Teachers' mathematical content knowledge (CK) is of vital importance and need
in teacher professional development (PD) programs. Computer-aided asynchronous
PD systems are the most recent proposed PD techniques, which aim to help
teachers improve their PD equally with fewer concerns about costs and
limitations of time or location. However, current automatic CK identification
methods, which serve as one of the core techniques of asynchronous PD systems,
face challenges such as diversity of user responses, scarcity of high-quality
annotated data, and low interpretability of the predictions. To tackle these
challenges, we propose a Multi-Agent LLMs-based framework, LLMAgent-CK, to
assess the user responses' coverage of identified CK learning goals without
human annotations. By taking advantage of multi-agent LLMs in strong
generalization ability and human-like discussions, our proposed LLMAgent-CK
presents promising CK identifying performance on a real-world mathematical CK
dataset MaCKT. Moreover, our case studies further demonstrate the working of
the multi-agent framework.

教师数学内容知识（CK）对于教师专业发展（PD）计划至关重要。我们提出了基于多智能体 LLMs 的框架，LLMAgent-CK，用于在没有人工注释的情况下评估用户反馈与确定的 CK 学习目标的一致性，并展示了在实际数学 CK 数据集 MaCKT 上有希望的 CK 识别表现。