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The article deals with one of the aspects of training the future teachers of mathematics in the process of study of elementary mathematics to implement the conceptual model of formation and development of creative thinking, to create a creative environment in the conditions of differentiated teaching mathematics – building the capacity of students to prepare pupils to participate in math competitions. Some results of the students’ questioning about their potential readiness to work with gifted students during diagnostic experiment are provided. The peculiarities of implementation of content, motivational-stimulating, personal, organizational, operational-activity units of creating a creative environment in the context of the study are revealed. Attention is focused on the content unit, examples of some tasks of contest character are presented, and it is advisable to offer these tasks to the students at the lessons of elementary mathematics. Creative environment in the process of teaching mathematics is interpreted as a system of interrelated interdependent units (content – determined by the peculiarities of the structure and content of educational material; motivational- stimulating – the peculiarities of the teacher’s work in the process of organization and management of educational-cognitive activity of the pupil; personal – specifics of the influence (self-influence) on the pupil’s personality with the purpose of developing his creative thinking; organizational – peculiarities of organization of pupils’ learning and joint activities of teachers and pupils, aimed at creating conditions for personal involvement of all the stakeholders (pupils, regardless of their level of academic success, and teachers; operational-activity – specifics of operating the educational material). It is stressed that in the process of preparing pupils for Olympiads in mathematics there is a large number of problems. It is noted that some of them are based on the fact that at the present stage most of the students of physics and mathematical faculties of pedagogical universities lack special math preparation. The results of a survey of students from the physics and mathematics faculties this year showed that only 35% of them were enrolled in classes in physics and mathematics according to the programs of profile (depth) level. Other students studied programs in mathematics of the academic level.
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