A Characterization of Van Hiele’s Level 5 of Geometric Reasoning Using the Delphi Methodology

Abstract

The Van Hiele model of geometric reasoning establishes five levels of development, from level 1 (visual) to level 5 (rigor). Despite the fact that this model has been deeply studied, there are few research works concerning the fifth level. However, there are some works that point out the interest of working with activities at this level to promote the acquisition of previous levels. Our goal is to describe this level through the construction and validation of a list of indicators for each of the processes involved in geometrical reasoning (definition, proof, classification, and identification). Due to the lack of previous research, we have decided to use the Delphi methodology. This approach allowed us to collect information from a panel of experts to reach a consensus through a series of phases about the indicators that describe each of the processes. The final product of the iterative application of this method is a list of validated indicators of the fifth Van Hiele level of reasoning. In particular, proof and definition processes have turned out to be the most relevant processes at this level.