Is the square a rectangle?

Abstract

The concept of a geometric object occurs, among other things, because of experiences on such object. The hypothesis of this study, is that performing a conceptualization process of an object, using a surrounding of dynamic geometry, helps not only to state, formalize and structure hierarchic and economic definitions of objects, but also to establish the definition used by the students working in a context of demonstrative activity. In supporting the hypothesis, sessions of classes of two consecutive academic spaces, of a teacher initial formation program, and a questionnaire applied to the students, were analyzed. The study sought evidences which lead, supported on the theoretic framework that guided the study, to determine the impact of working in a surrounding, where a software of dynamic geometry is used, as a mediator for learning. The results led to establish, among other things, that the work performed with dynamic geometry should be accompanied by intentioned actions guide by the teacher. It was proved that, even after using dynamic geometry, difficulties continue appear regarding the concept of the square geometric object, as predominance of figure aspects on conceptual ones, and difficulty to modify personal definitions of the concept and conceptual images, surged when the students realize any demonstrative activity.