Development of students' professionally significant competencies through the implementation of practice-oriented methods of teaching higher mathematics in the context of the digital transformation of education

Abstract

Mathematical training in higher education is oriented toward the logical completeness of the course, while the acquired apparatus is poorly converted into the ability to apply it to the tasks of a future profession. The digital transformation of education, fixed by strategic documents with a planning horizon up to 2030, shifts the assessment of training to the language of measurable competency-based outcomes and sharpens the gap between the fundamentality of the course and its professional relevance. The aim of the work is to substantiate a model in which practice-oriented methods of teaching higher mathematics and digital tools form a single didactic contour. Using structural-functional and conceptual-categorial analysis, classification of pedagogical means and content analysis of the regulatory framework of higher education, the methods, model components and their correspondence to the competency groups of the Federal State Educational Standard 3++ are systematized. A five-component model is constructed, combining the value-motivational, content-subject, instrumental-digital, reflexive-evaluative and transfer-activity links with independent means and observable results. A professionally significant competency takes shape at the intersection of the professionally rich content of a task, the digital tool of its solution and the reflexive correlation of the result with the norm of the specialty; instrumental command of the tools forms a necessary though insufficient condition, while the load-bearing link is the substantive coordination of mathematical training with profile disciplines.