Abstract
The article presents the the authors' opinions regarding various aspects of the process of training students capable of high performance in mathematics, focused on three important areas: intellectual development; development of communication skills; personal development. The design of the fields of training for this category of students is developed taking into account the concept of the resulting development, the Pedagogical Model for the development of the skills of children gifted in mathematics and the Integrative Model of the process of training teachers for extracurricular activity in mathematics.

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