Processos de visualização e representação de conceitos de cálculo diferencial e integral com um software tridimencional
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Data
2010-05-25
Autores
Gouveia, Carolina Augusta Assumpção [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho apresenta as dimensões implícitas nos processos de visualização e de representação de conceitos matemáticos, mediados por obras artísticas e pelo software K3DSurf, em uma perspectiva Semiótica, objetivando compreender os processos de visualização e de representação de conceitos matemáticos em Cálculo Diferencial e Integral (CDI), no contexto das Tecnologias de Informação e Comunicação (TIC). A abordagem metodológica utilizada foi qualitativa, dada pelos momentos de Observação, Entrevistas e de aplicação de um conjunto de Atividades Exploratório-Investigativas com base em algumas reproduções de obras de arte, desenvolvidas com um grupo de alunos de graduação em Matemática da UNESP /Rio Claro. Nela identificamos diversas formas de linguagem, tais como, a escrita, a fala, os gestos e os esboços, que auxiliaram no desenvolvimento dos conceitos matemáticos em CDI. A análise dos resultados, baseados em alguns pontos da Teoria Semiótica de Peirce (2008), foi abordada por categorias de análise constituídas, explicitadas como: a primeira categoria denominada Processos de exploração e percepção dos entes geométricos, refere-se à Primeiridade, a segunda categoria denominada Processos de visualização dos entes geométricos, refere-se à Secundidade, as terceira e quarta categorias denominadas Processos de representação dos entes geométricos e Processos de re-significação dos conceitos algébricos, referem-se à Terceiridade. Essas categorias levam a inferir que, no contexto deste estudo, diversas metodologias para a aprendizagem e desenvolvimento dos conceitos matemáticos por meio da visualização e da representação foram empregadas, entre elas os aspectos de experimentação, as relações nos processos de semelhança e os momentos de socialização. Também observamos e enfatizamos a importância dos conhecimentos matemáticos dos alunos...
This work shows the implicit dimensions within the process of visualization and representation of mathematical concepts mediated by artistic works and by the K3DSurf software under a semiotic perspective, aiming to comprehend the process of visualization and representation of mathematical concepts in the Differential and Integral Calculus (CDI), within the context of Information and Communication Technologies (TIC).The methodological approach used in this work was the qualitative research, given in moments of observation, interviews and application of a set of Exploration-Investigative Activities, based in art works, with a group of undergraduate students in mathematics. In these activities we identified some forms of language, such as writing, speech, gestures and sketches, which helped students develop mathematical concepts in CDI. The analysis of the results, based on Peirce‟s Semiotics Theory (2008), was addressed by categories of analysis that can be pointed out in the following way: the first one was called Exploration Procedures and Perception of the Geometric Entities, referent to the firstness; the second one was the Procedures of Visualization of Geometric Entities, referent to the secondness; the third and the fourth ones were called Procedures of Representation of Geometric Entities and Procedures of Re-Signification of Algebraic Concepts, both of them referent to the thirdness. These categories led us to conclude, on this research context, that many methodologies were applied in order to develop and to learn the concepts of CDI through visualization and representation, including aspects of experimentation, the relationships within the similarity processes and moments of socialization. We also observed the importance of mathematical knowledge acquired before the Exploration-Investigative Activities. This prior knowledge, in many instances, has led the first steps towards... (Complete abstract click electronic access below)
This work shows the implicit dimensions within the process of visualization and representation of mathematical concepts mediated by artistic works and by the K3DSurf software under a semiotic perspective, aiming to comprehend the process of visualization and representation of mathematical concepts in the Differential and Integral Calculus (CDI), within the context of Information and Communication Technologies (TIC).The methodological approach used in this work was the qualitative research, given in moments of observation, interviews and application of a set of Exploration-Investigative Activities, based in art works, with a group of undergraduate students in mathematics. In these activities we identified some forms of language, such as writing, speech, gestures and sketches, which helped students develop mathematical concepts in CDI. The analysis of the results, based on Peirce‟s Semiotics Theory (2008), was addressed by categories of analysis that can be pointed out in the following way: the first one was called Exploration Procedures and Perception of the Geometric Entities, referent to the firstness; the second one was the Procedures of Visualization of Geometric Entities, referent to the secondness; the third and the fourth ones were called Procedures of Representation of Geometric Entities and Procedures of Re-Signification of Algebraic Concepts, both of them referent to the thirdness. These categories led us to conclude, on this research context, that many methodologies were applied in order to develop and to learn the concepts of CDI through visualization and representation, including aspects of experimentation, the relationships within the similarity processes and moments of socialization. We also observed the importance of mathematical knowledge acquired before the Exploration-Investigative Activities. This prior knowledge, in many instances, has led the first steps towards... (Complete abstract click electronic access below)
Descrição
Palavras-chave
Matemática - Estudo e ensino, Semiotica, Arte, Obras artísticas, Software K3DSurf, Art Works, Mathematics Education, K3DSurf software
Como citar
GOUVEIA, Carolina Augusta Assumpção. Processos de visualização e representação de conceitos de cálculo diferencial e integral com um software tridimencional. 2010. 213 f. Dissertação (mestrado) - Universidade Estadual Paulista, Instituto de Geociências e Ciências Exatas, 2010.