An Analysis of Some of Piaget's Topological Tasks from a Mathematical Point of View

Abstract

During the 1950s and '60s, sweeping changes were made in the mathematics curriculum that were largely due to fundamental changes that had occurred in mathematics. Among these changes was a trend toward emphasizing the structural nature of mathematics. However, changes in the content of geometry represented more of a tentative groping than did changes in content dealing with the real numbers. Many approaches to geometry were proposed, such as those of transformation geometry, synthetic geometry, analytic geometry. and vector geometry. Although agreement was not reached as to approach nor indeed even as to the purpose of geometry in the curriculum, mathematics educators did agree that more geometry should be included and included much earlier than was done traditionally.