Mémoire de Maîtrise
DOI
10.11606/D.45.2018.tde-27112017-161157
Document
Auteur
Nom complet
Fernando Pavan Guido
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Paulo, 2017
Directeur
Jury
Druck, Iole de Freitas (Président)
Fonseca, Rogério Ferreira da
Valério, Barbara Corominas
Titre en portugais
Estudo de uma conceituação geométrica para os logaritmos
Mots-clés en portugais
Hipérbole
Logaritmo natural
Número e
Resumé en portugais
Titre en anglais
Study of a geometric conceptuation for logarithms
Mots-clés en anglais
Hyperbole
Natural logarithm
Number e
Specialized knowledge of content
Resumé en anglais
The main objective of this work is to contribute to the improvement of the mathematics teacher, whether in training or acting. We seek to offer a material that can serve as a technical, historical and epistemological reference for the study of the Natural Logarithm. We discuss here the concept of Specialized Content Knowledge, coined by University of Michigan researchers and led by Deborah Ball. In your article Content Knowledge for Teaching: What Makes It Special? (2008), they raise the question "What mathematics does the teacher need to know for teaching?", since the mathematical knowledge required for the teacher differs from the mathematical knowledge required in other professions. Here we present a critical analysis of the approach used for the subject in some high school textbooks. We describe in detail the construction of the Logarithmic Function as actually occurred in the seventeenth century, that is, through areas of regions under the curve xy = 1, and we define the exponential function as the inverse of it, a focus with a strongly geometric character that gave rise to the notion of definite integral. We also show the close relationship between Arithmetic, Geometric, Trigonometry and the main theme itself. We also obtain the formalization of the irrational number e, both by the traditional method used in Calculus and Analysis books and by the theory presented. Finally, we present some curious situations that directly or indirectly involve this constant and that can be worked with Basic Education students.

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Pavan.pdf (1.47 Mbytes)
Date de Publication
2018-04-16

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