  "Systems that Explain Themselves" appears a provocative wording, in
particular in the context of mathematics education -- it is as provocative as
the idea of building educational software upon technology from computer theorem
proving. In spite of recent success stories like the proofs of the Four Colour
Theorem or the Kepler Conjecture, mechanised proof is still considered somewhat
esoteric by mainstream mathematics. This paper describes the process of
prototyping in the ISAC project from a technical perspective. This perspective
depends on two moving targets: On the one side the rapidly increasing power and
coverage of computer theorem provers and their user interfaces, and on the
other side potential users: What can students and teachers request from
educational systems based on technology and concepts from computer theorem
proving, now and then? By the way of describing the process of prototyping the
first comprehensive survey on the state of the ISAC prototype is given as a
side effect, made precise by pointers to the code and by citation of all
contributing theses.
