The square as a figural concept

Abstract

In the geometry research we operate with mental entities, which contain an image as an essential component. This helps us in thinking, but it often does not coincide with the formal definition. In many cases, flat shapes are represented only with a curve, a boundary, and not as a part of the plane, which can lead to a false conception of flat shapes. The purpose of the research was to clarify pre-service elementary teachers' (N=186) concept image in the case of a square, whether it is hollow or filled, and what role it plays in problem solving. Qualitative methodology, specifically thematic analysis, was used in order to analyze participants' responses to a specially designed task. Only a very small part of participants gave expected answers. The results showed that the preservice teachers' image of a square as a frame totally dominated the conceptual part of the figural concept of a square.