementation is described in some detail, and we also discuss some of the issues that brought about the decision to engage in the project, as well as the implications for the technology driven teacher training program that provided the initial motivation for it.

Nicholas Jackiw, USA:

Functions as First-Class Dynamic Geometry Objects

The Geometer's Sketchpad version 4.0, arriving Summer 2001, includes support for functions as first-class objects in Dynamic Geometry, allowing users to define, combine, and differentiate functions symbolically, evaluate them numerically, and plot them through a variety of coordinate projections. While in isolation, these capabilities have been long present in other mathematics technologies (e. g. graphing calculators and CAS packages), their meaning is altered by the rich possibilities of interaction and manipulation afforded by the dynamic geometry environment. In this talk, Sketchpad's designer will summarize the research leading to these new developments, demonstrate some models of their classroom use observed in software field tests, and outline possibilities for how representations of functions as first-class dynamic geometry objects engage various strands of a secondary-level mathematics curriculum.

Victor Lysytsya, Ukraine:

University level Geometry Course and DG

Computer experiments within the course of "Analytical Geometry" are suggested. This course is taught at the Department of Mechanics and Mathematics of Kharkov National University. The most interesting are the tasks devoted to the geometrical sets of points on the plane. The experiments are constructed with the help of geometrical packet DG, which has been worked out at Kharkov State Pedagogical University.

Valentyna Pikalova, Ukraine:

Learning Explorations and its DG Support in Geometry Course for Secondary School

The article includes the analyses of DG support in geometry course for secondary school. As a result the Dynamic Demonstrative library was developed. It includes sketches for learning explorations in geometry. This library is recommended to use in geometry course by the minister of science and education of Ukraine. The attention is also paid to the methodological questions of implementing learning explorations in secondary school curriculum.

Chantal Randour, Belgium:

Cabri and anamorphoses

Des élèves de 17-18 ans ont traité le problème des anamorphoses, tant perspectives que celles utilisant des miroirs. La principale source utilisée est La Perspective Curieuse du Père Niceron (1652). La littérature peu abondante traite uniquement ce sujet sur le plan analytique. Nous avons préféré utiliser la géométrie descriptive pour concevoir des constructions simples pouvant être ensuite communiquées à Cabri. Les élèves ont ainsi réalisé des anamorphoses perspectives, coniques, cylindriques et pyramidales. Le travail mathématique s'est accompagné d'une recherche artistique en bibliothèque, dans les musées et sur internet. Un CD-rom (en power-point) montre quelques extraits de cette recherche. Une exposition des travaux a eu lieu dans l'école. Je me propose d'expliquer les différentes figures Cabri crées pour ce travail et de montrer le diaporama (+/- 20 min.) réalisé. Quelques modèles d'anamorphoses réalisées par les élèves seront visibles, ainsi qu'un pantographe (Scheiner-Parré) permettant de réaliser un type particulier d'anamorphoses coniques.

Harry Silfverberg, Finland:

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

The Voronoi diagram of a collection of points is a partition of space into cells, each of which consists of the points closer to one particular point than to any others. According to the prototype theoretical explanation students at the lowest van Hiele levels tend to classify geometrical figures on the basis of extent of the similarity of the figure and the visual prototypes. The poster will graphically show how well Voronoi diagrams and partitions based on the different selection of prototypes fit to the empirical data gathered in Silfverberg's research (1999) about the ways how students at the lowest van Hiele levels classified a given collection of triangles into acute, right, obtuse, equilateral and isosceles triangles.

Herrmann Vogel, Germany:

Use of Cinderella in higher elementary geometry

I will presentate a paper created with Cinderella, which deals with the "Wallace line" of a triangle and a generalaziation of this line. It demonstrate the possibilities of Cinderella how one can - illustrate well known geometry facts by using the moving mode or the animation mode, - find new suppositons by doing exercises, - create the envelope of a set of straight lines, - construct conics with certain conditions, - create algebraic curves of higher order.