Improvement of subject competence of a mathematics teacher in solving professional problems

The research problem and the rationale for its relevance. The article highlights professional difficulties in the teaching field on the basis of diagnostics of mathematics teachers. The article also presents recommendations to eliminate the identified problems, the issue of improving subject competence of mathematics teachers is analyzed. The goal is to determine and substantiate the pedagogical conditions for improving the subject competence of a mathematics teacher in the system of advanced training. The features of the formation of subject competencies among mathematics teachers in the system of additional professional education (APE) using various forms and technologies of teaching are described. The possibility of organizing a discussion of case assignments at methodological seminars for teachers has been demonstrated. The main emphasis is placed on substantiating the effectiveness of using an information and educational environment (IEE) based on the Moodle platform in developing the subject competence of mathematics teachers. The methodological basis of the research is the provisions of the competency-based approach in education, according to which there is a need to develop the necessary competencies among teachers and the creation of a special system for training and retraining of teaching staff. The need to use a synergetic approach is noted, due to the comprehension and rethinking of the content of subject knowledge, the correlation of its essence with actual meanings, the establishment of cause-and-effect and intuitive relationships by mathematics teachers within the framework of the additional education system. The description of the results is associated with the characteristics of professional deficiencies of mathematics teachers and possible ways to eliminate them within the framework of the system of APE for teachers based on the use of IEE. The scientific novelty of the work lies in determining the psychological and pedagogical features of advanced training for mathematics teachers in mastering methods for solving mathematical problems of increased complexity. The practical significance of the author's proposals lies in the possibility of their use in the system of advanced training, centers for continuous professional development and other institutions of additional professional education for teaching staff. The prospects for the research are associated with the development of advanced training programs for mathematics teachers based on network technologies, as well as the development of a system of ontologies to ensure interconnections and consistency of various studies, i.e. performing ontological engineering of the content of subject competence of a mathematics teacher.