The Effects of Formalism and Intuitionism on the Development of Mathematics Education

Two extreme philosophies about its orientation have been tacitly appeared almost from ithe origin of mathematics as an autonomous science: Formalism, where emphasis is given to the content and intuitionism, where the attention is turned to problem-solving processes. In this article the effects of the above two philosophies on the development of mathematics education are studied. Crucial problems for the future of mathematics education are also discussed, such as the role that computers could play for the teaching and learning of mathematics, etc. Although neither formalism nor intuitionism have finally succeeded to find a solid framework for mathematics, most of its recent advances were obtained through their disputations about the absolute mathematical truth. On the contrary, these disputations have created serious problems in the sensitive area of mathematics education, the most characteristic being probably the failure of the introduction of the “New Mathematics” to school curricula that distressed students and teachers for many years. Therefore, there is a need for those working in the area of mathematics education to search for a proper balance among the several philosophical aspects of mathematics. This will bring the required tranquillity in the area, in order to be developed smoothly for the benefit of future generations.