Memory in mathematical understanding

Whatever cognitive processes are involved in understanding mathematics, it is clear that one of them is learning. No one is born with an understanding of measure theory, abstract algebra or general topology; the very name mathematics means that which is to be learned (Boyer, 1968). One of the outcomes of learning is remembered knowledge. Indeed it is our contention that memory plays an essential role in the understanding of mathematics, However, what it is that is remembered by students who understand mathematics in contrast to those who do not is by no means a trivial question. In fact, we would like to suggest that there is a gap in this connection between recent developments in memory research and the theory and practice of mathematics education. A second purpose of the present article is to survey briefly the orgins of this gap.