Towards an Intelligent Tutor for Mathematical Proofs
This addresses the need for computer-supported learning tools in mathematics education, though it appears incremental by reusing existing theorem-proving representations and strategies.
The paper tackles the problem of developing an intelligent tutoring system for teaching mathematical proofs by building a prototype on an adapted assertion-level proof assistant, which was successfully evaluated on tutorial dialogs with good results.
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.