Activation of educational activities of schoolchildren under the development of mathematical methods of knowledge

The paper is devoted to the problem of improving the teaching of mathematics in a comprehensive school, enhancing educational and cognitive activities based on mathematical methods of cognition, identifying the most effective teaching technologies that promote students to develop creative thinking, the ability to independently solve non-standard problems, and modeling complex mathematical objects. In connection with the introduction of innovations in the general education school, which posed fundamental questions to scientists and teachers about the specifics of teaching and educating schoolchildren, it became necessary to resolve the dialectic contradiction between the desirability of implementing a competencybased approach based on methods and techniques of scientific knowledge, mathematical logic, and a system of algorithmic prescriptions providing creative activities for students and still practicing the deductive nature of traditional methods dove teaching mathematics. The paper focuses on the fact that in order to enhance the creative educational and cognitive activity of students, it is important to constantly correlate the studied mathematical models with their real prototypes by abstracting and generalizing the phenomena of the real world, substantive and methodological connection of theoretical conclusions with practical work. The methods and approaches proposed in the paper for teaching students how to solve problems and equations together form the methodological field of various teaching methods and techniques in new, more flexible combinations and in non-standard contexts for the general course of mathematics. The creative development of the richest opportunities, characteristic for the practice of the work of the best teachers, should be the property of all teachers of mathematics, should be reflected in innovative approaches to teaching mathematics, the formation of logical thinking among schoolchildren.

mathematical education, teaching of mathematics, mathematical modeling, solution of equations, proofs, theorems, independent work in mathematics, evaluation of results