THEOREMS ON THE NUMBER OF ROOTS OF A CUBIC EQUATION AND THEIR LOCATION AS A MEANS OF DEVELOPING STUDENTS' VISUAL THINKING

Abstract

Formulation of the problem. The basis of teaching mathematics is logical thinking, (which is associated with) based on the work of the left hemisphere. In scientific and methodological research, the volume of work related to the issue of organizing learning by coordinating the work of both the left and right hemispheres is increasing, that is, the development of other types of thinking, especially visual, along with logical thinking. Proposals have been developed on the methodology for the development of visual thinking of students in mathematics lessons. However, when studying the basics of algebra and analysis, improving the methodology for developing visual thinking and developing teaching materials for extracurricular activities are also urgent tasks.

Materials and methods. The research materials are pedagogical, methodical literature, experience of foreign and domestic scientists. In the process of research, empirical methods (observation, verification, experiment), general scientific methods (analysis, synthesis, concretization, systematization, generalization) were used. The method of reverse proof was used to prove the theorems.

Results. The study of graphs of a cubic function helps to build and prove hypotheses about the number of real roots of a cubic equation and their location, and makes it possible to clearly demonstrate the use of visual thinking.

Conclusions. Educational material on the location of the roots of a cubic equation helps to develop the visual thinking of students, to formulate visual tasks for students. These visual tasks serve as a means of organizing the mathematical activity of students. It helps readers understand how theorems are created and how to look for proofs. It also shows the relationship between the discriminant of a cubic equation and the product of the extreme values of the corresponding cubic function. We recommend studying the location of the roots of the cubic equation for high school students in maths club training.