ABSTRACT

Mathematical thinking is only one aspect of thinking in general. Therefore, questions concerning mathematical thinking raise questions concerning all thinking. Although mathematical thought is in many ways very special, it admits of a straightforward analysis that throws light on all thinking and suggests a powerful general approach to studying the latter. The basis of our analysis of mathematical thinking involves the abstract concept of structures. Furthermore, structures play the same essential role in all thinking as they do in mathematics, whether or not the thinker is aware of their presence.