Reliable ideas about fundamental mathematical concepts are an indispensable prerequisite for mathematics teachers to conduct high quality lessons. There are several (normative) basic ideas (“Grundvorstellungen”) associated with any mathematical concept, which give meaning to different aspects of the notion in question. In this article, we discuss ideas of learners on the limit of a real sequence. We present an empirical study, which collects student teachers’ written statements before and after an intervention by a didactically oriented analysis course. These statements are classified with respect to their coherence with the normative basic ideas. It turns out that explicitly addressing these basic ideas leads to a significant (albeit small) increase in quality of students’ statements.