Abstract

JACOME ANAYA, Ingrid Janeth; FIALLO LEAL, Jorge Enrique  and  PARADA RICO, Sandra Evely. An approach to the Fundamental Theorem of Calculus through Realistic Mathematics. Educ. mat. [online]. 2022, vol.34, n.1, pp.280-305.  Epub May 10, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em3401.10..

Here are reports the design, implementation and evaluation of an activity conformed by two realistic mathematical situations framed in the phenomenon of free fall, in the framework of an investigation supported by the theory of Realistic Mathematical Education, whose objective was to characterize the levels of mathematization achieved by students of a course of Integral Calculus in the study of the Fundamental Theorem of Calculus with the use of digital technologies. In the analysis of the models created by the students in the first three levels of mathematization described by the theory, it is evident that, from the tasks designed, the students manage to represent algebraically the existing relationship between variable quantity, accumulation of change and rate of change of accumulation, referring to the physical context presented. They identify the relationship between derivative and integral, explicitly stating that they are inversely related, since each one undoes what the other does, a relationship that is evidenced in the Theorem.

Keywords : Fundamental Theorem of Calculus; Mathematization; Levels of Mathematization.

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