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
