Common Visual Representations as a Source for Misconceptions of Preservice Teachers in a Geometry Connection Course

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students’ understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions posed on a cumulative final exam, which focused on computing and comparing areas of parallelograms, and triangles represented by atypical images. We use the notions of concept image and concept definition as our theoretical framework for an analysis of the students’ responses. Our findings have implication on how typical images can impact students’ cognitive process and their concept image. We provide a number of suggestions that can foster conceptualization of the notions of median and altitude in a triangle that can be realized in an enacted lesson.