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.

Adaptive Scaffolding for Cognitive Engagement in an Intelligent Tutoring System

The ICAP framework defines four cognitive engagement levels: Passive, Active, Constructive, and Interactive, where increased cognitive engagement can yield improved learning. However, personalizing learning activities that elicit the optimal level of cognitive engagement remains a key challenge in intelligent tutoring systems (ITS). In this work, we develop and evaluate a system that adaptively scaffolds cognitive engagement by dynamically selecting worked examples in two different ICAP modes: (active) Guided examples and (constructive) Buggy examples. We compare Bayesian Knowledge Tracing (BKT) and Deep Reinforcement Learning (DRL) as adaptive methods against a non-adaptive baseline method for selecting example type in a logic ITS. Our experiment with 113 students demonstrates that both adaptive policies significantly improved student performance on test problems. BKT yielded the largest improvement in posttest scores for low prior knowledge students, helping them catch up with their high prior knowledge peers, whereas DRL yielded significantly higher posttest scores among high prior knowledge students. This paper contributes new insights into the complex interactions of cognitive engagement and adaptivity and their results on learning outcomes.