In this essay I shall attempt to develop a few simple theorems about the nature of instruction. I shall try to illuse trate them by reference to the teaching and learning of mathematics. The choice of mathematics as a mode of illustration is not premised on the typicality of mathematics, for mathecics is restricted to well-formed problems and does not concern itself with empirical proof by either experiment or observation. Nor is this an attempt to elucidate mathematical teaching as such, for that would be beyond my competence. Rather, mathematics offers an accessible and simple example for what, perforce, will be a simplified set of propositions about teaching and learning.' And there are data available from mathematics learning that have some bearing on our problem.
The plan is as follows. First some characteristics of a theory of instruction will be set forth, followed by a statement of some highly general theorems about the instructional process. I shall then attempt, in the light of specific observations of mathematics learning, to convert these general propositions into workable hypotheses. In conclusion, some remarks will be made on the nature of research in support of curriculum making.