Bobyliev D. Methods of teaching functional analysis to future mathematics teachers

Theoretical and experimental substantiation of the methods of teaching functional analysis for professional purposes to future mathematics teachers has been delivered in the research. Certain specific features of the professionally directed skills formation with the students studying functional analysis are scientifically grounded; professional competences of the future mathematics teacher formed in the process of functional analysis training have been lined out. The competence model of the future mathematics teacher, who studies functional analysis, as well as the model of the methods of teaching functional analysis for professional purposes in the composition of motivation-targeted, content, process-organizational, control-estimating and productive components are developed. The goals and structure of the «Functional analysis» content in terms of the subject training are specified; the methods and organizational forms of teaching functional analysis in the context of students’ professionally oriented skills formation are distinguished; the system of teaching techniques has been elaborated. To implement the described methods, a training and methodological complex of teaching the discipline along with the computer support for the heuristic teaching method of functional analysis have been created on the platform «Moodle»; a training manual to «Functional Analysis» learning is developed. The effectiveness of the proposed methods has been verified experimentally.