Improving the methodology for teaching the «Differential Geometry and Topology» course to future mathematics and computer science teachers based on distance learning technologies

Abstract

This article examines the features of organizing the «Differential Geometry and Topology» course for future mathematics and computer science teachers using distance learning technologies. The relevance of the study is determined by the increasing role of digital technologies in higher pedagogical education and the need to develop effective electronic educational resources for studying complex mathematical disciplines. The aim of the study is to substantiate the structure and content of the distance learning course in differential geometry and topology, which ensures the systematic formation of students' theoretical knowledge, practical skills, and independent work skills. The study employed methods of scientific and educational-methodological literature analysis, pedagogical design, systematization of educational material, and structural-functional analysis of the distance learning course. The developed course includes five interconnected blocks: organizational-introductory, theoretical, additional, individual-practical, and control-evaluative. The course content includes lecture materials, practical assignments with examples of solutions, presentations, testing, individual and creative tasks, forums, a chat, a glossary, and a final assessment. It has been shown that the combination of various distance learning forms contributes to increasing students' independence, systematizing mathematical knowledge, and forming the professional competencies of future teachers. The proposed structure can be used in developing digital courses for other mathematical disciplines.

Keywords

distance learning; distance education technologies; differential geometry; topology; mathematical education; digital educational resources; teacher training.

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