Equações diferenciais ordinárias de variáveis separáveis na engenharia civil: uma abordagem contextualizada a partir de um problema de transferência de calor

• Autor(a) principal: Pinto, Rieuse Lopes
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://repositorio.pucsp.br/jspui/handle/handle/24368
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Educação Matemática no Ensino Superior; Engenharia Civil; Equações Diferenciais Ordinárias de Variáveis Separáveis; Mathematics Education in Higher Education; Civil Engineering; Ordinary Differential Equations of Separable Variables

In this qualitative research we investigated the learning of Ordinary Differential Equations (ODE) of separable variables from a contextualized approach with students from a Civil Engineering course, in line with the assumptions of The Theory of Mathematics in the Context of Science (TMCS) by Patricia Camarena Gallardo. Using the methodological procedures inherent to the TMCS epistemological phase and based on a situation related to Heat Transfer by conduction in flat masonry walls, we developed a Contextualized Event (CE), named according to TMCS: a problem that in the environment of learning plays an integrating role between mathematics courses (in this case Calculus) and non-math courses (in this case Heat Transfer) which are part of the curriculum of a given undergraduate program. This CE was the basis for the construction of a teaching sequence for the students to mobilize a set of mathematical and physical concepts. For the implementation of the EC, a field research was conducted with 21 students from the second period of the Calculus course of the Civil Engineering program of an institution located in the city of Montes Claros, State of Minas Gerais, structured according to the precepts of the didactic phase of TMCS. In order to answer the question What are the contributions brought by a Contextualized Event, built from a heat transfer problem, for the learning of Ordinary Differential Equations of separable variables by undergraduates in Civil Engineering ?, data related to the implementation of the EC were collected through audio recordings of students’ discussions, participant observation, written records with the development of activities, in addition to notes made by the researcher during the activities. Using the methods, coding procedures and categorization proposed by Charmaz and qualitative content analysis from the perspective of Graneheim and Lundman, the data obtained were organized and analyzed from the precepts of the cognitive phase of TMCS, from the assumptions of Vergnaud's Theory of Conceptual Fields (TCF) and Duval's Theory of Semiotic Representation Records (TSRR). The analysis showed that the EC resolution: enabled the understanding of the contents of Mathematics and Physics and the construction of concepts of Heat Transfer and Calculus, specifically of ODE; enabled the development of interdisciplinarity; provided the mobilization of different records of semiotic representations; provided a favorable environment for learning, with questions about other forms of resolution of ODE; and finally, it enabled the development of competences presented in the National Curriculum Guidelines for Engineering Undergraduate programs through the development of aspects related to the Contextualized Transposition process, which in the TMCS is related to the elements necessary to apply the knowledge of mathematics to a certain area