Compreensão dos conceitos perímetro da circunferência e área do círculo com o auxílio do GeoGebra

Abstract

The present research study suggests an application of a didactical sequence which the aim to the didacticalpedagogical relation on the learning and comprehension of the circumference perimeter (contour) and the circle area (superficial) with the aid of GeoGebra dynamical geometry (DG) software. For that, it was analyzed the learning results related to the done students comprehension after the didactical sequence application in order to compare the students development before and after the application, as well as to analyze if the GeoGebra is relevant in the aid to the learning and comprehension of the origin of the π number and its relation to the circumference perimeter, diameter and the area of its circle. On that, to identifying the possible limitations and advances on the study objects learning after the didactical sequence. Our research was theoretical based on French Didatical aspects by the Guy Brousseau´s Didactical Situation Theory and its four moments: action, formulation, validation and institutialization. As start point, we presented a scenario with some studies and views of many known researchers as Malkevitch (1998), Pavanello (1989,2004), Almouloud (2000, 2007), Andrade and Nacarato (2004) and Baldini (2004), among others, concerned on research the Geometry teaching in Mathematics classroom. Followed by that, we describe a health living and the contributions of the Information and Communication Technologies (ICT) with the knowledge, and with the school, in the Mathematics learning. The didactical sequence was composed by seven activities developed into five sessions to eight first year high school level students from a Paraiba state public school, in the Campina Grande city. In the last activity, postest, pedagogical and mathematical aspects were analyzed. We describe, still, qualitatively, all the elements of a case study including the results from the first activity, pretest, to know how the students who concluded the second school solve questions on circumference perimeter and circle area concepts. The data analysis showed that the students who had analytical knowledge about the study objects show clarity rarely obtained with ruler and compass on the comprehension of the π number origin and its relation with the circumference perimeter, diameter, and the area of the circle by working with the GeoGebra dynamism. From that, it emerges new didactical contracts by replacing the previous ones. In general, the research study showed that the established didactical contracts among students, teacher and knowledge, when broken, it opens as an opportunity of recovering and of new interactions between teacher and student to seeking a meaningful learning, which requires an open and flexible posture by the teacher. The acceptation of the student feedback urges from the context as need condition, but not enough, for that to happen the learning.