Development of professional competence of future mathematics teachers in the HEI educational process

Relevance. The importance of this study is due to the evolution of modern education towards excellence and the need to constantly monitor the relationship between teacher�s self-education, knowledge culture, professional training and social requirements. For that reason, it is important to use modern approaches and methods to prepare a mathematics teacher. Purpose. The purpose of the study is to describe and diagnose the methodological and technical features of teacher training, to determine the level of competence of mathematics teachers in their work, their ability to use self-education techniques and the main methods of theoretical and methodological preparation for students' educational activities. Methodology. Typical methods used in research on this topic � analysis, classification, reasoning, synthesis and comparison of approaches � make it possible to identify and highlight key areas for improving the professional training of future teacher. Results. The study examines methods for developing students' competence, analyses the literature, determines the components of mathematics teacher competence, highlights the functions and levels of development, provides the structure of the highest levels of teacher professional competence, determines the content of professional competence of a future mathematics teacher, presents models for the development of methodological knowledge about the professional competence of students and improving educational culture, diagnoses problems, related to the professional competence of students. Conclusions. Professional development is an ongoing, cyclical process because professionalism requires continuous enhancement. The advancement of this process largely depends on an environment that encourages self-development. A key objective in the professional training of mathematics teachers is to cultivate professional competence. This competence reflects students' readiness to apply both theoretical and practical knowledge in science and education, as well as their ability to enhance and refine their qualifications. The study indicates that the professional competence of a future teacher encompasses several aspects: motivational, cognitive, operational, creative, and reflective. Keywords: mathematics teacher; educational process; quality of methodological training; methodological knowledge; methodological culture; professional competencies