Generation and Use of Hints and Feedback in a Hilbert-Style Axiomatic Proof Tutor

Abstract

This paper describes logax, an interactive tutoring tool that gives hints and feedback to a student who stepwise constructs a Hilbert-style axiomatic proof in propositional logic. logax generates proofs to calculate hints and feedback. We compare these generated proofs with expert proofs and student solutions, and conclude that the quality of the generated proofs is comparable to that of expert proofs. logax recognizes most steps that students take when constructing a proof. Even if a student diverges from the generated solution, logax still provides hints, including next steps or reachable subgoals, and feedback. With a few improvements in the design of the set of buggy rules, logax will cover about 80% of the mistakes made by students by buggy rules. The hints help students to complete the exercises.

Does Knowing When Help Is Needed Improve Subgoal Hint Performance in an Intelligent Data-Driven Logic Tutor?

“…The pedagogical policy utilized historical student solutions to generate hints. In the future, we plan to explore automatic hint creation for logic proofs (Lodder et al 2021). Furthermore, we plan to build a policy that can differentiate between when students are ready to benefit from subgoal hints and when they need next-step hints.…”