THE IMPLEMENTATION OF PROJECT TECHNOLOGIES IN THE PROCESS OF SOLVING EXTREME TASKS USING ELE-MENTS OF FUNCTIONAL ANALYSIS - Hrabova, Ulyana; Tovkach, Roman; Kharkevych, Yurii (Physical and Mathematical Education, 2021)
Formulation of the problem. The reformation of the Ukrainian school requires a change of modern teacher's role positions. Thus, the problems of innovative organisation, search for new tools and technologies for the training of mathematics teachers in Bachelor's and Master's programs at universities are actualised. In order to train future professionals, it is necessary to pay attention to two dimensions of training results: subject knowledge, skills, abilities, experience in performing methods of activity, subject competencies, and subjective results - experience in creative activities, general educational skills, key competencies. In the system of professional training of future mathematics teachers, work on projects occupies an important place. It is the implementation of the project method that makes it possible to integrate the acquired knowledge, as well as to develop students' cognitive and creative skills.Materials and methods. During the process of research, the methodological literature on the research problem was analysed and generalised; the research information and the experience of the authors in organizing and conducting classes on methods of teaching mathematics and functional analysis  were classified and systematized.Results. Here is the example of the project for the implementation of knowledge of the fundamental mathematical discipline "Functional Analysis" in the course of solving extreme tasks of the school course of mathematics, which involves the modernization of the content of professional training of future mathematicians.Conclusions. The introduction of project technologies in the study of fundamental mathematical disciplines assures the formation of a professional who has knowledge of subject and modern practices, technologies, techniques, forms and methods of work on the basis of innovative educational approaches. At the same time, students conduct independent researches, solve current problems; students are trained according to their abilities, which helps to establish interaction between the subjects of study. The technique, described below, can be applied in the study of other fundamental mathematical disciplines, which will contribute to the professional development of future teachers and will give the opportunity to make the students interested in studying mathematics and conduct scientific researches.
Keywords: New Ukrainian School; professional competence of future mathematics teachers; project technologies; functional analysis; innovative technologies