Path of Science: International Electronic Scientific Journal

The paper considers digital innovations that are useful to introduce when studying calculus of variations: visualisation software (general and mathematical), open educational resources, artificial intelligence, and learning management systems. Among the visualisation software tools, MindMeister, Genially, GeoGebra, and MATLAB are considered, and examples of their use for creating mind maps and interactive posters, constructing graphs of extrema, and solving problems of variational calculus are given. The significance, forms, methods, and possibilities of using these tools in the study of calculus of variations are clarified. The possibilities of open educational resources (online courses and video lectures) and artificial intelligence (Gemini) in individualising learning, familiarising students with foreign experiences in teaching calculus of variations, and utilising digital educational resources are presented. It is advisable to use the Google Classroom platform to organise distance learning and ensure equal access to digital educational resources for all participants in the educational process. A survey of students before and after the systematic application of digital innovations showed a statistically significant positive trend in attitudes towards the study of calculus of variations (according to Wilcoxon's criterion). The results confirm the feasibility and expediency of introducing digital innovations comprehensively into the professional training process of future mathematics teachers.

digital innovations; calculus of variations; digital visualisation tools; future mathematics teachers; GeoGebra; MATLAB; artificial intelligence; Gemini; Google Classroom

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