Um estudo sobre a abordagem de limite de funções em livros de cálculo diferencial e integral

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Universidade Federal de Goiás


Books play a fundamental role as teaching instruments, which makes them important objects of study for researchers seeking to understand learning difficulties, especially with regard to Mathematics in higher education, a topic in which this type of research learning is still scarce. With a focus on teaching, this bibliographical work, of an explanatory and qualitative nature, aims to investigate the way in which the Differential and Integral Calculus books authored by Louis Leithold (1994), Hamilton Luiz Guidorizzi (2001) and James Stewart (2013) addresses the definition of the limit of functions of a variable. To achieve this objective, the methodological research framework of Depth Hermeneutics – HP, proposed by Jonh B. Thompson, was mobilized with the intention of answering the following questions: what types of semiotic representation records are it possible to identify these works and how Can they influence the teaching of function limits? What socio-historical aspects of the production of these books influenced the author in choosing a certain approach? Conceiving the book as a symbolic form, the phases that represent the HP were articulated: the socio-historical analysis, where this information was collected about the authors' biography, the evaluation of the preface and changes in the other editions, actions referenced by the Historical Analysis of Mathematics Books by Gert Schubring and the study of Editorial Paratexts by Gerrard Genette; formal analysis, in which the types of representations of limits and functions that appear in books were identified, as well as their transformations, through event activities, categorization and the construction of inventories, in the light of the Theory of Representation Records Semiotics - TRRS by Raymond Duval; and the interpretation/reinterpretation in which a creative synthesis of meanings on the works studied was constructed. The results demonstrated that, in the three books, there is a predominance of the algebraic register over the others and the absence of exercises proposed between registers, which, according to the TRRS, can make teaching the concept of limit difficult. Individually, influences from the Modern Mathematics Movement, the Bourbakist school and the Calculus Reforms were identified in the writing of these books.



SANTOS, L. G. Um estudo sobre a abordagem de limite de funções em livros de cálculo diferencial e integral. 2023. 470 f. Tese (Doutorado em Educação em Ciências e Matemática) - Pró-Reitoria de Pós-graduação, Universidade Federal de Goiás, Goiania, 2023.