This study aims at better understanding of the use of self-assessment to support high-achieving students in first-year university mathematics. The students, who had not previously self-assessed their skills and knowledge in mathematics, were given two self-assessment exercises during a calculus course: they assessed their prior knowledge and learning goals in the beginning of the course and the quality of their learning outcomes in the end. Their approaches to learning and perceptions of self-assessment were studied with questionnaires in the beginning and at the end of the course. The students felt that they were able to assess their performance and that self-assessment exercises helped them to learn. Their self-ratings agreed well with the teacher's grading. Self-assessment was implemented to support novice students to adopt a deep approach to learning, and the results showing a statistically significant decrease in unreflective approach give an encouraging signal.