Representing Pedagogic Content Knowledge Through Rough Sets
A Mani
TL;DR
This paper addresses how to formalize a teacher's pedagogic content knowledge amidst inherent vagueness by proposing a two-tier rough-set framework that integrates mereology and partial algebraic structures. It extends the real-number formalism taught in schools with a Vague Real Number System and companion models to coherently handle granularity, multi-modality, and meaning-aware reasoning. Through an extended equational reasoning example, the work demonstrates how rough-set operators can represent and compare student explanations and problem-solving steps with upper and lower approximations. The proposed RCQO-based companion systems aim to enable coherent formalizability and support AI tools for teachers, curricula design, and research in mathematics education. The approach promises practical impact for developing intelligent, meaning-aware educational software that can better model teacher and student knowledge in context-sensitive ways.
Abstract
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.