In this article, we use a case study to explore the views of first-year university students on the differences between mathematics at school and at university, and on the changes to their study methods as they make the transition to university mathematics. We also consider their views on the differences and affordances of tasks that they encounter on either side of the transition. The students in this study were registered on differential calculus modules where non-routine tasks were employed. We find that students are aware of the increased emphasis on conceptual understanding and reasoning at university and of the need to be an independent learner. We also see that this awareness is raised through engagement with mathematical tasks and that working on tasks is an integral part of students’ study methods. We conclude that mathematical tasks have a role in making lecturers’ expectations clear to students and also in giving students’ opportunities to develop mathematical thinking skills and work independently.