University students linking limits, derivatives, integrals and continuity

Mathematical concepts are mentally represented differently depending on individual, context and existing conceptions of related concepts among other things. The present paper reports on a study of students‘ representations in analysis with an emphasis on the types of representations and the links they have between their representations. The data collection was designed to evoke different parts of the students‘ concept images and also to return to the concepts several times over time at every data collection session. The results show that formal and intuitive representations in combination are rare. The number of links between concepts is not in itself a measure of the quality of the concept image, as there is a vast number of erroneous links misleading the students to think they understand the concepts.