MEDIA EDUCATIONAL TECHNOLOGIES IN TEACHING THE DEFINITE INTEGRAL IN THE COURSE OF MATHEMATICAL ANALYSIS

Abstract

The article substantiates the didactic potential of media educational technologies in teaching the definite integral in the course of mathematical analysis. The relevance of the study is due to the digital transformation of education, the need to implement competency-based, activity-based and personality-oriented approaches, as well as the preparation of future mathematics teachers for the effective use of digital resources in professional activities. The aim of the article is to determine the pedagogical conditions and methodological possibilities of using media educational technologies when studying the concept of the definite integral, its properties, geometric content and calculation methods. The study uses an analysis of scientific and methodological literature, generalization of pedagogical experience, observation, comparison and elements of a pedagogical experiment. The possibilities of digital graphic services, interactive models, presentations, educational videos and online forms for visualizing the area of a curvilinear trapezoid, demonstrating the dependence of the integral value on the limits of integration, checking the properties of the definite integral and forming skills in applying the Newton– Leibniz formula are revealed. It is proven that the combination of analytical, graphic and numerical presentation of the material contributes to a deeper understanding of abstract mathematical concepts, the development of logical, algorithmic and critical thinking, increasing cognitive activity and learning motivation of students. It is determined that media educational technologies should be used not only as a means of visualization or control, but as a tool for organizing research activities, modeling, self-control and differentiation of learning. The practical significance of the study lies in the possibility of applying the proposed approaches in teaching mathematical analysis and mathematics teaching methods. It is concluded that pedagogically justified integration of media educational technologies increases the effectiveness of mastering the topic “Definite integral. Properties of the definite integral. Theorem on the derivative of a definite integral with a variable upper limit. Calculation of definite integrals” and contributes to the formation of mathematical and information and digital competencies.