DIDACTIC POTENTIAL OF ISOPERIMETRIC TYPE PROBLEMS IN THE SCHOOL COURSE OF MATHEMATICS

Abstract

The article examines the problem of the formation of mathematical competencies of students in the modern conditions of reforming school education. The relevance of the topic is due to the presence of difficulties for schoolchildren when solving applied problems. Particular attention is paid to isoperimetric problems as an effective means of implementing the competence approach in teaching mathematics. Their didactic potential in the formation of students' skills of mathematical modeling, optimization and research activities is revealed. The historical origins of isoperimetric problems are analyzed, in particular the ideas of Zenodor, who proved that among polygons with a given perimeter, a regular polygon has the largest area, and a circle among all figures. It is shown that these ideas reflect the fundamental principle of optimality and symmetry, which remains relevant in modern mathematical education. The paper analyzes Ukrainian and foreign educational materials on the use of isoperimetric problems in the school course of mathematics. It has been established that such problems are widely used in the study of geometry, algebra and mathematical analysis, but their potential for the integration of knowledge and the development of competencies is not fully used. The paper proposes approaches to the design of problems that combine applied content and intramathematical ideas, which allows taking into account the interests of students of different educational areas. The expediency of using modern digital tools, such as GeoGebra, Desmos and others for the implementation of research teaching methods, which contributes to the development of logical and critical thinking, the ability to put forward and test hypotheses, is substantiated. Examples of practical problems on isoperimetry are given, for the solution of which it is enough to know the properties of quadratic functions. It is concluded that the systematic use of isoperimetric problems contributes to the formation of a holistic view of mathematical patterns, the development of interdisciplinary and intra-subject relationships, as well as the effective implementation of STEM/STEAM/STREAM approaches in teaching mathematics.