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1 Introduction

Computer-supported training and education is one of the most promising application areas of the multimedia-augmented computing technologies that have emerged during the last years. A prominent example is the computer algebra system Mathematica^© [11] which has become a popular component of modern scientific education, not only because of its facilities for solving complex mathematical problems but also for its sophisticated support for typesetting, presentation, and visualization [3]. Mathematica allows to organize education material in form of notebooks, hypertext documents with executable components, which may serve as the basis of classroom presentations as well as of interactive exercises and of work assignments.

Apart from the apparent pedagogical benefits, computer-supported education has another dimension which arises from the more and more advancing integration of computing and communicating technologies: computers may serve as the enabling devices of education scenarios that overcome the limitations of physical proximity and lead to distributed ("virtual") classrooms. While these prospects are very appealing with a large number of potential applications [10], many approaches to tele-learning and tele-education still concentrate on a straight-forward extension of the traditional classroom model by broadcasting lectures with the help of conventional video-conferencing systems.

In our opinion, this focus on video is unfortunate, because it tends to overshadow the importance of other communication and cooperation technologies [4]. Actually, a short analysis reveals that in modern computer-supported education most of the information content of a lecture is not provided by video: verbal communication requires high quality audio connections (which may be even harder to establish over wide area networks than decent video support [1]) while non-verbal communication is nowadays more and more based on digital sources (electronic slide shows and computer-aided demonstrations).

There exist various approaches to provide integrated environments for distance learning that take these new facilities into account and combine video/audio technologies with shared software tools for distributed presentation and collaboration [8]. However, a major problem of such systems is how to integrate existing commercial software packages developed for particular science/education domains into the respective distributed frameworks.

In this paper, we present the design of a distributed environment for mathematical education based on Mathematica. This environment is not intended to compete with general purpose distance learning systems; instead it should be viewed as a case study that demonstrates how a special purpose application package can serve as a component of distributed education sessions considering the constraints of commercial software (limited control interfaces). Nevertheless we believe that this design already covers many important usage scenarios; in combination with public domain video/audio support based on Mbone [7] it may itself already present an interesting tool for practical purposes.

The rest of the paper is structured as follows: Section 2 gives a short overview on Mathematica and its essential building blocks. Section 3 sketches the overall design of the distributed environment. Section 4 deals with the problems that arise in the interaction with the Mathematica notebook frontend. Section 5 outlines the protocols handling the various operation modes of a distributed education session. Section 6 describes the multicasting communication interface in somewhat larger detail. Section 7 concludes the paper with an outline of our further plans.