Auditing the Reliability of Automated Risk Evaluators in Agentic Tutoring Systems Under Pedagogical Style Variations
Agentic tutoring systems increasingly rely on large language models (LLMs) to generate real-time feedback, yet risky outputs, such as answer leakage, contradiction, and hallucination, can directly affect learning. Answer leakage is a central concern in this setting. It exposes problem solutions to students and can be verified through human annotation. This article presents a pedagogical style-conditioned audit protocol for automated evaluators that detect answer leakage in LLM-generated tutoring feedback before deployment. Using 1100 mathematics problems from the MATH dataset and 4400 feedback items generated under Baseline, Direct, Socratic, and Encouragement styles, we compare rule-based, embedding-based, natural language inference-based, and two LLM-as-a-Judge evaluators from different model families (Qwen2.5-32B and Gemma3-27B) and validate them against a 314-item human-annotated gold standard. The results show that pedagogical style changes how answer-leakage signals appear in feedback and how reliably automated evaluators detect them. Rule-based and LLM-Judge evaluators that perform well under Baseline, Direct, and Encouragement show consistent degradation under Socratic feedback. The primary LLM-Judge (Qwen2.5-32B) achieves overall F1 = 0.726 but drops to 0.427 on Socratic items, and a second LLM-Judge (Gemma3-27B) reproduces this degradation with Socratic F1 = 0.342. The four factorial prompt-sensitivity variants reach overall F1 up to 0.844, but their Socratic F1 remains at or below 0.390. These findings show that automated tutoring-feedback auditing must be style-specific, prompt-calibrated, and human-grounded before deployment.