I lay a new theoretical framework across my own lecturing in order to understand what is happening. On the one hand, this is a test of the framework. On the other, I gain insights into both better practices and better course design. The framework constructs undergraduate teaching as the interaction between the discipline and the university…

In this article, I present some "axioms" that relate to undergraduate mathematics education. When I first heard the word axiom, it was defined as a "self-evident truth"; but an axiom is not a truth, it is a subjective assumption on which an argument or proof can be based. My purpose in presenting these axioms is to stimulate debate about…