Prototyping "Systems that Explain Themselves" for Education
This work addresses the problem of making mechanized proof technology accessible and useful for students and teachers in mathematics education, though it appears incremental as it focuses on prototyping and surveying an existing project.
The paper tackles the challenge of developing educational software that explains itself using computer theorem proving technology, specifically through the ISAC project, by prototyping and surveying its current state with code pointers and thesis citations.
"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.