Teaching According to Students' Aptitude: Personalized Mathematics Tutoring via Persona-, Memory-, and Forgetting-Aware LLMs

Large Language Models (LLMs) are increasingly integrated into intelligent tutoring systems to provide human-like and adaptive instruction. However, most existing approaches fail to capture how students' knowledge evolves dynamically across their proficiencies, conceptual gaps, and forgetting patterns. This challenge is particularly acute in mathematics tutoring, where effective instruction requires fine-grained scaffolding precisely calibrated to each student's mastery level and cognitive retention. To address this issue, we propose TASA (Teaching According to Students' Aptitude), a student-aware tutoring framework that integrates persona, memory, and forgetting dynamics for personalized mathematics learning. Specifically, TASA maintains a structured student persona capturing proficiency profiles and an event memory recording prior learning interactions. By incorporating a continuous forgetting curve with knowledge tracing, TASA dynamically updates each student's mastery state and generates contextually appropriate, difficulty-calibrated questions and explanations. Empirical results demonstrate that TASA achieves superior learning outcomes and more adaptive tutoring behavior compared to representative baselines, underscoring the importance of modeling temporal forgetting and learner profiles in LLM-based tutoring systems.