The article highlights the peculiarities of forming primary school teachers' readiness to work with gifted students in the system of continuing teacher education. The phenomenon of «formation of primary school teachers' readiness to work with gifted students in the system of continuing pedagogical education» is considered as a process of acquiring by primary school teachers the motivational and value orientations, knowledge, skills, professional and personal qualities necessary for working with gifted students in the system of higher pedagogical education and improving them in the system of postgraduate pedagogical education on the basis of continuity, continuity and perspective. The peculiarities of forming the readiness of primary school teachers to work with gifted students are as follows: 1) the continuity of the relevant teacher training at the bachelor's and master's levels and in the conditions of scientific and methodological work, which is due to the determining role of the teacher in the formation of the personality of gifted primary school students; 2) recognition of the conceptual goal of this training as the formation of the teacher as a subject of professional and pedagogical activity aimed at developing the giftedness of primary school students, since primary school age is sensitive to the development of intelligence and creativity as systemic components of giftedness. It has been established that the concept of «continuity» is interpreted as continuity, the absence of divisibility into fragments. It is substantiated that the continuity (continuity) of the formation of primary school teachers' readiness to work with gifted students is ensured through the implementation of the principles of continuity and perspective in the goal (formation of a teacher as a subject of work with gifted students, capable of professional and personal self-development), content (as an organic unity of blocks-directions aimed at forming motivational, cognitive, activity and reflective-personal components of the studied readiness in primary school teachers), methods and forms (traditional and innovative). In the context of the study of the problem of forming the readiness of primary school teachers to work with gifted students, the subjectivity of the teacher is considered as an essential property of the personality, which is manifested in the attitude to oneself as a subject of one's own professional activity with gifted students and the attitude to gifted students as subjects of their own activity, which ensures the recognition of the gifted student as the main subject of learning and initiates the creation of favorable conditions for the disclosure of the potential of the student's individual giftedness, his/her self-development.
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