Proof assistants such as Lean 4 offer machine-checkable verification of mathematical reasoning, but their adoption is limited because formal languages have a steep learning curve and can be challenging to use. Large language models offer a way to lower this barrier to entry through natural-language co-reasoning systems: proof assistants that users interact with entirely in natural language, and which use formal verification to provide feedback to users who submit incomplete and incorrect proofs. This paper explores such a co-reasoning system in an educational setting.

We explore metrics for three properties that are important for natural language co-reasoning systems—faithfulness, accuracy and appropriate granularity. We introduce an evaluation framework for these properties in the context of educational proofs. Second, we present a case study on an educational natural-language co-reasoning system for math proofs, evaluating its autoformalization harness on student-written proofs from an undergraduate linear algebra class using these three properties.

Evaluating Artificial Intelligence (AI) tutor feedback before deployment requires anticipating student engagement, typically assessed through real interaction data. We introduce ParaStudent, a fine-tuning framework for simulating novice programming revisions to support AI tutor evaluation. Compared with prompted baselines, ParaStudent’s revisions more closely match real student code distributions across functional, stylistic, and semantic metrics. Our best variant achieves AUCs of 0.80 for both feedback relevance and successful uptake when distinguishing streams with real engagement above versus at or below the median, while prompted baselines remain near chance on successful uptake. These findings demonstrate the promise of simulated engagement for pre-deployment feedback triage.