Um estudo de fractais geométricos através de caleidoscópios e softwares de geometria dinâmica
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Data
2005-08-31
Autores
Gouvea, Flavio Roberto [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho abordamos um tema pouco explorado nos cursos de graduação em Matemática, que é a Geometria Fractal, resgatando conceitos básicos da Geometria Euclidiana, utilizando caleidoscópios e softwares educacionais. Assim, foram tecidas algumas considerações a respeito da utilização de computadores na sala de aula, através de um estudo que investigou: Que contribuições pode trazer, para o ensinoaprendizagem de Geometria, um estudo de Fractais Geométricos através de caleidoscópios e softwares de Geometria Dinâmica ?. Foram elaboradas atividades e aplicadas a alunos da Licenciatura em Matemática (do 1º e 2º semestres) da Unesp de Rio Claro, que participaram de um Curso de Extensão. A utilização de materiais diferentes do tradicional, como o caleidoscópio e o computador (este último como elemento inserido no contexto educacional), e a contextualização da Geometria contribuíram para o estabelecimento de um ambiente de aprendizagem agradável e participativo. Nosso estudo mostrou uma maneira inovadora de obterem-se fractais geométricos: através de bases caleidoscópicas, o que enseja um grande estudo sobre espelhos e caleidoscópios, e traz em si a oportunidade de estudarem-se muitos conceitos geométricos (reflexão, simetrias, transformações geométricas, bissetriz, mediatriz, seqüências, etc.). Apresentamos, ainda, alguns aspectos pedagógicos e matemáticos relacionados à aplicabilidade dos Fractais Geométricos no processo de construção de conceitos geométricos, por meio da interação aluno-aluno, aluno-computador e alunoprofessor, tendo como pano de fundo a resolução de problemas. Dessa forma, nosso estudo proporcionou para os alunos uma maior relação com os conceitos fundamentais de Geometria Euclidiana e Geometria Fractal, além de uma alternativa metodológica inerente ao ensino da Geometria.
In this work we approached a theme little explored in the degree courses in Mathematics, that it is the Fractal Geometry ransoms basic concepts of the Euclidian Geometry, using kaleidoscopic and educational softwares. At his, are some woven considerations respect the use computers in the classroom, through a study that enquired: What contributions can bring, for teaching-learning of Geometry, a study of the geometrical fractals that include kaleidoscopic and softwares of Dynamic Geometry? Activities were elaborated and applied to students of the degree in mathematics (of the 1st and 2nd semesters) of Unesp de Rio Claro, who participated in a Course of Extension. The use of different materials from the traditional as the kaleidoscopic and computer (this last one as element inserted in the education context), and the contextualization of the Geometry contributed to the establishment of an environment of the pleasing learning and interest. Our study showed an innovator way of they be obtained fractal geometrics: through of kaleidoscopic bases, that wish a great study with mirrors and kaleidoscopic, and bring in itself the opportunity of they be studied many geometric concepts (reflection, symmetric, geometric transformations, bisector, mediate, etc). We presented, still, some pedagogic and mathematic aspects related to the applicability of Fractal Geometrics in the process of construction of geometrical concepts, through the interaction student-student, student-computer and student-teacher using as backdrop the problem solve. Of this form, our study it provided for the students a bigger relation with the basic concepts of Euclidean Geometry and Fractal Geometry, beyond inherent a metodology alternative to the teaching of Geometry.
In this work we approached a theme little explored in the degree courses in Mathematics, that it is the Fractal Geometry ransoms basic concepts of the Euclidian Geometry, using kaleidoscopic and educational softwares. At his, are some woven considerations respect the use computers in the classroom, through a study that enquired: What contributions can bring, for teaching-learning of Geometry, a study of the geometrical fractals that include kaleidoscopic and softwares of Dynamic Geometry? Activities were elaborated and applied to students of the degree in mathematics (of the 1st and 2nd semesters) of Unesp de Rio Claro, who participated in a Course of Extension. The use of different materials from the traditional as the kaleidoscopic and computer (this last one as element inserted in the education context), and the contextualization of the Geometry contributed to the establishment of an environment of the pleasing learning and interest. Our study showed an innovator way of they be obtained fractal geometrics: through of kaleidoscopic bases, that wish a great study with mirrors and kaleidoscopic, and bring in itself the opportunity of they be studied many geometric concepts (reflection, symmetric, geometric transformations, bisector, mediate, etc). We presented, still, some pedagogic and mathematic aspects related to the applicability of Fractal Geometrics in the process of construction of geometrical concepts, through the interaction student-student, student-computer and student-teacher using as backdrop the problem solve. Of this form, our study it provided for the students a bigger relation with the basic concepts of Euclidean Geometry and Fractal Geometry, beyond inherent a metodology alternative to the teaching of Geometry.
Descrição
Palavras-chave
Geometria euclidiana, Geometria fractal, Caleidoscópios, Geometria dinâmica, Fractal geometry, Euclidian geometry, Kaleidoscopic, Dynamic geometry
Como citar
GOUVEA, Flavio Roberto. Um estudo de fractais geométricos através de caleidoscópios e softwares de geometria dinâmica. 2005. v, 259 f. Dissertação (mestrado) - Universidade Estadual Paulista, Instituto de Geociências e Ciências Exatas, 2005.