Analyzing the role of shapes in the process of writing proofs in model of p-m combinations


George Dimakos, Emmanouil Nikoloudakis


The figure, that a student draws, when attempting to write a proof, does not represent a unique shape; it represents rather many shapes. All these shapes are representations that result from the unique figure. Moreover, a plane geometrical figure consists of points, line segments, rays, and lines. We call these ``figure components''. We stress that it is not quite easy for senior high school students to recognize either all the representations that result from a unique static figure or the roles that figure components play in a geometric sketch. In this article we analyse the role of shapes in the process of writing proofs in Model of p-m Combinations focusing both on three extremely important questions that help studentsÂ’ geometry thinking and on the representations that result from dynamic geometry software (DGS) environments.