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1 | The level of modern fundamental sciences and technologies, based on them, not only require an increase in the general level of natural science education, but also should attract talented young people to these areas of activity. These problems are directly related to the problems of activating cognitive interest and cognitive activity in the learning processes. In pedagogy and psychology, considerable scientific and practical materials have been accumulated on the study of cognitive interest and the formation of cognitive activity among children of junior and high school age, by various psychological and pedagogical means, including the introduction of specialized educational subjects. An important role in solving these problems plays extracurricular work with schoolchildren. In the sixties of the last century, the need to involve scientists into the study processes was recognized and therefore developing new ways to organize the teaching process for the schoolchildren. So the combination of physics and mathematics schools appeared (PhMS). Despite more than a half-century history of the physics and mathematics school existence, the PhMS in the context of activating cognitive interest and cognitive activity is considered for the first time. Illustrated by the example of Tomsk State University Physics and Mathematics School, the structure, directions and methods used in this form of extracurricular work are shown. Such forms as a correspondence physics and mathematics school, an evening physics and mathematics school, a summer full-time physics and mathematics school combining rest and training for schoolchildren, as well as a winter physics and mathematics school are considered. Examples of curricular are given, organizational forms of work for different age groups of schoolchildren are described. It is shown how PhMS can be useful for all schoolchildren but at the same time help to identify gifted students. The efficiency of the PhMS was analyzed based on the results of the Unified State Exam. Keywords: cognitive activity, cognitive interest, physics and mathematics school, gifted children, Unified State Exam | 827 |