Variative Components of the University Course of Mathematical Analysis: The Experience of Introduction into the Practice of Teaching

Introduction . The change in general paradigm of education, its transition to a competent model and the permanent change in federal state standards of higher education have created the problem associated with selecting the content of course programmes studied by university students. In the field of mathematical knowledge, the problem of strengthening students’ mathematical training is particularly acute in connection with the declared task, in which mathematical analysis is central. One of the ways to solve this problem is to distinguish the invariant and variable components in the content of the university course. The aim of the present research is to describe the content of variable components developed by the authors for the university course of mathematical analysis and to present the results of their introduction into the practice of teaching. Methodology and research methods . The conducted research is based on the principles of continuity and systemacity of modern education, its current concepts (fundamentalisation, humanisation, humanitarisation, individualization and differentiation) and the provisions of competency-based, activity-based, personality-oriented and interdisciplinary approaches to teaching. The theoretical analysis and experiment were used as the main methods, the results of which were evaluated through empirical and praximetric methods. Results and scientific novelty . The present study, carried out for many years at Vyatka State University, has shown that the system-forming factor of variable education, determining the means and forms of its implementation, is the variable content of education. Firstly, this particular content provides additional information on key concepts, theories and mathematical analysis, taking into account the specifics of students’ specialties, which facilitated their successful professionalism. Secondly, the variable content of education offers the possibility to systematically rethink and rapidly revise educational material, taking into account new scientific facts and discoveries. Finally, it can develop cognitive autonomy of junior students, encouraging them to carry out regular and informal research activities. The coverage of students of several mathematical directions of education, their obligatory involvement in independent research activities and support for mechanisms of interdisciplinarity and transprofessionalism ensured the scientific novelty of the research undertaken. The results of the formation of professional competencies of future graduates obtained during pedagogical measurements (questionnaires, surveys of students, observation of their educational and research achievements) confirmed the effectiveness of using the designed variable components of the discipline “Mathematical Analysis” in the learning process. Practical significance . The research material and the authors’ conclusions described in the present article can be useful for methodologists of higher school and teachers of mathematics interested in improving the quality of mathematical training in universities.