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

TL;DR

This work tackles the challenge of dynamic, personalized mathematics tutoring using large language models by modeling each student’s aptitude through a forgetting-aware framework. It introduces TASA, which jointly models a student’s persona, event memory, and individualized forgetting curves to adapt instruction and scheduling of practice. A formal forgetting score $F_c(t)=1-s_{t,c}\exp(-\Delta t_c / S_c) \approx (1-s_{t,c})\frac{\Delta t_c}{\Delta t_c+\tau}$ connects knowledge tracing with content generation, enabling temporally calibrated explanations and questions. Empirical evaluations on four public math benchmarks show that TASA outperforms strong baselines in learning gains and personalization, demonstrating the value of integrating temporal forgetting and learner profiles into LLM-based tutoring. The results highlight a cognitively grounded path toward more effective, long-horizon educational AI systems with potential applicability beyond mathematics.

Abstract

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.

Figures (3)

• Figure 1: Given the same query, TASA generates personalized tutoring responses for two students based on their forgetting-adjusted persona and memory.
• Figure 2: Illustration of our proposed TASA framework. TASA first extracts the student’s persona and event memory from historical interactions. During tutoring, it retrieves relevant persona and memory, applies forgetting-aware decay through a Rewriter, and generates personalized instruction via a Generator conditioned on the decayed student state.
• Figure 3: Impact of dialogue rounds (left) and retrieval weight $\lambda$ (right) on normalized learning gain.