ON SOME APPLICATIONS OF DIVERGENT PROBLEMS

Abstract

The paper is devoted to identifying possible effective applications of divergent problems in school courses in mathematics and physics. The article first outlines the essence of the divergent task, its contributing role in the formation and development of the logical and creative thinking of students, after which the varieties of divergent tasks are interpreted, and then, for each variety, examples of divergent tasks found in school courses in mathematics and physics are discussed in detail. The first kind of divergent problems are problems that allow different solutions. As an example, this paper discusses one mathematical problem of determining the largest value of an expression. In addition to the standard method, as a means of stimulating the creative abilities of students, three more options for solving the problem are proposed, which, differing significantly from each other, contribute to a comprehensive consideration of the problem. The next problem discussed in the article is from the "Mechanics" section of the school physics course. Three different approaches to solving this problem are presented. At the same time, these approaches differ not so much in mathematical solutions as in the accepted physical ideas. The next type of divergent problems are problems that have ambiguity, freedom or uncertainty in their conditions. The article analyzes in detail the mathematical problem of motion and the non-standard problem of dynamics, as divergent problems of the second type. The study provides guidelines, the use of which will contribute to the search for ways to solve divergent problems, and will allow you to protect as much as possible from mistakes made in the preparation or solution of such problems, which is the scientific and pedagogical novelty of the article