Integrated approach to teaching higher mathematics: the relationship between fundamental training and professional disciplines

The purpose of the article is to substantiate an integrated approach to teaching higher mathematics in higher education institutions as a system of interconnected fundamental and professionally oriented components aimed at bridging the gap between theoretical mathematical training and its practical application in the professional activities of education seekers. The research used a set of methods, including analysis and generalization of scientific sources to determine modern approaches to mathematics education, system-structural analysis to model the integration of mathematical and professional disciplines, as well as the method of pedagogical modeling to develop didactic examples and interdisciplinary tasks. The empirical basis of the research was the results of a questionnaire survey of students and teachers, which allowed us to assess the effectiveness of the integrated approach in the educational process. As a result of the study, it was found that the implementation of an integrated approach to teaching higher mathematics contributes to the formation of a holistic understanding of mathematical methods as a tool for analyzing, modeling and solving professionally oriented tasks. It was found that students positively perceive the integration of mathematical and professional disciplines, especially in the format of professionally oriented tasks, interdisciplinary cases and STEM-/project learning. At the same time, it was determined that the most significant for students are the sections related to mathematical statistics, probability theory and economic and mathematical modeling, which confirms the strengthening of the applied orientation of mathematical training. The positions of teachers on the advantages of the integrated approach and the existing organizational and methodological barriers to its implementation are also summarized. The scientific novelty lies in the systematization of the structural and content components of the integrated approach to teaching higher mathematics and the clarification of the mechanisms of its practical implementation in the conditions of the competency paradigm of higher education. The practical significance of the results lies in the possibility of their use for improving the methodology of teaching higher mathematics, developing interdisciplinary tasks and training courses, as well as increasing the efficiency of the formation of professional competencies of students.