Teaching a Large Language Model Tutor to Withhold the Answer: A Supervisor Architecture and an Evidence-Driven Method for Tuning Socratic Behavior

An effective large language model (LLM) tutor must often decline to give an answer it could easily produce. In a randomized study, students who used an unguarded chatbot scored higher while practicing but lower on a later test taken without it, whereas a Socratically guarded version of the same model kept the practice gain and removed the later loss [4]. Reliable answer-withholding is therefore central to a tutor's value, yet a capable model pressed by a frustrated student does not withhold reliably on a prompt alone. We report a deployed tutoring system that enforces answer-withholding as a per-turn, machine-checkable contract, and a method for tuning that withholding against evidence. A non-LLM policy core, reading only trusted learner state, sets a per-turn ceiling on an eight-rung help ladder; a deterministic detector strips solution code; and a separate LLM judge checks each risky reply against the contract. We tune the behavior with an automated evaluation that uses no human subjects: scripted student personas are driven through the live pipeline and re-scored by a stronger model, and we record each rejection's stated reason so failures are fixed by cause. Doing so revealed an interpretable "over-help ladder," from blatant solution leaks, to naming the exact bug, to over-citing general facts, with each fix exposing the next. The tutor reached full compliance on all four acceptance criteria. We offer the measure, diagnose, and fix loop as a reusable recipe for any LLM agent that must refuse a capability it has.