Abstract
This chapter discusses the nature of mathematical concepts, the main points of view regarding the learning of mathematical concepts, and how valuable the work of Piaget is from the point of view of understanding the nature and learning of mathematical concepts. Mathematical concepts are one class of concept; they are terms that exist in thought indicating generalizations about systematic patterns of relations. It is sometimes useful to classify mathematical concepts in three ways: (1) pure mathematical concepts, (2) notional concepts, and (3) concepts of length, weight, time, and the like. The viewpoints concerning the learning of mathematical concepts may be classified along two main dimensions: (1) intuition and constructive thinking compared with analytic thinking and (2) the behaviorist or neobehaviorist approach compared with that of ontogenetic studies. Piaget's vast collection of data and his conceptualization of the process of cognitive development throw light on some of the problems that are confronted in the field of concept formation in mathematics, but they are at a loss to explain others.
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