Igor Kiselnikov

The article is devoted to topical issues related to the development of a methodology for teaching mathematics, aimed at stimulating the educational and cognitive activity of students. There are the contradictions, the resolution of which can contribute to an increase in the activity of students in the process of learning mathematics. The purpose of the article is to develop the main provisions of the methodology for teaching irrational equations, aimed at stimulating the cognitive activity of students. The author uses modern works on the problem of stimulating the cognitive activity of students in the following directions: organization of independent cognitive activity; development and organization of creative research cognitive activity; stimulating of schoolchildren in learning; formation of the cognitive interests of schoolchildren in the general educational aspect; search for rational methods and individual techniques of cognitive activity and teaching students to use them; particular methodological procedures contributing to the stimulation of cognitive activity. The leading approach is the process approach to learning, ensuring that students understand the mathematical content. The causes of reduced attention and understanding of the studied material are revealed, and the methodology for teaching irrational equations at school is built on this basis. The developed teaching methodology meets the requirements of modern federal state educational standards. The main result is the selection and substantiation of the conditions for the stimulation of students to study irrational equations in the secondary school. The theoretical significance of the article lies in the development of methodological approaches to the study of irrational equations in secondary school. The results of the study can serve as a basis for writing other scientific papers on a given topic. The practical significance is due to the fact that the results of the study can be used for educational purposes, as well as the possibility of applying and implementing the program of extracurricular activities in mathematics "Mathematical Workshop on Solving Irrational Equations".