Dmitri A. Droujkov
Publications
When Verification Hurts: Asymmetric Effects of Multi-Agent Feedback in Logic Proof Tutoring
Large language models (LLMs) are increasingly used for automated tutoring, but their reliability in structured symbolic domains remains unclear. We study step-level feedback for propositional logic proofs, which require precise symbolic reasoning aligned with a learner's current proof state. We introduce a knowledge-graph-grounded benchmark of 516 unique proof states with step-level annotations and difficulty metrics. Unlike prior tutoring evaluations that rely on model self-assessment or binary correctness, our framework enables fine-grained analysis of feedback quality against verified solution paths. We evaluate three role-specialized pipelines with varying solution access: Tutor (partial solution access), Teacher (full derivation access), and Judge (verification of Tutor feedback). Our results reveal a striking asymmetry: verification improves outcomes when upstream feedback is error-prone (<70% accuracy), but degrades performance by 4-6 percentage points through over-specification when feedback is already reliable (>85%). Critically, we identify a shared complexity ceiling; no model or pipeline reliably succeeds on proof states exceeding complexity 4-5. These findings challenge the assumption that adding verifiers or richer context universally improves tutoring, motivating adaptive, difficulty-aware architectures that route problems by estimated complexity and upstream reliability.
Data-Driven Hints in Intelligent Tutoring Systems
This chapter explores the evolution of data-driven hint generation for intelligent tutoring systems (ITS). The Hint Factory and Interaction Networks have enabled the generation of next-step hints, waypoints, and strategic subgoals from historical student data. Data-driven techniques have also enabled systems to find the right time to provide hints. We explore further potential data-driven adaptations for problem solving based on behavioral problem solving data and the integration of Large Language Models (LLMs).