The increasing heterogeneity of student populations poses significant challenges for teachers, particularly in mathematics education, where cognitive, motivational, and emotional differences strongly influence learning outcomes. While AI-driven personalization tools have emerged, most remain performance-focused, offering limited support for teachers and neglecting broader pedagogical needs. This paper presents the FACET framework, a teacher-facing, large language model (LLM)-based multi-agent system designed to generate individualized classroom materials that integrate both cognitive and motivational dimensions of learner profiles. The framework comprises three specialized agents: (1) learner agents that simulate diverse profiles incorporating topic proficiency and intrinsic motivation, (2) a teacher agent that adapts instructional content according to didactical principles, and (3) an evaluator agent that provides automated quality assurance. We tested the system using authentic grade 8 mathematics curriculum content and evaluated its feasibility through a) automated agent-based assessment of output quality and b) exploratory feedback from K-12 in-service teachers. Results from ten internal evaluations highlighted high stability and alignment between generated materials and learner profiles, and teacher feedback particularly highlighted structure and suitability of tasks. The findings demonstrate the potential of multi-agent LLM architectures to provide scalable, context-aware personalization in heterogeneous classroom settings, and outline directions for extending the framework to richer learner profiles and real-world classroom trials.

翻译：摘要：学生群体的日益多样化给教师带来巨大挑战，尤其是在数学教育中，认知、动机和情感差异会显著影响学习成果。尽管人工智能驱动的个性化工具已涌现，但多数仍聚焦于学习表现，对教师提供的支持有限，且忽视了更广泛的教学需求。本文提出FACET框架——一种面向教师的、基于大语言模型的多智能体系统，旨在生成融合学习者画像中认知维度与动机维度的个性化课堂材料。该框架包含三个专业化智能体：（1）学习者智能体，模拟包含主题熟练度与内在动机的多样化画像；（2）教师智能体，根据教学原则调整教学内容；以及（3）评估智能体，提供自动化质量保障。我们使用八年级数学课程真实内容进行测试，并通过以下方式评估其可行性：（a）基于智能体自动评估的输出质量分析；（b）基础教育阶段在职教师的探索性反馈。十次内部评估的结果表明，生成材料与学习者画像之间具有高度稳定性和一致性，教师反馈尤其强调了任务的结构性与适配性。研究结果展示了多智能体大语言模型架构在异构课堂环境中提供可扩展、情境感知个性化支持的潜力，并指出了扩展该框架以覆盖更丰富学习者画像及开展真实课堂实验的方向。