Abstract
The article examines various aspects of extracurricular activities in mathematics. In particular, principles and rigors regarding the selection of contents for the in-depth study of mathematics and the organization of this process are formulated. For the first time, a pedagogical model for developing the skills of children gifted in mathematics elaborated on the basis of their own professional experience is described. The model integrates resources and processes aimed at harmonizing the development of mathematically gifted children's skills. The basis of the Model is the methodology and the conception of the resultant regarding the general mental development and the development of any individual particularities of students capable of high performance in mathematics.

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