The relevance of this study is due to the ever-growing demands that the rapidly developing society makes to the education system, according to which the priority factor in the development of students is the ability to independently plan their activities to acquire the necessary knowledge and skills during joint creative and cognitive activity. It is confirmed that it is during the implementation of projects that it is possible to reveal the potential of students in self-realization, interaction with others and development of critical thinking. The goal of this article is to study the theoretically grounded and practically proven effectiveness of the use of project-based training in the study of mathematics by students of the secondary school. The main method of this research is a pedagogical experiment, as well as observation, a quantitative method and statistical processing. In the process of teaching mathematics, the specifics of project training as a student-centered method aimed at improving analytical and creative skills were taken into account. Gradual methodological methods for the organization of the project activity of students are developed. In the course of testing, model images of lessons were obtained, substantive content was determined and specified, thematic lines of the project activity in teaching mathematics in basic school were built, and the use of variable forms of the project activity was justified. The peculiarities of the author's approach to the study of the features of project-based learning are the allocation of special criteria for project assessment; comparative analysis of approaches of foreign and domestic scientific schools to the project activity. The study revealed the effectiveness of project-based training in teaching mathematics. The materials of the article are valuable for primary and secondary school teachers, teachers of secondary vocational and higher educational institutions. The use of the project activity in teaching mathematics in basic school contributes to increasing the level of motivation to study the most difficult topics of the course, ensures the implementation of an integrated approach to the study of natural sciences.

The relevance of the research problem lies in the determination of the foundations of structural-level concept of self-regulation of personality in realization of professional activity and possibilities of its interpretation in the practice of management. The goal of the article is in the description of component and structural-level constituents of the self-regulation psychological system of successful professional activity, development of the concept of "successful self-regulation of professional activity" on the basis of the explication of the relations between levels of the system. The leading approach and methodological basis for the study of this problem is the systemogenesis concept of professional activity, the concept of self-regulation and implicit theories of professional success of personality. The theoretical background for the design of psychological structural-level regulation system to achieve success in professional activities and the grounds for its level structure are revealed in the article; a methodological apparatus for the diagnosis of successful self-regulation of professional activity is developed, reliability of the theoretical model of the structural-level concept of self-regulation is proven. The experimental part of the study describes the structure and levels of psychological system of self-regulation of successful professional activity, the content of which meets the basic positions of the psychological theory of professional activities. The article can be used in the context of professional coaching for career growth and professional development of managers and specialists in the sphere of management.