I. YAKOVLEV CHUVASH STATE PEDAGOGICAL UNIVERSITY BULLETIN

basic mathematical concepts, genetic approach, logical approach, mathematical language

The article considers the possibilities of forming mathematical concepts based on a “logical-linguistic” or “verbal-logical” approach. The authors have reviewed the publications dealing with the problems of formation of the basic mathematical concepts, considered the features of the genetic approach, and showed its limitations in the formation of mathematical views of students. The authors see the reason for the limitations in the fact that the classical methodology is based on a historical approach to the formation of concepts, which provides for duplication in teaching the main stages of their evolution in the process of scientific development. As a result, over time, the disunity of various branches of mathematics increases: some are of an applied nature, others are purely theoretical. Applied problems are an incentive for the development of theory. Until now, the traditional teaching methods used are characterized not only by the isolation of academic disciplines from life, but also by their isolation from each other. The authors substantiate the necessity of using a logical approach to the formation of mathematical concepts in a modern school. The study showed that the difficulties of understanding abstract theories are due to poor knowledge of the logical foundations of modern science and insufficient study of a specific scientific language, as well as with the indicated disunity of different branches of mathematics. The authors see one of the solutions to this problem in practicing the presentation of mathematics in the languages of its different sections.

Чекмарев Георгий Евгеньевич – кандидат физико-математических наук, доцент кафедры математики и физики Чувашского государственного педагогического университета им. И. Я. Яковлева, г. Чебоксары, Россия, https://orcid.org/0000-0001-9179-4552, chekmarevge@mail.ru,

Фоминых Светлана Олеговна – кандидат физико-математических наук, доцент кафедры математики и физики Чувашского государственного педагогического университета им. И. Я. Яковлева, г. Чебоксары, Россия, https://orcid.org/0000-0002-8679-8687, ermakovaso@rambler.ru