Abstract
In the process of training mathematics teachers at pedagogical universities, an important task is the formation of research activities and professional-methodological skills necessary for their future professional practice. The solution to this problem lies in the development of tools and methodological approaches aimed at fostering the research activities of students – future mathematics teachers.
The article considers the theoretical and methodological foundations of introducing project-based and research activities in order to actively engage students in the educational process and to reveal their creative potential. The methodology for solving research-oriented tasks in the process of teaching the theory of numerical series is presented with specific examples. The purpose of the article is to propose methodological approaches to the formation of students’ research activities in the process of teaching the theory of series to future mathematics teachers. The research methods include the analysis of scientific and methodological literature related to didactics and the theory of numerical series, analysis of the content of educational materials; observation of the learning process in order to determine the level of development of students’ research abilities; the introduction of problem-based questions, projects, and research tasks into the teaching of numerical series; statistical processing of the obtained results and their pedagogical interpretation.
The results of the study showed that the use of problem-based and project-based teaching methods, as well as tasks aimed at analyzing the properties and criteria of numerical series, had a positive impact on students’ deeper understanding of concepts, their active participation in the learning process, and the improvement of their research skills. The significance of the study lies in the fact that it contributes to the development of students’ independent research skills when mastering the educational material on the theory of numerical series, as well as to the formation of research and methodological competencies necessary for their future professional activities, while also enhancing logical and analytical thinking.
The conducted research results indicate that mastering the theory of numerical series by future mathematics teachers can be deepened not only at the level of subject knowledge, but also from the perspective of developing research activities. The application of project tasks and research problems promotes the development of students’ creative and critical thinking, improves their professional-methodological preparation, and helps to form teaching experience that can be effectively applied in their future pedagogical practice.