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1 | Modern educational realities are such that the teacher must be ready for constant self-improvement, self-education in the field of professional activity. Changes in the content, technological, evaluative components of the educational process require the teacher to update and refresh the methodology of teaching the subject, which can cause certain difficulties. The purpose of the study is to determine the list of methodological difficulties for mathematics teachers and their causes based on the diagnosis of methodological competencies. To achieve this goal, both theoretical and empirical research methods were used. In the course of the research carried out by the authors, a number of methodological competencies of a mathematics teacher were identified – components of his professional competence: he is able to design the results of teaching mathematics in accordance with the current educational standards; is able to design the content of teaching mathematics, focused on the achievement of educational results by various categories of students; is able to design educational and cognitive activities of students in the process of teaching mathematics in accordance with modern requirements and on the basis of variable forms of its organization; is able to objectively assess the educational results of students’ mathematical training. The level of formation of these competencies was diagnosed through diagnostic work, self-assessment and expert assessment of the teacher’s activities. A number of methodological difficulties that teachers experience in the implementation of the process of teaching mathematics in modern conditions were identified. Possible reasons for the identified difficulties are identified and some recommendations for their elimination are indicated. Keywords: methodological competencies, mathematics teachers, professional difficulties of teachers, mathematical training of students | 722 |