arXiv:2403.04772v1 Announce Type: new
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. 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. 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.
Teacher knowledge is a complex and multi-disciplinary concept that involves understanding mathematics content, student epistemology, and pedagogical practices. In order to improve teaching and learning, it is important to have a formalized understanding of these different types of knowledge. The article recognizes the need for approximating and formalizing teacher knowledge, but also highlights the challenge of coherence in doing so.
A key issue discussed in the article is the use of AI-based software systems in education. While these systems can be responsive and smart, they often lack an understanding of meaning. Additionally, trained AI systems can have their own limitations and biases. This raises the question of how to model teachers’ understanding of content in a coherent and meaningful way.
To address this challenge, the author proposes a two-tier rough set-based model. This model has the advantage of being able to handle vagueness, granularity, and multi-modality. By incorporating these features, the model can better capture the nuances and complexities of teacher knowledge.
The article gives an extended example of equational reasoning to demonstrate the effectiveness of the proposed model. Equational reasoning is a fundamental concept in mathematics and is often challenging for students to grasp. By using the two-tier rough set-based model, teachers can better understand student misconceptions and provide targeted instruction.
Overall, this research highlights the importance of considering the multi-disciplinary nature of teacher knowledge and the need for coherent formalization. By developing models that can capture the complexity of teacher knowledge, we can enhance teaching and learning in mathematics and other domains.