Teorema Fundamental do Cálculo: uma proposta de abordagem a partir da modelagem matemática com auxílio do Geogebra

Abstract

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.