Dynamic Folding and the Development of Geometric Thinking

Abstract

This article presents research developed from the proposal for exploring dynamic folding that result in geometric figures, constructed in an environment of dynamic geometry and analyzes the development of geometric thinking and argumentation based on the exploration of this material. The investigation was conducted by an experiment, with students in the ninth grade of elementary school. Based on the elaborated dynamic activities, it was possible to develop essential aspects of geometric thinking, such as exploration, formulation and conjecture testing, as well as encouraging argumentation in the basic school. The material was developed in a digital book format at GeoGebrabook, and proposes the manipulation of dynamic geometric objects that simulate folds on sheets of paper, in which students were encouraged to explore and argue. We used the Van Hiele model of levels of understanding that sequentially describe characteristics of the geometric thinking process for the analysis of the experiment. The results show that, with the exploration of the virtual dynamic folds and the incentive to argumentation, it is possible to develop essential aspects of geometric thought and to recover the argumentation in the basic school.