Do coeficiente angular da reta ao conceito de diferencial: Crítica ao ensino atual e proposta alternativa

Abstract

We start a meeting report of a study group, produced by students who are working towards their Master's Degree in Mathematics Education at UNESP, Rio Claro. The discussion has shown that difficulties faced by these students in dealing with differential approximations in their calculus courses, were due to the conceptions of slope of a straight line that they had learned in high school analytic geometry. We arrived at a didactical proposition to high school analytic geometry and trigonometry, intended to prevent this difficulty. The proposition includes suggestions for teaching derivatives in high school. The slope should be thought of, not only as Δy divided by Δy, but also as the number that, when multiplied by Δy, leads to Δy. The slope should be thought of as a multiplier. Similar remark holds for tan, sin, and cos. The meeting report is analyzed from the perspective of the production of meaning under Lacan's concepts. The didactical proposition is based on the theory of semantic fields and its practical feasibility is being tested in a freshmen calculus course. The paper describes a first attempt of carrying out research in Mathematics Education under a psychoanalytical approach.