Mathematics as a social practice? Antagonisms as a conceptual tool for examining discourses

This paper discusses the notion of antagonism as a conceptual tool for examining discourses in mathematics education, with a focus on the political dimensions of discourse. Drawing upon a short university classroom interaction about a visual proof, I suggest that the discourse of mathematics as a product and the discourse of mathematics as a social practice are in an antagonistic relation. I illustrate this relation by exploring how each discourse tries to fix the meaning of concepts like proof, formal proof, and mathematics. Finally, I explore how antagonisms can describe political aspects of discourses, by discussing the limits of both hegemonic discourses and counter-discourses, as well as the space for challenging hegemonic discourses