Orientation of modern society on developing scientific potential makes the problem of developing intelligently gifted students relevant. In this connection many countries pay attention to creating systems of identification, support and development of intellectually gifted students and talented youth.
Currently there is extensive material in science that allows to characterize intellectual endowments as a capability, which provides successful achievement of a certain level (I.A. Bevz ); as high intelligence (M. A. Birzheva ); as efficiency index of intellectual activity (N. A. Babiyeva ); as a set of knowledge and abilities of intellectual activity (V. M. Rafikova ); as personal dynamic integral education (T.A. Klimontova ); as developing property of a personality (N. V. Kalacheva ).
We adhere to M.A. Holodnaya  point of view who gives the following definition. "Intellectual endowments is such a state of individual psychological resources (first of all intellectual resources), which provides possibility of creative intellectual activity, that is the activity connected with creation of subjective and objective new ideas, with usage of nonstandard approaches to the problem development, with sensitivity to the most perspectives, key lines to search solutions in various knowledge domain, openness to any innovations" .
Obviously, characteristic features, specificity of developing intellectually gifted students portray the very teacher and determine specificity of his activity. The "average" teacher will not be able to develop students' intellectual endowments. Such teacher will not cope with an objective; will not be able to organize educational process. He is not ready to manage with the process of endowments development.
METHODS AND MATERIALS
For developing students' endowments we suggest to use constructivist, person-oriented approaches in education.
Ideas of the constructivist approach in education are reflected in works by L.S. Vygotskiy , J. Piaget , J. Bruner , J. Dewey , G. Gardner . Modern basic points of this approach in education are shown in the form of basic principles of constructivism by Ye.S. Polat , M.A. Choshanov . This approach is chosen because students' thinking development can happen at the expense of combining already available knowledge with the acquired. When using traditional lessons in teaching, students can remember information mechanically, pass examinations well, but they will not be able to apply that knowledge further, in various life situations. When using the constructivist approach, students are supposed to understand the studied information as well as to have skills of further application of gained knowledge.
The person-oriented approach (K.A. Abulkhanova-Slavskaya , L.S. Vygotsky ) has allowed creating...