Managing the understanding of mathematical phenomena in the context of digitalization

Teaching mathematical activity is almost completely reduced to learning how to manage information processing. The author identifies three levels of mathematical information processing: the level of typical algorithms (for example, calculating the value of an arithmetic operation), the level of typical strategies (for example, solving equations) and the level of methodology (for example, the choice of a mathematical language for solving a task). Work at the level of typical algorithms and the simplest strategies of activity can be carried out without a deep understanding of the phenomena involved. But work at the level of strategies, and even more so, at the level of methodology, already requires understanding. We propose to interpret the term “understanding” as a system of associations with a mathematical phenomenon, i.e., concept, theorem, strategy, decision, etc. With a formal-constructive interpretation of the model, the considered interpretation of understanding includes the “creation of meanings” and other components of understanding. To control the completeness of the system of associations, it is proposed to apply the classification of associations with a phenomenon: 1) as an object or product of modeling activity (prototype, image and an interface, i.e. a system of information exchange between a prototype and an image); 2) as with a tool or operations; 3) as the management system and its components (with the motive of activity, with typical goals, with typical strategies and, in particular, algorithms, with systems for evaluating the adequacy of the model). The conditions for the success of the formation of priority associations among students are indicated: 1) adjustment of educational and methodological support; 2) adjustment of control and measuring materials; 3) purposeful formation of basic associations and, in particular, learning to translate information into different mathematical languages; 4) multi-aspect positioning of the studied phenomena relative to the information already learned by the student.

understanding, model, mathematical phenomenon, association with a mathematical phenomenon, classification of associations