Prototyping "Systems that Explain Themselves" for Education

TL;DR

This paper discusses prototyping educational systems that can explain themselves, leveraging advances in computer theorem proving, and surveys the development process and current state of the ISAC prototype.

Contribution

It presents the process of prototyping self-explaining educational systems using theorem proving technology and provides a comprehensive survey of the ISAC prototype's development.

Findings

Advances in theorem proving enhance educational system capabilities.

Prototyping reveals user requirements and technical challenges.

The ISAC prototype demonstrates potential for self-explaining educational tools.

Abstract

"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.