BASIC IRONY: EXAMINING THE FOUNDATIONS OF SCHOOL MATHEMATICSWITH RESERVICE TEACHERS.

This article reports on an inquiry into what tends to he taken for granted with regard to the teaching and learning of mathematics. The inquiry, undertaken in the context of a course on methods for mathematics teaching. was developed around an examination of the mathematical notions that infuse conventional theories of cognition and that permeate the structures and practices of school mathematics. In particular, concepts drawn from or aligned with Euclidean geometry were examined. Specifically, alternatives drawn from fractal geometry were explored. The importance of interrogating the often-transparent figurative underpinnings of our thinking about thinking is highlighted. [ABSTRACT FROM AUTHOR]