Math club as a form of additional education at school

The article is devoted to a new vision of the activities of school additional education, as an important component of the modern educational space, which has an advantage in shaping the personal characteristics of students due to a more flexible structure. The article describes the pedagogical potential and modern approach to understanding additional education in general and the school subject circle in particular regarding the formation of students’ subjective experience in cognition. The author has formulated a set of organizational and pedagogical conditions for the activity of a school subject circle as a form of additional education, which makes it possible to fully contribute to the formation of students’ subjective experience in cognition at all its levels. The example of a practice-oriented lesson taking place on the territory of the Vladimir-Suzdal Museum-Reserve, conducted in accordance with the presented provisions, underlines the need to modernize the activities of modern additional education.