AN INNOVATIVE DIDACTIC APPROACH TO TEACHING THE THEORY OF ELEMENTARY FUNCTIONS

This paper presents an innovative pedagogical approach to teaching the elements of mathematical analysis in schools through the theory of elementary functions. The proposed approach modifies the traditional sequence of topics — limit of a sequence, limit of a function, derivative, and integral — into a new logical order based on the properties of continuous functions: limit of a sequence → limit, derivative, and integral of a continuous function. The key idea is to simplify the concept of function continuity by introducing a didactic axiom that affirms the continuity of elementary functions without formal proof. This makes it possible to present the limit, derivative, and integral as natural consequences of continuity, thus creating a more intuitive and logically connected learning process for students.