Theorem Provers as a Learning Tool in Theory of Computation

Abstract

This paper presents first results of an evaluation study investigating whether an interactive theorem prover like Coq can be used to help undergraduate computer science (CS) students learn mathematical proving within the field of theory of computation. Set within an educational design research approach and building on cognitive apprenticeship and socio cultures cognition theories, we have collected empirical, mainly qualitative observational data focusing on students' activities with Coq in an introductory course specifically created for that matter. Our results strengthen the assumption that a theorem prover like Coq, indeed, can be beneficial in mediating undergraduate students' activities in learning formal proofing. In comparison to pen & paper proofs, students were profiting strongly from the system's immediate feedback and scaffolding. These results encourage the idea to extend the scientifically dominated use of theorem provers like Coq to pedagogical use cases in undergraduate CS education.