Methodological aspects of teaching schoolchildren to solve mathematical problems of increased complexity

Various solutions to mathematical problems can cause certain difficulties for schoolchildren. The use of a scheme allowing to organize and systematize the search for a solution to a problem makes it possible to ensure the interaction of participants in the educational process, aimed at creative initiative, mathematical intuition, activity, and independence in reasoning. The result is the ability of the student to solve various problems individually. The goal is to substantiate a step-by-step scheme for solving the problem for its application in the process of teaching mathematics to schoolchildren. The system and activity approach compose the research base. The work used such methods as generalization, systematization, classification, analysis of domestic and foreign studies. Russian and foreign researchers in their works divide the activity of schoolchildren in solving problems into separate stages, which contributes to the formation of the main methods of action aimed at obtaining educational results. The proposed schemes differ in content, as well as in the number of allocated stages.. Generalization and systematization of the studied experience made it possible to modify them taking into account the needs of the participants in the educational process. During training, the task of increased complexity is solved not only by the student, but also by the teacher. The above scheme summarizes their activities, makes it possible not only to analyze the problem, but also to characterize the methodological and methodological aspects of the solution. Accordingly, it includes the following stages: analytical, schematic, methodological, descriptive, verification, research, methodical. At the analytical and schematic stages, the actual search for a solution to the problem is carried out, its main content is represented using mathematical models and various schemes. At the methodological stage, the task is characterized from the point of view of the methods used and the mental operations used. The descriptive and verification stages are directed by recording the problem solution and his validate that includes logical, computing and other mistakes. During the research phase, an analysis of the conditions of the problem is carried out, the existence of its solution is determined when they change. The methodological stage enables the teacher to generalize and systematize issues related to learning to solve a problem. The scheme considered in this paper systematizes and structures the activities of both the teacher and students in solving problems for the gradual formation of the ability to search for it.

teaching mathematics to schoolchildren, difficult problem, mathematic problem solution stages, student development