Properties and relations between quadrilaterals: contributions from geoboard and geoGebra. A study in the 4th grade

Abstract

This article is part of a study with 4th grade pupils whose main goal was to understand which contributions from Dynamic Geometry Environments (Geogebra) and from geoboard to the understanding of properties and relations among quadrilaterals. For that was produced, implemented and analyzed a set of tasks developed in Geogebra and with geoboard, stressing the role of representations and visualization in identifying the properties of quadrilaterals: trapezius, parallelogram, rectangle, square and rhombus. Given the problem under study, we chose a qualitative methodology based on three case studies. This article focuses on one of the cases and reasoning that students have developed around the identification of the properties of quadrilaterals with either geoboard or with Geogebra. As a result it is stressed that pupils identified the properties based on representations, but have focused on particular cases, according to his/her mental image of the figure, specifically the prototype, indicating the influence of visualization. It is also evident the difficulty that students felt to consider a figure as representative of a class and distinguish essential and non-essential attributes. Both the geoboard and GeoGebra were an added value in achieving the teaching experience of this study.