The validity of students' conceptions of differentiability and continuity

University students’ conceptions of differentiability, continuity and relations between the concepts were studied to reveal their choices of representations and their strategies to justify their relational claims. Questionnaires and interviews were used to collect data (questionnaires in the part presented here). The results were analysed and categorized through a framework based on Skemp’s (1976) definitions of relational and instrumental understanding, and Tall’s (2004) three worlds of mathematics. The students showed ambiguous representations opposing their own statements in some cases. The most common feature among the students to describe a continuous function was incorrect implying a need to develop the students’ concept images in that area.