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• Geometry expressions: an interactive constraint based symbolic geometry system

  303-310

  Philip Todd

  Views:

  24

  Dynamic geometry systems such as Geometers' SketchPad or Cabri are productive environments for the exploration of geometric relationships. They are, however, strictly numeric, and this limits their applicability where the interplay between geometry and algebra are being studied. We present Geometry Expressions – a dynamic symbolic geometry environment. While retaining the ease of use of a typical dynamic geometry environment, Geometry Expressions diverges by using constraints rather than constructions as the primary geometry specification mechanism and by working symbolically rather than numerically. Constraints, such as distances and angles, are specified symbolically. Symbolic measurements for quantities such as distances, angles, areas, locus equations, are automatically computed by the system. We outline how these features combine to create a rich dynamic environment for exploring the interplay between geometry and algebra, between induction and proof.

• Analyse von Lösungswegen und Erweiterungsmöglichkeiten eines Problems für die Klassen 7–11

  231-249

  Gabriella Ambrus

  Views:

  30

  Making several solutions for a problem i.e. the generalization, or the extension of a problem is common in the Hungarian mathematics education.
  But the analysis of a problem is unusual where the connection between the mathematical content of the task and of its different formulations is examined, solutions from different fields of mathematics are presented regarding the knowledge of different age groups, the problem is generalized in different directions, and several tools (traditional and electronic) for solutions and generalizations are presented.
  This kind of problem analysis makes it viable that during the solution/elaboration several kinds of mathematical knowledge and activities are recalled and connected, facilitating their use inside and outside of mathematics.
  However, an analysis like this is not unfamiliar to the traditions of the Hungarian problem solving education – because it also aims at elaborating a problem – but from several points of view.
  In this study, a geometric task is analysed in such a way.

• Experimentieren um einen Satz zu finden - vollständig separierbare Mosaike auf der Kugel und ihre Anwendungen

  297-319

  Éva Vásárhelyi

  Views:

  25

  This paper reports a case-study which took place within the project named "Inner differentiation and individualization by creating prototypes and analogies under consideration of motivational constraints (taking into account computer-based teaching and learning)" as a part of a pre-service teacher training at the University of Salzburg (Herber, H.-J. & Vásárhelyi, É.).
  The goal of the experiment was to help students to learn the fundamental concepts and basic constructions of spherical geometry using the Lénárt Sphere (a transparent plastic ball with construction-tools) and some self-made interactive worksheets with the Windows version of the dynamical geometry software Cabri.