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The article contains explanations of the importance of developing the competence of teachers with teaching mathematics and introduces the idea of constructive approximation of the methodical activity of school teachers and lecturers of pedagogical universities. It describes certain features of the Ukrainian system of methodical training of future mathematics teachers at pedagogical universities. The objective of the study is to experimentally discover the influence of teachers` participation in special geometry teaching competitions on the methodological development of practicing and future mathematics teachers. For the purposes of the study, the Vinnytsia State Pedagogical University hosted a competition of geometry teaching methodological findings for practicing teachers and a methodological skills contest for future math teachers in 2017, 2018, and 2019. We surveyed 32 participants of the above competitions. Practicing math teachers have laid stress upon the high quality of discussions on current problems of teaching geometry, new opportunities to share the experience gained, the high level of expertise and recognition of their own ideas about teaching geometry within the cooperation with the Pedagogical University organized by us. Future mathematics teachers have indicated the growing interest in future methodical activities at school, decided upon their own own aspirations for methodological development. The main conclusions: the educational environment for training the future mathematics teachers at the university should promptly respond to the new requirements for methodical performance of a teacher of the modern school; future math teachers have more opportunities for methodological development in specially created conditions of communication with experienced practicing teachers; practicing math teachers have more opportunities for methodological self-development in the process of active discussion of methodological issues with future teachers, lecturers of pedagogical universities, and scientists in the field of mathematics teaching methodology. We bring your attention to topicality of the problem of math teachers' creative approach to teaching, their willingness to comprehend, analyze and adopt innovations.
Matiash et al. (Sun,) studied this question.