PRIORITY COMPONENTS OF THE CULTURE OF WORK WITH THE CONCEPTUAL APPARATUS OF MATHEMATICS

In the minds of most people, mathematics is associated with calculations. But the functions of the computing apparatus of mathematics are increasingly being taken over by computer information technologies. Therefore, although there is no mathematics without calculations, in teaching mathematics the priority is the task of mathematical formalization of information (in particular, building a mathematical model, translating from one mathematical language to another, forming a mathematical concept), perceiving and processing mathematical information, etc. There are many problems in the course of discrete mathematics, the solution of which requires practically no computational skills; the main problems lie precisely in formalization. As experience shows, knowledge of definitions is not enough; it is necessary to master the culture of working with the conceptual apparatus. To do this, based on learning experience and previously obtained theoretical results (in particular, the hardware model of mathematics), we built models of the conceptual apparatus and its use and, on this basis, identified the priority components of working with the conceptual apparatus: (1) the habit of starting the analysis with definitions of concepts; (2) knowledge of definitions and ability to use them; (3) the ability to independently enrich the conceptual apparatus with new concepts: (3a) to single out a set of objects as the scope of a special concept; (3b) to formalize the scope and content of a concept as a definition; (3c) the ability to independently formulate definitions; (3d) comprehensively analyze their adequacy; (4) the ability to use the conceptual apparatus to formalize information, i.e. its presentation of information in appropriate terms. The paper provides examples of using the model from different areas of mathematics.

teaching mathematics, discrete mathematics, conceptual apparatus, culture of the conceptual apparatus, definition of a concept, scope of a concept, content of a concept, languages for representing concepts, hardware model of mathematics, teaching problem solving

Melnikov Yu. B., Belousova V. I. Priority components of the culture of work with the conceptual apparatus of mathematics. Biznes. Obrazovanie. Pravo = Business. Education. Law. 2024;3(68):480—487. DOI: 10.25683/VOLBI.2024.68.1076.