Abstract
The article is devoted to the problem of the formation of students' research skills when learning to solve Olympiad problems in mathematics. The peculiarity of the Olympiad task is that it is non-standard, outwardly similar to the academic task on the subject and requires logic and research. In this regard, the solution of the Olympiad problem in mathematics requires research skills in constructing a graphical and physical model, drawing up equations to describe the state of interacting objects, mastering the mathematical apparatus in atypical conditions. In addition, to determine the relevance of the research topic, a questionnaire was conducted through the Google platform, the participants of which were received from students of the educational program «training of a mathematics teacher» at a university and young professionals working in high school. As a result, situational tasks and critical situations were identified, which instantly contribute to the formation of research skills to meet modern requirements. Accordingly, it was analyzed that Olympiad tasks will help to break away from the usual system of thinking and look for new things. Based on historical data, it is known that students participating in the Olympiad have a high IQ. And, judging by the PISA results, the formation of research skills is important for the intellectual development of schoolchildren. For the formation of such skills and, as a consequence, cognitive independence of the individual when studying each topic of mathematics, it is recommended to include students in solving Olympiad problems. An example of a task system developed taking them into account in the preparation of mathematical Olympiad tasks is given.