A New Pedagogical Approach To Teaching The Theory Of Elementary Functions In School
DOI:
https://doi.org/10.37547/pedagogics-crjp-06-09-06Keywords:
School mathematics, didactic approaches, continuous line and continuous functionAbstract
The article recommends teaching elements of mathematical analysis in school as the theory of elementary functions. It proposes changing the traditional order of topics "Limit of a sequence, limit of a function, derivative and integral" based on the properties of elementary functions to the following: "Limit of a sequence, limit, derivative and integral of a continuous function."
The simplification of the traditional approach was achieved by modifying the didactic axiom confirming the continuity of elementary functions and, consequently, altering the conditions in Heine's definition of function continuity. We believe that this pedagogical approach to teaching helps reduce theoretical gaps and associated complications in traditional teaching methods.
This work can be considered a simplified version of Academician A.N. Kolmogorov's idea that the theory of continuous functions should be taught in schools and the theory of general functions in higher education. In our opinion, basic and specialized schools can use the proposed project in developing their curricula.
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