Estudo das três dimensões do problema didático de sistemas de equações lineares

• Autor(a) principal: Paiva, Renne Garcia
• Data de Publicação: 2023
• 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/32227
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Sistemas de equações lineares; Dimensão epistemológica; Dimensão econômico-institucional; Dimensão ecológica; Praxeologia; Linear systems of equations; Epistemological dimension; Economic; Institutional dimension; Ecological dimension; Praxeology

This research deals with the study of the three dimensions of the didactic problem of systems of linear equations This research deals with the study of the three dimensions of the didactic problem of systems of linear equations for initial teacher education. With the contribution of the Anthropological Theory of Didactics (ATD), we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the Epistemological, Economic-institutional and Ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. With the contribution of the ATD, we chose to start with the teaching question related to Systems of Linear Equations: how and why to teach systems of linear equations to students in initial teacher training? To answer it, we considered our teaching question and carried out our research based on the development of the didactic problem proposed by Gascón (2011), which led us to elaborate our research question: How different aspects referring to the epistemological, economic-institutional and Ecological dimensions of the didactic problem related to the mathematical object system of linear equations can they contribute to the development of a Didactic Reference Model (DRM) as a basis for proposing study and research pathways in teacher education? In search of answers with meanings inherent to the raison d'être of this mathematical object, we aim to understand how different aspects related to the epistemological, economic-institutional and ecological dimensions of the didactic problem related to systems of linear equations can contribute to the development of a Reference Didactic Model (RDM) as a basis for proposing study and research pathways in teacher education. To achieve this objective, we carried out a study based on the assumptions of the Anthropological Theory of Didactics (ATD) and sustaining ourselves, initially in the analysis of the epistemological dimension related to the origins and development of mathematical knowledge associated with systems of linear equations, we generate an Epistemological Reference Model (ERM). Based on this model, we carried out a study of the economic-institutional and ecological dimension of the praxeologies relevant to the development of the study of linear systems of thought in the scope of teacher training in search of the peculiarities of the Dominant Epistemological Model (DEM), described and interpreted in the documents official and teaching materials. The economic study allowed us to locate the systems of linear equations in four disciplines in the undergraduate curriculum (Analytical Geometry, Linear Algebra, Numerical Calculus and Ordinary Differential Equations). On the other hand, the ecological analysis of the object revealed conditions and restrictions that favor and hinder putting into practice the imposed tasks identified by the MED. With the analysis of these studies, we propose an Alternative Reference Didactic Model (ARDM) correlating the ERM and the MED for the analysis of a possible change in the raison d'être linear systems of equation. Finally, when considering the contributions revealed by the theory through the research, we proposed an Alternative Reference Didactic Model (ARDM) with a map of questions for the realization of possible study and research pathways