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The research interest to such phenomenon as giftedness has already been taken place in the discussions in some areas: anthropological about human nature, pedagogical about the interaction between bringing up, education and training of a gifted child, social about the circumstances of revealing of special abilities of children, psycological about nature, classification and sources of giftedness. On the base of theoretical-empirical methods of scientific research (theoretical analysis of philosophical, pedagogical, psychological, methodical, historical literature; content-analysis of normative-methodical documents, methods of comparison and classification) the following results of retrospective analysis of theories of giftedness. The stages in the development of the idea of giftedness and its fundamental distinctive definitions are highlighted, the methodical principles of theories of giftedness are defined, the necessity of working out the methodological basis of the process of continuous development of gifted children. The retrospective analysis of evolutional development of the theories of giftedness points out that their conceptual differences are based on different scientific theoretical and methodological researches, are determined by the dynamics of socio-political, economical and socio-cultural processes. On the other hand, the diversity of concepts is the consequence of versatility and difficulty of giftedness nature, impossibility to work out the general references and strategies of development for all its demonstrations. The giftedness is defined as gradually developing competence, performing as the basis of effective activity of the talented personality. The study, analysis and generalization of the main elements of the giftedness theories given in the works of Russian and foreign scientists, form the scientific platform for search and working out the scientific and practical methods of giftedness development aimed to find out and develop of potential and hidden opportunities of schoolchildren, aimed to individual accompaniment of their educational paths, aimed to formation of social motivation.

In the article, the authors consider the problem of a teacher's readiness to interact with gifted students in the process of their continuous development. In modern Russian society, there is a growing need for people who are extraordinarily thinking, creative, active, capable of solving tasks in an unconventional way and formulating new, promising goals. In these conditions, the support and development of gifted students undoubtedly become one of the priority tasks of the education system. The relevance of the work is due to the fact that the transition of general and vocational education to a new educational paradigm, caused by the transformations of Russian society, is accompanied by increased attention to gifted students, and as a result, by the preparation of teachers at all levels of the education system to interact with students, whose intellectual and creative potential is considered as state capital stock. The article presents the results of content analysis of scientific works in the field of the development of gifted students, as well as regulatory and legal acts of the Russian Federation in the field of education. The concept of pedagogical management is introduced (a set of approaches, principles, methods, organizational forms and technological and methodological teaching methods aimed at improving the quality and effectiveness of the continuous development of gifted students, which consists of the stages: identification, diagnosis, training, development, support and support ). As a result of the study, the authors, based on the principle of identifying the types of teacher's activities on the main stages of pedagogical management, proposed a component structure of the teacher's readiness to interact with gifted students, integrating motivational-value, cognitive-methodological, normative-organizational, reflexive-evaluative and communicative-tutoring components

Наука России: Цели и задачи Наука России: Цели и задачи Ключевые слова: формы и механизмы взаимодействия, одаренные обучающиеся, система взаимодействия, комплекс мер. AbstractThe article considers the problem of organization of pedagogical work with gifted schoolchildren, and offers forms and mechanisms of the work in Samara region and events, which organized and held with the aim of their improvement. The authors point out to the decision of a number of tasks, which lead to the formation of well-established system of pedagogical work with gifted schoolchildren.Keywords: forms and mechanisms of work, gifted schoolchildren, the system of work, complex of measures.

In the article, the authors consider the problem of forming a teacher's readiness to interact with gifted students in their professional activities. The educational policy of Russia today is aimed at supporting gifted children and young people, which are becoming one of the priority tasks of the education system (The Сoncept of a National System for Identifying and Developing Young Talents, approved by the Ministry of Education of the Russian Federation by the President of the Russian Federation on April 3, 2012, № Pr-827). The main contradiction is the need to introduce pedagogical strategies of interaction with gifted students to implement the trajectory of their continuous development at all levels of education and the lack of a system for forming teachers ' readiness to interact with gifted students. The article presents a methodological justification of the developed system of forming a teacher's readiness to interact with gifted students, which includes three interrelated elements: methodological, substantive and procedural. It is proved that the system of forming the teacher's readiness to interact with gifted students in professional activities ensures their continuous development during the implementation of certain educational strategies.