A disciplina de cálculo I do curso de matemática da Universidade de São Paulo: um estudo de seu desenvolvimento, de 1934 a 1994

• Autor(a) principal: Lima, Gabriel Loureiro de
• Data de Publicação: 2012
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/10907
• topic: Ensino superior; Cálculo; Curso de matemática da USP; Análise matemática para o cálculo; Higher education; Calculus; Mathematics graduation course at USP; Mathematical analysis to calculus; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The present study aims to analyze the development of early discipline of Differential and Integral Calculus in Mathematics graduation course of Universidade de São Paulo (USP) since 1934, when this institution was founded and in which the first Mathematics graduation course was implemented, until 1994, when the subject Calculus I of Teaching Course became officially different from that offered in the Bachelor. Through interviews, conducted in accordance with the methodology of Thematic Oral History, with involved people, in different years, in the process of teaching and learning of Calculus at USP, by the analysis of the textbooks contents used at different times and by the obtained data in official documents or in the researches done by other scholars, it is noticed that initially there was not in the curriculum of Mathematics course of the investigated institution a discipline called Calculus. It was implanted at USP the European model, in which the studied concepts in this discipline had been worked which formal an high level of rigor in the course of Mathematical Analysis, introduced by Italian mathematician Luigi Fantappiè in 1934 and taught to the students since they attended the higher education, by mean that followed against the historic development of Calculus and Analysis as fields of knowledge. As time passing, by didactic reasons, some professors, especially Elza Furtado Gomide, Omar Catunda e Carlos Benjamin de Lyra, were led to defend that before studying Analysis, students should go attend on initial course of Calculus, in which the concepts would be discussed with a lower level of rigor and more manipulative way, an idea that culminated in the introduction to the discipline called Differential and Integral Calculus in the Mathematics course of the institution in 1964. This discipline had been conducted essentially with analytical orientation for many years. The process of transition from Analysis to Calculus often seen as a pre-Analysis - was slow, gradual, full of comings and goings and its detail is one of the aim to this research, which focuses its attention also in the didactic concerns and levels of rigor present in different years in the discipline of Calculus I and in the textbooks used as reference by professors. For the presented analyzes it has not recourse to a general theory that establishes the study; in it chapter specific theoretical considerations referring to studied theme are searched. In the beginning, it is noticed that the professors did not accept the existence of different levels of rigor then they did not consider necessary to adequate to the target public of the discipline that was being taught. Gradually, however, the adaptation of the way how the concepts were presented became to be defended, considering the mathematic maturation of the students, the course in which the discipline was inserted and the professional profile that would like to be formed. It is noticed that the most part of manifested concern by the authors of textbooks and by the professors of analyzed discipline was strictly related with the intention of these professors and/or the authors in giving conditions to the students in order to get, in fact, comprehension of the Calculus study done in high levels of rigor and the formalism. Furthermore, it may observed that the distinction between the discipline of Calculus I for Teaching Course and Bachelor´s Degree also was given by didactical reasons: it was searched to offer to the future teachers an initial course that would enable them to review, with a way that was more suitable to the goals of higher education, concepts even studied in the Basic Education that students do not usually dominate them when they enter the university, and at the same time, introducing the specific contends of Calculus in a appropriated way to the future teacher