Evento contextualizado: uma proposta de ensino e de aprendizagem de autovalor e autovetor no curso de Engenharia de Controle e Automação e áreas afins

• Autor(a) principal: Philot, Juliana Martins
• Data de Publicação: 2022
• 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/30945
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Educação Matemática no Ensino Superior; Engenharia de controle e automação e áreas afins.; Álgebra linear; Teoria de controle moderno; Teoria a Matemática no contexto das Ciências; Teoria da modificabilidade cognitiva estrutural; Mathematics Education in Higher Education; Control and automation engineering and related areas; Linear algebra; Modern control theory; Theory mathematics in the context of science; Structural cognitive modifiable theory

Research in Mathematics Education has pointed out the importance of teaching and learning Linear Algebra due to the interdisciplinarity of this discipline with other topics in Mathematics and even with other areas such as physics, chemistry, biology, economics, engineering, among others. Another fact that these articles present is the difficulty of students regarding this subject, considering it to be very theoretical and abstract. In addition, some research points out that this difficulty may be linked to the fact that this discipline is offered for courses, which do not aim at the formation of Mathematics, in a decontextualized way, not causing meaning for the students. Given these facts, this thesis aims to determine what are the necessary subsidies for the elaboration of a Contextualized Event aimed at the construction of the concepts of eigenvalues and eigenvectors, to apply this as a teaching tool for students of the second year of the Control Engineering course and Automation and related areas of a Higher Education Institution in the state of São Paulo and finally, identify which cognitive functions are manifested from this contextualized teaching. To prepare the Contextualized Event, we based ourselves on the curricular, epistemological and didactic phases of The Mathematics in the Context of Sciences Theory, for the collection of data in this part we analyzed pedagogical projects of Engineering courses, we carried out semi-structured interviews with teachers of specific disciplines and, we analyzed materials didactics and classes of the Control System II discipline, taught in the fifth grade of the Engineering course under study. In this Event, we investigated the dynamics and stability of the SIR Model for a hypothetical situation for the COVID19 disease using Modern Control Theory, content taught in the same discipline. After the construction of this Event, we elaborated 8 meetings that were applied to the students and, finally, we analyzed the results of these meetings according to the Theory of Structural Cognitive Modifiability, seeking to identify which cognitive functions were manifested. For this analysis, we used the transcripts of the meetings, the students' manuscripts and the observations reported by the researcher. With the application of this Contextualized Event we verified that the students were motivated to study not only the content of eigenvalue and eigenvector but also other topics of Linear Algebra, that they understood in a satisfactory way the definition of eigenvalue and eigenvector, how to calculate, the geometric interpretation, as well as an application in its future area of expertise, in addition to an initial familiarization with basic terms and concepts of Control Theory. Another important fact to highlight is that this work can serve as support for Mathematics teachers who teach classes in service courses, and who want to make their teaching more attractive and contextualized, being able to apply this same Event or even serving as a subsidy for creating of new contexts