Um estudo sobre a abordagem de limite de funções em livros de cálculo diferencial e integral
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Data
2023-08-31
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Universidade Federal de Goiás
Resumo
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.
Descrição
Palavras-chave
Cálculo , Hermenêutica , Análise , Forma simbólica , Calculus , Hermeneutics , Analysis , Symbolic form
Citação
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.