通过粗糙集表征教学内容知识
Representing Pedagogic Content Knowledge Through Rough Sets
AI总结：
针对教师内容知识难以近似且连贯形式化的问题，提出基于粗糙集的两层模型，以统一处理模糊性、粒度和多模态性，并通过等式推理示例验证。
摘要：
教师的知识库由数学内容知识、学生认识论知识和教学知识构成。它对理解学生的内容知识以及总体学习情境具有重大影响。教育研究文献已经认识到，有必要在近似意义上将不同的内容知识形式化。一个相关问题是连贯的可形式化性。现有的响应式或基于智能AI的软件系统并不关注意义，而经过训练的系统也充满自身问题。在本研究中，识别了教师内容理解建模中的许多问题；作者提出了一个基于粗糙集的两层模型，旨在开发可辅助教师完成多样化任务的软件。所提方法的主要优势在于能够连贯地处理模糊性、粒度和多模态性。文中使用一个关于等式推理的扩展示例来证明这些能力。本文面向希望构建逻辑模型或开发具备意义感知能力、可辅助教师的AI软件的粗糙集研究人员，以及教育研究专家。
英文摘要：
A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning context in general. The necessity to formalize the different content knowledge in approximate senses is recognized in the education research literature. A related problem is that of coherent formalizability. Existing responsive or smart AI-based software systems do not concern themselves with meaning, and trained ones are replete with their own issues. In the present research, many issues in modeling teachers' understanding of content are identified, and a two-tier rough set-based model is proposed by the present author for the purpose of developing software that can aid the varied tasks of a teacher. The main advantage of the proposed approach is in its ability to coherently handle vagueness, granularity and multi-modality. An extended example to equational reasoning is used to demonstrate these. The paper is meant for rough set researchers intending to build logical models or develop meaning-aware AI-software to aid teachers, and education research experts.
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。
