  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.
