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In the article the organization of teaching gifted students in rural schools using didactic opportunities of heuristic methods is revealed. In particular, a variety of heuristic teaching methods are characterized, among them: involvement; pretending; if; hyperbole, agglutination, brainstorming; inversion; focal objects; heuristic tasks decision. The main approaches to training and education of gifted children are analyzed, namely: accelerated learning (this approach takes into account the innate abilities of children who during one year study the program of several years, graduating from educational institutions before their peers); modification and enrichment of the content of education (as the result of in-depth study of certain subjects takes place the acquisition of a range of knowledge from one or more branches of science); review and redesign of learning objectives (the basis of this approach makes the direction of the educational process on the development of a creative personality). The basic laws of heuristic learning aredescribed. The principles of heuristic learning, which contribute to the development of gifted students, in particular, in rural schools are highlighted. To them belong: the principle of personal goal setting of a student: the education of each student is based on his/her personal goals in each branch of education; the principle of productivity of training: the main landmark of learning is personal educational increment of the student, which makes the sum of his/her internal and external educational products of learning; the principle of contextuality of accompanying training: the educational process is based on situations involving determination and heuristic search for their solution by the student, the teacher guides the student in his educational movement; the principle of educational reflection: the educational process is accompanied by its reflexive awareness by the subjects of education. The implementation of these laws by teachers in rural schools will contribute to the education of gifted students. The author concludes that in heuristic learning is implemented stability and deep trust in creative potential of every student, i.e. his cognitive-creative (search, research, design) activity takes the first place in the education system. Perspective can become a research of other ways of development of gifted students in rural schools in modern conditions.
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