PROBLEM-BASED TEACHING OF ADVANCED MATHEMATICS AT THE UNIVERSITY


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Abstract

The relevance of the research topic is caused by the wide possibilities of problem-based teaching while training a specialist having competencies formulated by FSES. The problem-based training during lectures and practical classes in higher mathematics is a method of improvement of the effectiveness of training and the development of a student’s personality. The goal of the study is to develop the methodological materials for lectures and practical classes using the problem-based teaching while studying higher mathematics by the university students. The paper highlights the main blocks of implementation of problem-based learning during the classes with the students. The first block is related to the creation of a problem-based situation in a lecture or practical class. This block includes the elements of problem-based learning directly related to a problem situation. The second block is related to the delivering a problem lecture or a problem practical class in higher mathematics. This block includes the elements of problem-based learning directly related to the organization and carrying out of a training session.

The paper presents the fragments of lectures organized with the application of problem-based training on the following topics: “Primitive” (the creation of a problem situation through a practical task); “Multiplication of matrices” (the creation of a problem situation on the basis of generalization of available particular knowledge); “Determinants” (the creation of a problem situation through identifying and analyzing different points of view on the same issue); “Systems of linear algebraic equations” (the creation of a problem situation through the search for new ways of practical application of this fact); “Improper integral of the second kind” (the situations that arise when the students perform the supportive learning tasks are used as the problem ones).

About the authors

Natalya Anatolievna Demchenkova

Togliatti State University, Togliatti

Author for correspondence.
Email: ndemchenkova@yandex.ru

PhD (Pedagogy), Associate Professor, assistant professor of Chair “Higher Mathematics and Mathematical Education”

Russian Federation

Sofiya Gennadievna Emelyanova

Togliatti State University, Togliatti

Email: esg1979@mail.ru

senior lecturer of Chair “Higher Mathematics and Mathematical Education”

Russian Federation

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