SETTING AND SOLVING RESEARCH PROBLEMS IN TEACHING MATHEMATICAL DISCIPLINES: ПОСТАНОВКА ТА РОЗВ’ЯЗАННЯ ДОСЛІДНИЦЬКИХ ЗАДАЧ ПРИ ВИКЛАДАННІ МАТЕМАТИЧНИХ ДИСЦИПЛІН - Stegantsev, Eugene; Chernienko, Аlena (Physical and Mathematical Education, 2025)
Formulation of the problem. Research tasks are a necessary component of the educational process, and their use contributes to the development of critical and creative thinking, and the formation of the ability to act in a non-standard situation. Along with the need for thorough pedagogical research on the theoretical foundations of the implementation of research-based learning technology, a number of practical issues arise related to the preparation of teachers for the organization of research activities in the educational process. The purpose of this article is to review the available research on the research approach to teaching, to describe my own experience of setting research tasks in teaching mathematics and organizing their solution by students, to analyze the possibilities of finding sources of research tasks and creating them independently.Materials and methods. Methods used: analysis of the application of individual components of the theory of research problem solving, analysis of existing studies on the impact of research results on increasing student motivation. The study used textbooks on higher mathematics, algebra and number theory, and the basics of mathematics for higher education institutions, as well as scientific publications and their discussions..Results. The article demonstrates the possibilities of organizing students' research activities in teaching mathematical courses, using the theory of solving research problems, analyzes some possibilities of creating research problems, and considers methods of solving the proposed research problems (the method of focal object, accumulation of educational material, brainstorming).Conclusions. Mathematical courses are a favorable basis for ensuring research activities of university students. The article emphasizes the inclusion of research tasks into the learning process on a regular basis. University professors should improve their own experience in organizing students' research activities, as well as the experience of professors from foreign universities who have been working on the implementation of research-based learning for some time. It is clear that the transition to this technology will be long and will require gradual changes in the curricula of the specialties. Research will also be needed on methods of increasing student motivation to ensure the effectiveness of research activities.
Keywords: research activity; learning process; continued fraction; Farey sequence; Stern-Brocot tree; irreducible over the field polynomial; reciprocal polynomial; axiomatic theory