The research interest in this thesis concerns novice university students of mathematics. The aim of my thesis is to understand the transition between mathematics studies at upper secondary school and university from a student perspective. It is a qualitative study of five teacher students during their initial university studies in mathematics. The students were interviewed before beginning their mathematics studies, during their courses and observed during lectures, during problem solving lessons and while working with mathematics out of class both individually and with fellow students. The transcriptions from the preliminary interviews have been analyzed using methods inspired by Grounded Theory. The main result consists of three categories that describe students’ learning of mathematics.

Mathematical learning objects refer to students’ conceptions of the main goals and/or contents of studying mathematics, for example their views of the subject, the usefulness of knowing mathematics and what is needed to learn mathematics. Students’ mathematical learning objects should be considered as an individual and relational phenomenon between the student and his or hers mathematics studies that can change over time.

Mathematical resources relate to phenomena and objects that students use to approach and possibly acquire various mathematical learning objects. The teacher, fellow students, the textbook and own preliminary knowledge are some examples of entities that students may use as mathematical resources. These entities become mathematical resources only when the students use them in relation to mathematical learning objects. 

The third category, student acting as a learner, captures students’ actions, intentions and conceptions in relation to learning mathematics. Students use different mathematical resources to acquire different mathematical learning objects. This is expressed in students’ actions and reasoning, which serve as empirical data for understanding the student acting as a learner.

The three categories are theoretical concepts that elucidate essential aspects of learning and teaching of mathematics as seen from a student perspective and serve as a foundation for a theoretical framework that may be used to describe the transition. A theoretical description of the transition has been obtained by investigating how the respective categories, and the relations between the categories, change or endure during the transition. Results from the analysis of subsequent interviews and observations indicate that the transition can be understood in terms of an increasing gap between mathematical learning objects and mathematical resources, a reorientation of mathematical learning objects and a requirement of supplementing mathematical resources.