There is no lack of suggestions concerning how Dynamic Geometry Software (DGS) may support heuristic approaches to problem solving. However, uses of DGS are often limited purely to a verifying role, in the sense that students are expected to vary or confirm empirically at the computer geometric data which are more or less given. By contrast, it seems worthwhile to seek other uses of DGS which go beyond mere confirmation so that the geometric situation is recognised in its particularity. This paper provides a case study that emerged from a project in which DGS formed an integral part of the pedagogical arrangement. The study is intended to show how the contrasting power of DGS might be utilised in a guided discovery setting.

Using Dynamic Geometry Software to Add Contrast to Geometric Situations – A Case Study

The theme of this thesis is dynamic geometry, a new way of exploring classical geometry using interactive computer software. This kind of software allows the user to make geometric constructions on a computer's screen. The constructions might consist of points, lines and conics whose positions have been constrained in various ways. The constraints, which may involve incidences, distances and angles, can be added and removed dynamically. For example, to force a line to always be incident on a point, the user would simply grab the line with the cursor and drop it onto the point. Any object whose position is not completely determined by the constraints can be grabbed and dragged around on the screen. The rest of the objects will then automatically self-adjust in order to keep the constraints satis ed. Dynamic geometry software is primarily used for teaching mathematics, but is useful in any situation where it is important to understand the geometric properties of a dynamic system. Over the last few years, a number of tools for dynamic geometry have been developed. Most of them have focused on elementary Euclidean geometry. In this thesis we present a new software that has been based entirely on projective concepts and thus allows us to illustrate the classical theorems of projective geometry. The software has also extensive support for di erent types of metrics, which makes it possible to explore both Euclidean and non-Euclidean geometry. In fact, the user is given direct access to the absolute elements which de ne the metric. Moreover, the system can handle objects in the complex projective plane, which permits, for example, the circular points in Euclidean geometry to be used in geometric constructions. We discuss how the user interface of a dynamic geometry system should be designed and we identify a number of problems and shortcomings which the user interfaces of all previous systems seem to su er from. Most of these defects are related to the fundamental problem of choosing the right solution of an underdetermined system of constraint equations. We show how this problems can be solved by letting the system automatically add extra constraints if necessary, and by using a richer internal representation based on oriented projective geometry. The thesis is written in English.

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Dynamic projective geometry

Despite its low relevance for teaching in schools the desideratum “Algebraic Curves’ has always been an issue within mathematical didactics. This article aims to continue this tradition with respect to a project oriented mathematics instruction by applying current dynamic geometry software (Cabri II+).

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A dynamic approach to 'simple' algebraic curves

Can learning of mental imagery skills for visualizing shapes be accelerated with feature masking? Chemistry, physics fine arts, military tactics, and laparoscopic surgery often depend on mentally visualizing shapes in their absence. Does working with ‘spatial feature-masks’ (skeletal shapes, missing key identifying portions) encourage people to use visualization strategies? This experimental study tested that hypothesis using an online computer game involving rotating and stamping a 3D cube on a 2D pattern. According to a chi-squared test, people who trained with 3D feature-masks reported using significantly more visual imagery strategies on a related visualization posttest. Spatial feature-masks provide a new building block for instructional designers to address educational outcomes involving visual imagery of shapes.

Feature Masking in Computer Game Promotes Visual Imagery

Napoleon triangles and adventitious angles

Discovering geometry with a computer, by Heinz Schumann and David Green. Pp. 282. £19.95 (accompanying disk £3.00, Mac or DOS). 1995. ISBN 0-86238-373-0 (Chartwell-Bratt).

Richard Bridge

Papers

Discovering geometry with a computer, by Heinz Schumann and David Green. Pp. 282. £19.95 (accompanying disk £3.00, Mac or DOS). 1995. ISBN 0-86238-373-0 (Chartwell-Bratt).