Mathematical knowledge for teaching as a didactic praxeology

Abstract

It is widely acknowledged that teachers' work has both practical and theoretical dimensions, both praxis and logos, and that teacher education should address both dimensions. However, as argued in this article, existing discourses for describing the mathematical knowledge of teachers and what it takes to become competent in it are not always clear to what extent these discourses address knowledge about the practices of mathematics teaching or theories that provide arguments for the practices. Specifically, I argue for the coordination of the framework of mathematical knowledge for teaching (MKT) with the analytical distinction of logos and praxis combined in teaching practices. Moreover, I have backed this argument with examples of the proposed categories of the adjusted framework from the existing body of work in mathematics education. Each category of the proposed framework, whether concerning a teaching method or a theoretical consideration, was indeed exemplified by some concept, approach, or perspective from the field of mathematics education. The framework, I believe, would prove useful in engaging mathematics teacher education discursively, for instance, in analyzing teacher education materials to determine the extent to which they offer mere methods, theoretical arguments, or a combination of both.

Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function

“…In this regard, praxeological analysis provides an effective way to analyze teacher actions. These analyses make visible the ideas beyond teacher actions (Pansell, 2023). In other words, they provide insight into how teachers analyze the curriculum and why they choose specific approaches when teaching particular information.…”