When analyzing episodes of mathematics instruction from an epistemological perspective, it is seen that the disparity between teacher and student knowledge is not simply due to their knowing more or their knowing less. The independent and frequently incompatible levels of understanding knowledge which are peculiar to teachers and to students show how essential it is to make allowance for conceptual as opposed to material aspects, and how the conditions of classroom processes nevertheless always tend to regress to a form of mathematical knowledge strongly determined by subject matter and method.