CHANGE OF VARIABLES METHOD IN THE SCHOOL COURSE OF MATHEMATICS

Abstract

The article investigates the peculiarities of using change of variebles method in solving various mathematical problems, which are common both in school mathematics courses and in higher mathematics courses. Studying mathematical concepts and methods requires consistent, systematic learning from students, which in case of violations can lead to difficulties at later stages of learning. The main focus of the research is on the role of change of variables method in ensuring the continuity of mathematics education. The main tasks that were performed in the study: analysis and generalization of the importance of applying this method in the context of the formation of students’ mathematical competence, revealing the features of the formation of skills in its use at various stages of education, identifying its potential for compensating educational losses that occurred as a result of distance learning, caused by the pandemic and military operations. In the process of working on the research, the analysis of scientific and methodical sources, dissertations, educational programs and concepts, study and analysis of school textbooks on mathematics was carried out. It has been established that change of variables method is a universal technique for solving equations in a school mathematics course, the mastery of which opens up opportunities for further study of higher mathematics courses. This method is based on the idea of replacing one variable with another to transform the original equation into a simpler, or standard, form. Usually, as a result of applying change of variables method, the equations are simplified to such a form that the value of the variable can be determined by simpler operations. Of fundamental importance here are the knowledge of ways to solve quadratic equations, to which substitution most often leads, as well as the ability and skills to apply them. The article presents the steps of mastering the change of variables method at school, starting from the 8th grade and until the completion of the school mathematics course. The prospects of using the method in solving higher mathematics problems are outlined.