In the light of reforms in the field of education in Kazakhstan, it is necessary to revise approaches to meeting the cognitive needs of students, taking into account their abilities and motivation to learn.Special attention should be paid to children who have increased motivation to learn and pronounced abilities in certain school subjects. These are the so-called "Olympians". The article proposes a solution to the problem that arises in every secondary school, namely, how to teach such children to promote their optimal development. The authors of the article analyzed the work of secondary schools and, on its basis, identified positive and problematic aspects. To solve the identified problems, the system of work of the school in the direction of work with children with increased motivation for learning and gifted children was proposed: a cyclic plan of the school, recommendations on the organization of the school of the Olympic reserve, a strategy for training a selected group of children was proposed

In this article the modern understanding of giftedness is considered. The author having passed through scientific disputes of many psychological schools argues that it is based on the dominant cognitive motivation and research creative activity, expressing in the discovery of new in the formulation and solution of problems in secondary school through individual technologies.