The concept of "Grundvorstellungen" in higher geometry

A discussion on the basis of the concept of parallel lines

Abstract

The theory of “Grundvorstellungen” (engl. basic mental models) is well established in German research of didactics of mathematics. Besides the broad investigation in different areas of school mathematics, the role of Grundvorstellungen in tertiary education and especially in higher geometry is still an open question. To clarify this issue, we identified Grundvorstellungen for parallel lines using an empirical and theoretical approach. This article presents the results focusing on the description of the different Grundvorstellungen in distinct geometric contexts (e. g. on a sphere). It turns out that normatively developed Grundvorstellungen can reveal difficulties students have to face in the transition from euclidean to non-euclidean geometry.