O cálculo diferencial e integral para ensinar : a matemática para a licenciatura em Matemática

• Autor(a) principal: Grotti, Rogério
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFMT
• Texto Completo: http://ri.ufmt.br/handle/1/5371
• topic: Cálculo diferencial e integral; Ensino; Licenciatura em matemática; Matemática; Saberes para ensinar; CNPQ::CIENCIAS EXATAS E DA TERRA; Differential and integrative calculus; Degree in mathematics; Knowledge to teach; Teaching

This study aims to analyze the process(s) of constitution of a professional knowledge of the Mathematics teacher: the objectivation of Differential and Integral Calculus to teach. He is justified in the need of the teacher trainers in the Degree in Mathematics, to discuss the teaching of this discipline. The research revolves around the following problem: what processes are underway for the elaboration of the "Calculation to Teach" as a work tool for the training of Graduates in Mathematics? It is based on the hypothesis that, since the consolidation of the Mathematical Education Movement in Brazil, mainly in Post-Graduation Programs, a series of questions about the Initial Formation – Degree in Mathematics – has been developed and, in a first moment, the Pedagogical Disciplines were privileged as an object of study and, as this process matures (discussion of the Degree in Mathematics), research will increasingly tend to insert the Mathematical Disciplines (hard core) as object of study, among them the Differential and Integral Calculus. Initially, this work took as reference the theory produced by the Research Team on History of Educational Sciences (ERHISE) of the University of Geneva, and discussed in Brazil by the Mathematical Education History Research Group (GHEMAT), led by Researcher Wagner Rodrigues Valente (UNIFESP), about a crucial question in teacher training, adopted as the focus of the initial discussion of the present study, namely, "Knowledge to Teach", in other words, the knowledge that are the tools of our work. This research discusses the Degree in Mathematics in Brazil and the Movement of Mathematics Education: historical aspects of the formation of Mathematics teachers and the constitution of Post-Graduate Programs in Mathematics Education. Through a retrospective of the creation and development of the Degree in Mathematics, a panorama was presented about: a) Formation (Initial) of the Mathematics teacher in Brazil; b) the contributions of the Movement of Mathematical Education for the consolidation of the Degree in Mathematics in Brazil; and c) the emergence and development of the Graduate Programs in Mathematics Education as the main instrument of this movement (MEM) for the Research and Training of Teachers (Trainers) in the courses of Mathematics Degree. This study draws on Qualitative Research, based on dissertations and theses produced (and made available electronically) by Graduate Programs in Mathematics Education or by Graduate Programs in Education with Lines of Research in Mathematics Education, which discuss the Teaching of Differential and Integral Calculus in the Degree in Mathematics. The choice for the discussion of the Teaching of Differential and Integral Calculus was based on the fact that this discipline is one of those that presents the highest level of avoidance and reprobation, not only in the degree in Mathematics, but in several other graduations. A total of 65 (sixty-five) papers were produced from 20 (twenty) Graduate Programs in Brazil, produced between 2000 and 2017, of which 46 (forty-six) dissertations and 19 (nineteen) theses contributed to the formation of 16 (sixteen) Categories of Analysis, which are: 01) Information Technology / Softwares / Graphical Representation; 02) Virtual Learning Environments; 03) Collective / Collaborative Work / Reflection; 04) Semiotic Representation; 05) Intuition and Rigor / Conceptual Image and Conceptual Definition; 06) Significant Learning Theory; 07) Theory of Formation by Stages of Mental Actions; 08) Engineering (Sequence) Didactics / Fedhati Sequence; 09) Epistemological Obstacles / Learning Difficulties; 10) Knowledge Teachers; 11) Application; 12) Problem Solving / Mathematical Modeling; 13) Processes of Advanced Mathematical Thinking; 14) Inclusion; 15) History; and 16) Panorama / State of the Art / State of Knowledge. After the Data Analysis we can make the following considerations: Among the 65 (sixty-five) papers analyzed, the great majority was produced in the Southeast Region of Brazil. In the analyzed works – patent the concern to look for alternatives of CDI Teaching –, in view of the high reprobation indices in this discipline, being emphasized the use of Information and Communication Technologies (TICs), which facilitate the development, mainly in the "representation" of the concepts worked on in this discipline. This study found that the use of the TICs has been configured, as well as a trend, also as the main mechanism for teaching Calculus for future teachers, and are often adopted as teaching strategies and pointed as necessary for the teaching of this discipline. However, there is concern that, in using these technologies, the teacher does not stray from his role of mediator of knowledge. The analysis of the data still pointed a strong critical direction to the traditional model of Differential and Integral Calculus, which, according to aspects analyzed in the study, carried out a scenario of student failure in the Calculus discipline.