Esquemas cognitivos e mente matemática inerentes ao objeto matemático autovalor e autovetor: traçando diferenciais na formação do engenheiro

• Autor(a) principal: Nomura, Joelma Iamac
• Data de Publicação: 2014
• 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/10989
• topic: Autovalor e Autovetor; Engenharia; Teoria APOS; Conceito imagem e definição; Mente matemática; Eigenvalue and Eigenvector; Engineering; APOS Theory; Concept image and concept definition; Mathematical mind; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The objective of this research harnesses to the results obtained in the Master's Dissertation defended in September 2008 in Postgraduate Studies Program in Mathematics Education at PUC - SP. In this same essay, issues related to teaching and learning of linear algebra sought to answer and find new ways of targeting and perspectives of students in a graduate in Electrical Engineering, asking Why and How should it be taught the discipline of linear algebra on a course with this profile? Among the results, we identified that the interdisciplinarity inherent to the topics of Linear Algebra and specific content of engineering or applied constituted an essential factor for the recognition of mathematical disciplines as theoretical and conceptual basis. Interdisciplinarity reflected in specific mathematical objects of linear algebra and practical situations of engineering materials for the formation of conceptual and general engineer seeking the theoretical foundation and basic justification for the technological improvement of its area. Based on a scenario and results envisioned in the dissertation we propose to investigate the cognitive structures involved in the construction of mathematical object eigenvalue and eigenvector in the initial and final student education phases in Engineering courses, showing the cognitive schemes in their mathematical minds. For this, the following issues are highlighted: ( 1 ) What conceptions (action - process -object- schema ) are evidenced in students after studying the mathematical object eigenvalue and eigenvector in the initial and final phases of their academic training courses in Engineering? and ( 2 ) these same phases, which concept image and concept definition are highlighted in the study of eigenvalue and eigenvector mathematical object? Substantiated by the theoretical contributions of Dubinsky (1991), on the APOS Theory and Vinner (1991), about the concept image and concept definition, we consider the cognitive processes involved in the construction of mathematical object, identifying the nature of their cognitive entities portrayed in mathematical mind. The discussion focuses on mathematical mind both the mathematical structure that is designed and shared by the community as the design in which each mental biological framework handles such ideas. To do so, we consider the relationship between the ideas which constitute the APOS theory, concepts image and definition and some aspects of Cognitive Neuroscience. Characterized as multiple case studies, data collection covered the speech of students in engineering courses in various training contexts, established by the institutions. The analysis of the specific mathematical concept called genetic decomposition led to this concept, which was proposed by System Dynamic Discrete problem, described by the difference equation K K x A.x 1 = + , (K = 0,1,2 , ... ) . Based on the ideas of Stewart (2008) and Trigueros et al. (2012) it was possible to us to identify some characteristics of showing the different conceptions of the students. Moreover, we consider some ideas that characterize the concept image and concept definition according Vinner (1991) and Domingos (2003). As a result of our investigation, we identified that the students of the first case study, at different stages of training, present the design process and the concept image on an instrumental level mathematical object eigenvalue and eigenvector. Have students in the second case, particularly, all of the first phase, and two of the second, showed signs of action and concept image incipient level. As a student of the second phase, have also highlighted the design process and the concept image on an instrumental level as the subject of the first case study. Therefore, we find no significant evolution between the inherent APOS Theory concepts and the concepts image of the object of study. We show that all students presented their speeches in relations between the Linear Algebra course and other courses in the program, such as Numerical Calculation, Electrical Circuits , Computer Graphics and Control Systems, with lesser or greater degree of depth and knowledge. We realize that students attach importance to mathematical disciplines in its formations and seek for a new approach to teaching that address the relationships between them and the disciplines of Engineering