Elements of the methodology of routine mathematical activity in teaching undergraduate and graduate students

Digitalization of all areas of life in education is manifested mainly in the introduction of distance technologies, electronic learning tools and electronic tools for monitoring and management. In our opinion, this is not enough, it is necessary to change priorities in the content and activity components of training. In particular, in teaching mathematical activity, one cannot limit oneself to management at the algorithm level. Based on theoretical research and the analysis of teaching practice, the authors identified three levels of activity management: the level of typical algorithms, typical strategies of subject activity, and the level of methodology. The aim of the study is to build a model of the methodology of routine mathematical activity adapted for use in the digital environment and applicable in the practice of teaching mathematics to undergraduate and graduate students. In the article, the methodology of activity is considered from an applied point of view, based on many years of practice of teaching mathematics to students and the author’s interpretation of the concept of “activity strategy”, thought of as a mechanism for creating activity plans (the mechanism is understood here as an objective component of the activity management system). The scientific novelty of the study consists in the fact that, firstly, a model of the methodology of routine mathematical activity has been built and tested in practice (during the development of educational and methodological support, conducting classes, organizing independent work), and secondly, priority components of the methodology of routine mathematical activity have been identified based on the analysis of this model and teaching practice. As a result of the study, the authors proposed a model of the methodology of routine mathematical activity in the form of a system of three components: 1) building sufficiently adequate models for implementing already mastered strategies; 2) a system of “internal meta-strategies”, i.e., strategies for forming typical components of strategies; 3) a system of “external meta-strategies”, i.e., strategies for combining known strategies. On this basis, priority components of the methodology of routine mathematical activity have been identified. Examples of using the methodology for building strategies for solving mathematical problems are given.