ABSTRACT
In this chapter, the author says that he is a professional mathematician and a very amateur psychologist. He wants to present a class of mathematical systems that a valuable tool for research in the learning of mathematics. If psychologists would become interested enough to use these systems in their research, then they may find it worthwhile to study mathematics learning. One of the problems of psychologists is that the variety of behaviors involved in the learning of mathematical structures is so large that they are unable to get much of a hold on them. To overcome these difficulties, the author proposes a specific class of mathematical systems which is varied enough to include mathematical learning problems at a great variety of levels and in a great variety of contexts and at the same time be specific enough to provide the researcher with some answers. These mathematical systems are based on the canonical systems of Post.
