O que sabem sobre as curvas cônicas?: uma possível leitura para o processo de produção de significado em um grupo de estudos
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Data
2019-05-27
Autores
Ferreira, Bruno Leite
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
A presente pesquisa partiu da motivação do seu autor sobre o processo de investigação matemática com estudantes. Entendendo que a Matemática não é produzida do mesmo modo que é apresentada nos livros voltados para o seu estudo, foi intencionado na tese elaborar compreensões sobre o processo de produção de significado para determinadas noções matemáticas em um contexto investigativo de aprendizagem. Desse modo, a pesquisa configurou-se em uma abordagem qualitativa, apoiando-se na Teoria do Modelo dos Campos Semânticos para realizar uma possível leitura desse processo, enfatizando-se a contribuição deste trabalho no diálogo do referencial teórico com o campo da Geometria. Para tal, foi organizado um Grupo de Estudos Independente sobre curvas cônicas composto por quatro estudantes do curso de graduação em Matemática e o pesquisador, autor desta tese de doutorado. Não houve um programa pré-definido, permitindo que os participantes conduzissem as discussões partindo da seguinte pergunta: O que vocês sabem sobre curvas cônicas? Como instrumento de produção de dados, foram utilizadas gravações em vídeo-áudio dos vinte e dois encontros que ocorreram ao longo do ano de 2016, conversas no aplicativo para smartphone WhatsApp (em grupo e em pares) e diários dos participantes. Em consonância com o objetivo, o estilo de escrita da tese adorado como estética buscou evidenciar tanto o processo de produção de conhecimento (matemático) como também o de conhecimento científico (o fazer pesquisa). A análise consistiu em realizar uma leitura plausível da dinâmica de produção de significado do ponto de vista de um dos sujeitos. Por meio dela, foi possível estabelecer sete Movimentos caracterizados pelas operações de elementos das cônicas em variados Campos Semânticos. Destacou-se a operação do elemento ponto impróprio no processo de generalização das cônicas como também o uso preferencial da elipse e da parábola para realizar as analogias de elementos nas outras curvas. Por fim, considerou-se que, ao trabalhar com diferentes abordagens e/ou modelos, é necessário analisar os elementos que são operados a fim de que se possam fazer as devidas analogias e evitar desconexões.
The present research is based on the motivation of its author on the mathematical investigation process with students. Understanding that Mathematics is not produced in the same way as it is presented in textbooks, it was intended in elaborating understandings about the producing meaning process for certain mathematical notions in a research context of learning. In this way, the research is framed on a qualitative approach, based on Semantic Field Model Theory to carry out a possible reading of this process, so that the contribution of this work is emphasized in the dialog of the theoretical reference with the Geometry’s field. For that, a Study Group on conic curves was composed by four undergraduate students in Mathematics and the researcher, author of this doctoral thesis. There was no predefined program, allowing participants to conduct the discussions from referrals through the following question: What do you know about conic curves? As a data production tool, video-audio recordings of the twenty-two meetings that took place throughout 2016, conversations in the WhatsApp smartphone application (in group and in pairs) and participants' diaries were used. In agreement with our aim, the text form of the thesis sought to evidence both the process of production of knowledge (mathematical) as well as of scientific knowledge (to do research). The analysis consisted in making a plausible reading of the dynamics of meaning production from the point of view of one of the subjects. Through it, it was possible to establish seven Movements characterized by the operation of conic elements in various Semantic Fields. The operation was emphasized in the notion of an improper point in the process of generalization of the conics as well as the preferential use of the ellipse and the parabola to perform the analogies of elements in the other curves. Finally, it is considered that, when working with different approaches and/or models, it is necessary to analyze the elements that are operated in order to make the necessary analogies and avoid disconnections.
The present research is based on the motivation of its author on the mathematical investigation process with students. Understanding that Mathematics is not produced in the same way as it is presented in textbooks, it was intended in elaborating understandings about the producing meaning process for certain mathematical notions in a research context of learning. In this way, the research is framed on a qualitative approach, based on Semantic Field Model Theory to carry out a possible reading of this process, so that the contribution of this work is emphasized in the dialog of the theoretical reference with the Geometry’s field. For that, a Study Group on conic curves was composed by four undergraduate students in Mathematics and the researcher, author of this doctoral thesis. There was no predefined program, allowing participants to conduct the discussions from referrals through the following question: What do you know about conic curves? As a data production tool, video-audio recordings of the twenty-two meetings that took place throughout 2016, conversations in the WhatsApp smartphone application (in group and in pairs) and participants' diaries were used. In agreement with our aim, the text form of the thesis sought to evidence both the process of production of knowledge (mathematical) as well as of scientific knowledge (to do research). The analysis consisted in making a plausible reading of the dynamics of meaning production from the point of view of one of the subjects. Through it, it was possible to establish seven Movements characterized by the operation of conic elements in various Semantic Fields. The operation was emphasized in the notion of an improper point in the process of generalization of the conics as well as the preferential use of the ellipse and the parabola to perform the analogies of elements in the other curves. Finally, it is considered that, when working with different approaches and/or models, it is necessary to analyze the elements that are operated in order to make the necessary analogies and avoid disconnections.
Descrição
Palavras-chave
Geometria gráfica, Seções cônicas, Geometria projetiva, Grupo de estudos independente, Modelo dos campos semânticos, Graphic geometry, Conics sections, Projective geometry, Independent study group, Semantic fields model