Integrais duplas: um estudo à luz de uma articulação entre a teoria antropológica do didático e a teoria a matemática no contexto das ciências

Abstract

Through this research, with a qualitative approach, adopting the articulation of the Theory of Mathematics in the Context of Sciences with the Anthropological Theory of Didactics as a Praxeology of Didactic Investigation, we carried out the study of the epistemological, economic-institutional and ecological dimensions of the didactic problem to carry out an investigation that allows the development of a proposal for teaching Double Integrals for students of the Civil Engineering Course in order to transform them into a support tool for these students, aiming at the exercise of the profession, so that they can interpret and apply them as a useful instrument without losing sight of the scientific character and the formal discourse inherent to them. The study of the epistemological dimension allowed us to identify that the problems that gave rise to the double integrals emerged from social and cultural contexts that were built from the needs related to the calculation of measurements of three-dimensional surface areas; the calculation of measurements of solid volumes; the need to calculate the amount of heat that passes through a point of a solid mass; and the need to reduce differential equations to algebraic equations with simpler solutions. In addition, based on the epistemological study carried out, we developed the Epistemological Reference Model (ERM) that allowed us to understand and question what is put in the reference institution considered in the study (a private institution in the North of Minas Gerais). In turn, the study of the other dimensions of the didactic problem showed how the double integrals are described and interpreted in the Civil Engineering course of the reference institution, as well as the conditions and restrictions that favor or prevent the elaboration and implementation of a Proposal Alternative for teaching these integrals as opposed to the Dominant Epistemological Model (DRM) in this institution. As an alternative proposal, we suggest a contextualized event - a problem that plays the role of an integrating entity between disciplines in the Mathematics and Engineering area - elaborated from a situation discussed in the discipline of Fluid Mechanics describing a laminar flow of an incompressible fluid that meets applications in civil construction, in situations of flow of very viscous lubricating oils and at low speed, boundary layer and flow in porous media (soils)