ABSTRACT
Mathematics (including arithmetic, algebra, and geometry) is traditionally viewed as part of our cultural heritage that must be transmitted from one generation to another. From a Piagetian point of view, however, mathematics grows out of the logico-mathematical knowledge that each child constructs from within, through his or her own ability to think (Piaget, Inhelder, & Szeminska, 1948/1960; Piaget & Szeminska, 1941/1952). To clarify the nature of mathematics, it is necessary to review the distinction Piaget made among three kinds of knowledge according to their ultimate sources-physical, logicomathematical, and social-conventional knowledge (1967/1971; 1936/1951.
