In this paper, we discuss the relevance of 'Grundvorstellungen' (GVs), a didactical category to analyze students' mental models in comparison to the intended mathematical meanings in the context of Linear Algebra and Analytic Geometry. Diagnostic tasks were used to reveal students' conceptual understanding in this field of expertise. In particular, an open item format was chosen to elicit students' individual GVs and to explore how they use them while working on mathematical tasks. 30 students from upper secondary school participated in our study; data was collected by a paper-and-pencil test. The results show that elaborated representations of GVs foster students' understanding of mathematics and facilitate the process of finding problem solving strategies. [For the complete proceedings, see ED597799.]