This thesis presents a study of the mathematical behaviour of students in a first year undergraduate course entitled Introduction to Mathematical Thinking. Previous data collected from a design experiment carried out in the same course (see Hardy et al. 2013) proved insufficient to discuss/characterize the mathematical behaviour that emerged in the classroom.  I suggest that a new generation of research in this area needs to address the lived experiences of students as they are learning to think mathematically. This thesis is motivated by two research goals: (1) to construct a rich characterization of mathematical behaviours, and (2) to explore a methodological approach that allows us to discuss and construct accounts of these behaviours as they emerge in institutional education settings (in this case an undergraduate classroom). 
The educational philosophy of John Dewey, who claims that all education comes about through experience, is central to the theoretical perspective of this research. Drawing on previous characterizations, a model of mathematical behaviour is proposed and used as a tool for characterizing students’ mathematical behaviours. In order to foreground individual experience, I use Clandinin and Connolly’s (2000) methodological framework to conduct a narrative inquiry. This methodology allows me to construct meaningful narrative depictions of students’ mathematical behaviour, and to explore the significance of these experiences within the continuity and wholeness of their individual narratives.  The findings from this research provide rich characterizations of some elements of mathematical behaviour, and offer insight into my own experiences using narrative inquiry methodology. Implications for teaching and future research are discussed.