On the Behavioral Foundations of Mathematical Concepts

The title of this paper will perhaps mean different things to different people. Philosophers and mathematicians interested in the foundations of mathematics and the philosophy of language may think I intent to pursue a systematic pragmatics built around such notions as Ajdukiewicz’ concept of acceptance. Actually, I am going in a different direction. What I want to do is outline present applications of mathematical learning theory to mathematical concept formation. The aims of this paper are primarily constructive, that is, to contribute to the development of a scientific theory of concept formation. Before I turn to this subject, however, I want to comment on two general aspects of the teaching of mathematical concepts.