O estudo do paralelismo no ensino da geometria analítica plana: do empírico ao dedutivo

Abstract

This dissertation involves a study of argumentation and proof in relation to the teaching and learning of analytic geometry and particularly the property of parallelism in this topic. The work seeks answers to the following questions: in what form can dynamic geometry environments contribute in students attempts to construct mathematical arguments and proof? What difficulties and resistances emerge in learning situations which address the concept of parallelism in analytic geometry? To respond to these questions, sequences of activities, based on some aspects of didactical engineering was designed. For the conception of these activities, the research drew from the work of Parsysz concerning the levels of development of geometrical thinking and the analysis of students´ interactions with the activities was based on the Balacheff´s classification of different types of proof. Analysis of the results obtained in the application of the activity sequence showed that the dynamic geometry environment contributed to the creation of situations that supported the construction of meanings for the concept of parallelism and that the students engaged with the activities in the manner proposed, producing some kind of relevant proof