METHODS OF FORMING THE CONCEPT OF SEQUENCE LIMITS FOR STUDENTS OF HIGHER EDUCATION INSTITUTIONS

Abstract

Formulation of the problem. The modern development of society is characterized by the wide use of mathematical methods in various fields of human activity. In this regard, society needs quality specialists' mathematical training in many specialties. Students' possession of the conceptual apparatus of relevant mathematical disciplines is essential to mathematical training. For courses in higher mathematics and mathematical analysis, the key concept is the concept of limit because by the fact that such fundamental concepts as the limit of a function, the continuity of a function, the derivative of a function, and various types of integrals are introduced based on the operation of the limit transition. Students' success in mastering these courses is primarily determined by how well they master the concept of the limit. It is better to form the concept of a limit using the example of a limit of sequence. Some formal definitions of this concept need to be explained by students. Therefore, the problem of developing an effective method of forming students' concept of the sequence limit becomes urgent.

Materials and methods. Analysis of scientific and methodical literature on the problem of research, textbooks on higher mathematics and mathematical analysis; systematization and generalization of national and foreign experience; generalization of own experience; comparative analysis of students' mastery of the concept of the limit of a sequence under the conditions of using different methods of introducing this concept (concrete-inductive and abstract-deductive methods).

The results. The method of forming the concept of the limit of sequence among students of higher education institutions has been developed. An approach has been implemented based on using two definitions of the limit of the sequence: in the language of neighborhoods and the language «e-n₀». Moreover, two options are described: first, the concept of the limit of the sequence is introduced in the language «e-n₀» and then - in the language of neighborhoods, and vice versa. Considering the complexity of the formal definition of the concept of sequence limit, its introduction was carried out using the concrete-inductive method. At the same time, appropriate visualization methods allowed students to master this concept better.

Conclusions. The features of the proposed method of introducing the concept of the sequence limit are that the assumptions put forward based on clarity considerations receive appropriate analytical justification; students independently come to the formulation of different definitions of the sequence limit. This technique involves the active inclusion of students in introducing the concept of sequence limit and formulating its meaning, which ensures their conscious mastery of this concept.