因材施教：基于角色、记忆与遗忘感知大语言模型的个性化数学辅导
Teaching According to Students' Aptitude: Personalized Mathematics Tutoring via Persona-, Memory-, and Forgetting-Aware LLMs
AI总结：
针对现有大语言模型辅导系统难以捕捉学生知识动态演化的问题，提出融合角色、记忆与遗忘机制的TASA个性化数学辅导框架，实验证明其学习效果与辅导适应性优于基线方法。
摘要：
大语言模型（LLMs）正越来越多地被整合到智能辅导系统中，以提供类人的自适应教学。然而，现有大多数方法未能捕捉学生知识在能力水平、概念漏洞和遗忘模式方面的动态演化过程。这一挑战在数学辅导领域尤为突出，因为有效的数学教学需要根据每个学生的掌握程度和认知记忆保持情况精准设计细粒度的教学支架。为解决该问题，我们提出了TASA（因材施教），这是一种整合学生角色、记忆和遗忘动态的学生感知辅导框架，用于个性化数学学习。具体而言，TASA维护着记录能力画像的结构化学生角色，以及记录先前学习交互的事件记忆。通过将连续遗忘曲线与知识追踪相结合，TASA动态更新每个学生的知识掌握状态，生成符合上下文、难度校准的问题与讲解。实验结果表明，与代表性基线方法相比，TASA实现了更优的学习效果和更具适应性的辅导行为，凸显了在基于大语言模型的辅导系统中对时序遗忘和学习者画像建模的重要性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
