Large language models can increasingly adapt educational tasks to learners characteristics. In the present study, we examine a multi-agent teacher-in-the-loop system for personalizing middle school math problems. The teacher enters a base problem and desired topic, the LLM generates the problem, and then four AI agents evaluate the problem using criteria that each specializes in (mathematical accuracy, authenticity, readability, and realism). Eight middle school mathematics teachers created 212 problems in ASSISTments using the system and assigned these problems to their students. We find that both teachers and students wanted to modify the fine-grained personalized elements of the real-world context of the problems, signaling issues with authenticity and fit. Although the agents detected many issues with realism as the problems were being written, there were few realism issues noted by teachers and students in the final versions. Issues with readability and mathematical hallucinations were also somewhat rare. Implications for multi-agent systems for personalization that support teacher control are given.

翻译：大语言模型日益能够根据学习者特征调整教育任务。本研究考察了一种教师参与的"人在环路"多智能体系统，用于个性化生成中学数学题目。教师输入基础题目和期望主题，大语言模型生成题目后，四个AI智能体分别依据各自专长的评价标准（数学准确性、真实性、可读性和现实性）对题目进行评估。八名中学数学教师在ASSISTments平台中使用该系统创建了212道题目，并将其布置给学生完成。研究发现，师生均希望修改题目现实情境中的细粒度个性化元素，这表明存在真实性与适配性问题。尽管AI智能体在题目编写过程中检测到诸多现实性问题，但师生在最终版本中很少发现此类问题。可读性问题与数学幻觉现象也相对罕见。本文最后探讨了支持教师控制的多智能体个性化系统的设计启示。