Strong Solvers, Leaky Tutors: Evaluating Answer Leakage in LLM Math Tutors

Abstract

Educational digital libraries may grant large language model (LLM) tutors access to worked solutions, but access to repository content should not automatically authorize a model to reveal final answers. This study evaluates whether LLM tutors can leverage private solution context to generate pedagogical hints without disclosing final answers to students. Four models, two general instruction-following models and two math-specialized models, are evaluated across 5,000 aligned problem–message cases per condition, constructed from 500 MATH benchmark problems paired with ten fixed student prompts that ask for, or attempt to confirm, the final answer. Three prompting strategies are compared: a plain assistant prompt, a basic tutoring prompt, and a two-step method that generates a private solution before producing numbered hints. The basic tutoring prompt reduces detected answer leakage from 47.4% to 0.3% for GPT-4o-mini and from 30.2% to 1.0% for LLaMA-3.1, but produces no comparable improvement for Qwen2.5-Math or DeepSeek-Math. Under identical strict hint rules, adding private solution context has minimal effect on GPT but significantly improves tutoring compliance for LLaMA; Qwen produces the most accurate private solutions yet shows the highest leakage and solution-to-hint overlap. These results indicate that private solution access can support hint generation in some architectures but is not a reliable answer-withholding mechanism on its own. For educational digital libraries, access to solution content and authorization to disclose it should be treated as distinct access-control decisions.