Open olympiad as a means of mathematical enlightenment of school students

Mathematical Olympiad movement plays an important role in the development of mathematics, enhancing the prestige of education in the international arena, as well as in shaping the student’s personality, fostering a desire to achieve high results, determination, readiness for long-term work. The question of classical mathematical olympiads is well described in literature, but non-standard forms of intellectual competitions in mathematics, which include open olympiads, are practically not considered.The article provides a historical overview of the open olympiads appearance and development, describes the characteristics that make it possible to classify the olympiad to an open type, justifies the use of open olympiads as a means of mathematical enlightenment for students, discusses the competition period of the olympiad and the approaches to the choice of themes for the open organized olympiad.The paper provides a comparative analysis of open and traditional mathematical competitions according to different criteria. The goals and objectives of both types of olympiads as well as the requirements that are put forward to the formulation of tasks for open olympiads are described. Special attention is paid to the issue of preserving the health of schoolchildren participating in the olympiad, the interdisciplinary nature of the tasks, and possible informative blocks of open mathematical olympiads are described.The article describes the organizing experience of an open competition dedicated to N. I. Lobachevsky, gives examples of original authors’ assignments, describes a mechanism for checking students’ works, describes the possible difficulties that are missing when testing regular olympiads, but occurring in open type olympiad works. The analysis of the pedagogical and psychological results is given, the development of general educational skills of students participating in the open olympiad is described, conclusions on the prospects of using the open type olympiads for mathematical education of schoolchildren are made.