Teorema Fundamental do Cálculo: uma proposta de abordagem a partir da modelagem matemática com auxílio do Geogebra
Resumo
The disciplines Differential and Integral Calculus for STEM students require a
precise understanding of the themes to avoid it being an arduous path of learning
and building a solid foundation, and it is the teacher's responsibility in their
teaching process for the best options. This paper aims to present an approach to
the Fundamental Theorem of Calculus, but specifically, applications of integrals
and assumptions of mathematical modeling, using technological resources. For
this purpose, a study of a historical-epistemological nature was carried out in an
attempt to understand how this concept has developed throughout history, from
the Ancient Age to Newton and Leibniz, who arrived at the Fundamental Theorem
or derivation as inverse operations. Next, carried out a study on the use of
mathematical modeling as a teaching methodology following the assumptions of
Biembengut and Hein (2019), Bassanezi (2015), and Bassanezi (2018). And
finally, two sequences of activities based on assumptions of mathematical
modeling were elaborated. Sequence 1 was developed to achieve the calculation
of the area of an image of a lake and sequence 2 was elaborated to provide a
road map for the calculation of the volume of an image of glass. In both, the
development of the solution was carried out according to the steps of the
mathematical shaping and modeling process and had the GeoGebra software as
a calculation tool.
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