EvoTeach: Evolving Personalized Teaching Policies with Constrained LLM-Guided Evolution

Personalized adaptive instruction necessitates teaching strategies that dynamically tailor pedagogical actions to individual learners, presenting a complex challenge that requires both accurate student modeling and the principled synthesis of effective tactics. This paper introduces EvoTeach, an evolutionary framework that automates the synthesis of personalized teaching policies for structured domains such as introductory probability and statistics. Unlike its predecessor designed for mathematical discovery, EvoTeach is built around a three-layer architecture: a student cognitive diagnosis layer that maintains a probabilistic knowledge state, a pedagogical strategy synthesis layer that explores the space of teaching actions, and a novel constraint-guided evolutionary layer. This core layer employs Large Language Models (LLMs) to evolve policy programs, guided by inviolable pedagogical constraints-such as prerequisites and cognitive load limits-to ensure safety and instructional effectiveness. Experiments in a simulated educational environment demonstrate that EvoTeach significantly outperforms rule-based and one-shot LLM baselines, achieving a 34% higher average pedagogical utility. An extensive ablation study confirms the critical role of each component, with the removal of pedagogical constraints resulting in the largest performance drop (29.5%). Moreover, EvoTeach attains an average success rate of 89% on specific learning objectives, underscoring its ability to produce robust, interpretable, and highly effective personalized teaching strategies.