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Using methods of functional analysis to describe the process of learning

Keywords:

M.N. Ryzhkova – Ph. D. (Eng.), Associate Professor, Department of Physics and Applied Mathematics, Vladimir State University named after A.&N. Stoletovs (Murom Branch). E-mail: masmash@mail.ru


The educational system as a system of acquiring knowledge is complex because of inlying relations and a large number of items. Therefore, to facilitate the study of such a system behavior and its components is necessary to make some restrictions, that is, to go from the real system to its model. Simulation is the primary method of research in all fields of knowledge and science-based method for estimating the characteristics of complex systems used for decision-making in various fields of engineering. One of the objectives of education systems modeling can serve the need to create student individual learning paths in e learning, dis-tance and additional education or in the system of advanced training. Using of the information about the student\'s existing knowledge and requirements to their level after training allow us to calculate the individual program of educational activities and, thereby, increase the educational quality. Using of functional analysis methods can be one of the possible approaches to the modeling of the learning process. The proposed model uses the concept of a vector of the student knowledge, as well as training operator – matrix, which components determine the individual educational path. The model uses the concepts of the learning process elements – keywords, however, can be extended to paragraphs of the course or curriculum subjects. This model has quite simple mathematical calculations, and is transparency in the work.
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