Here are some very brief ideas on ways that I have used Geometer's Sketchpad scripts for hyperbolic constructions in the classroom. When time allows, I hope to provide more complete materials and discussion when I have the opportunity, perhaps in Summer 2001.
Students develop the scripts themselves.
The construction tools in hyperbolic geometry offer a great opportunity for students to do this, as the different constructions span a wide range of complexity. For example, in the Klein model, constructing segments and lines is trivial, dropping and raising perpendiculars is fairly straightforward, measuring angles can provide a nice application of hyperbolic trigonometry, and drawing circles is hard. Developing tools in any of the three models can serve as a great class project. Use the tools to illustrate hyperbolic theorems. A difficulty with non-Euclidean geometry is visualization.