Conceptual change in mathematics

In traditional educational contexts, mathematics is considered a hierarchical structure in which new concepts logically follow from prior ones. From the viewpoint of the theories of conceptual change, however, the learning of mathematics is characterized more by discontinuity than gradual and continuous enrichment. These theories stress the crucial role of prior knowledge in learning. According to these theories, prior knowledge does promote learning, but it can also restrict it and lead to misconceptions. This is the case especially with those kinds of concepts where learning demands a radical change in prior knowledge, which is typical of mathematics and science. One example of these kinds of changes in mathematics is the enlargement of number concept from natural to rational numbers. In this article, three different theories of conceptual change are presented and the perspectives of these theories on the difficulty of the above-mentioned enlargement are discussed. Results of empirical research and some implications for teaching mathematics from the viewpoint of theories of conceptual change are also dealt with.