Exploração de construções geométricas em ambientes computacionais dinâmicos

Abstract

On a computer dynamic geometry environment(DGE) one can make constructions and drag them, keeping invariant the relations set up. The literature shows that by using a DGE it is possible to build powerful strategies for the personal and social construction of geometric knowledge. In this framework, we investigate how students of a 9th-grade class made and explored constructions on a DOE and how this allowed them to understand geometric objects and relations, to make conjectures, and to make deductive and inductive reasoning.

The students themselves found processes to make the proposed geometric constructions. They privileged the appearance of the figures and reproduced sequences of objects and relations they had experienced to be drag resistant. To justify the constructions they mainly used empirical evidence, but, through dialogue, some students recognized properties of the figures and related them to each other. In exploring the constructions their attention was mainly attracted by what they saw changing and needed orientation to see invariants and to formulate conjectures. In exploring the constructions three levels were found that were associated to the van Hiele levels 1, 2 and 3.