Онтология и практика преподавания математики в высшей и средней школе

Abstract

Discussed are problems of modern mathematical education: the development of the conceptual apparatus of mathematics, as well as the development of thinking in modal categories when proving mathematical propositions and solving probabilistic problems. The work is based on the results of the explication of the ontological foundations of mathematics obtained earlier. It is shown that the basis of a holistic, deep perception of the mathematical laws of being is categorical intuition with subsequent rationalization of mathematical objects. It is emphasized that such objects are not always possible to describe by means of extensional logic: an important place in the categorical structuring of mathematical knowledge is occupied by ontic modalities of the necessary and possible. The author expresses concern about the tendency of algorithmization of mathematical thinking in the learning process as opposed to historically established methods of creative search for proofs, alternatives, and opportunities. Special attention is paid to the topic of the teacher’s implementation of the ideological and educational function of mathematical science. Taking into account the enormous development of computing and information technologies, it is necessary to remember about the anthropological and humanitarian components of modern science and education. In substantiation of the relevance and discussion of the raised issues, the points of view of specialists from various fields are given: mathematicians, historians, teachers. This article is addressed to a wide range of readers: scientists, teachers, graduate students, freelance researchers.