A abordagem do teorema fundamental do cálculo em livros didáticos e os registros de representação semiótica

Abstract

In this research, we verify as four didactic books present the Fundamental Theorem of Calculus. For this we search that basic differences are evidenced in the approach given for different authors, and, moreover, we observe if these authors, in its texts, explore the coordination of the registers of representation in the presentation of FTC. The used theoretical referential is the Registers of Representation Semiotics of Raymond Duval. This writes that for the acquisition of the mathematical knowledge, two registers of representation must be used simultaneously and not each one taken separately. To guide our research, we elaborate criteria (indicator) of organization for the analysis, based in the book Analysis of Content of Bardin that suggests stages for an elaboration of results. To the measure that we verify through these indicators the way for which the author presents the Theorem, was analyzing on the basis of the representation registers. From these analyses, we observe that one of books does not argue explicit, in the unit of prominence of our analysis, the referring question to the interrelation between Derivative and Integral, that it is given by the Fundamental Theorem of Calculus, however makes it two of its book by vol. How much to the representation registers, we verify that the authors explore the coordination of these in its books, although some make it of a more evident form that one suggested in the others, however, it has justifications for in such a way, being that they meet in the preface of the same ones; thus, we can notice that this if also must to the type of reader for which if it destines each one of books. We observe that the date of publication of books does not have direct relation with the diversity of registers used for the same ones