Made available in DSpace on 2014-12-17T14:36:44Z (GMT). No. of bitstreams: 1 ClaudiannyAN.pdf: 1040244 bytes, checksum: ad1fdad987ef4b04e5da0f991183dbdd (MD5) Previous issue date: 2006-06-28 / The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse / O objetivo principal deste trabalho ? propor uma abordagem metodol?gica do ensino da Geometria e, mais particularmente, de constru??o dos conceitos de circunfer?ncia e elipse por alunos de 7? e 8? s?rie. Desenvolvemos um estudo te?rico-pr?tico, baseado na modelagem matem?tica e nas Geometrias Urbana e Isoperim?trica, a fim de oportunizar aos alunos construir o seu entendimento sobre circunfer?ncia e elipse. A an?lise dessa constru??o foi realizada com base na Teoria da Equilibra??o de Jean Piaget. Foi enfatizado o uso da intui??o que estes estudantes j? tinham acumulado em situa??es cotidianas. Eles foram encorajados a levantar hip?teses, testar, discutir com os colegas e tirar suas conclus?es. No entanto, o uso das Geometrias Urbana e Isoperim?trica implica que os gr?ficos das circunfer?ncia e elipse tomem formas diferentes. A compara??o dessas formas ?s produzidas na Geometria Euclidiana foi usada para consolidar o entendimento desses conceitos, desde que s?o id?nticos, independente das m?tricas. A interven??o foi efetivada mediante o uso de uma s?rie de atividades cumpridas em pequenos grupos. Ao final do estudo percebemos que os 53 alunos da 7? e 55 da 8? s?rie, participantes do mesmo, foram capazes de obter um melhor entendimento dos conceitos de circunfer?ncia e elipse