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In the following, we list a couple of applications/components which may cooperate to form a distributed education session:
However, our experience shows [ATM96] that decent audio connections are much more important than video broadcasts because it is the voice which delivers the actual information contents of a lecture (provided that it is supported by the techniques presented below) while video usually just shows the lecturer's appearance. Fortunately audio can be transmitted in reasonable quality on generally available infrastructure (as demonstrated by the audio extensions of various WWW browsers).
Electronic whiteboards are certainly required for various presentation modes (gradual developments of chains of reasoning) but in the context of virtual classrooms their role is that of a supplement rather than that of a core presentation technology.
The essential characteristics of slide shows is that they are available in electronic format4 and can be transmitted with comparatively little bandwidth requirements, possibly ahead of the session. However, for their presentation the lecturer needs explicit control/synchronization facilities (even for automatically running slide presentations, "start/stop/rewind" buttons are necessary). This requires interfacing with the corresponding viewers/browsers/interpreters, which may be easy (freeware available in source code), possible (WWW browser plugins, application with "dynamic linking" facilities), or hard to impossible ("closed-world" applications).
The core of the system is an interpreter for the Mathematica programming language in which a large number of packages of mathematical algorithms have been implemented. Highly elaborated visualization features support the display of results in graphical form. Mathematica "notebooks" allows the typesetting of hypermedia documents that embed executable Mathematica code. "MathLink" allows (network) communication between Mathematica and external programs via serial channels.
A lecturer might use Mathematica simply in an interactive way, entering commands and running programs. The Mathematica window image should then be multicast to the audience. The lecturer might also prepare a Mathematica notebook and use the system as a presentation tool to display mathematical slides, possibly executing embedded Mathematica code. While it is also here possible to simply multicast the window image, a better use of network resources is to load the notebook on each participating host and invoke remote instances of Mathematica executing the local copies of the notebook. However, as described for slide shows, then synchronization with (or control by) the lecturer's presentation is required.
An even more advanced use of the system is possible, if the lecturer can switch control to the remote instances of Mathematica allowing the audience to run own test examples using the downloaded notebook ("exercise mode") and resume control when returning to presentation mode. For discussing questions and problems (see the next item), it would be also necessary to broadcast the particular screen image of a particular Mathematica invocation to lecturer and audience.
In a more general setting, the system might be also used in an "assessment mode" where questions are posed and results have to be computed/programmed/proved. These results have to be collected in stored for later retrieval from the lecturer.