This paper reports and describes some of the observations and conclusions drawn from a study developed to find information on undergraduate students' spontaneous actions and reactions to mathematical definitions that are new to them. There were 23 participants from a transition-to-proof course. They were interviewed individually on a particular mathematical definition. The analysis of the interviews was iterative and consisted mainly of three phases. During the first two phases students' behaviors were observed and identified in order to categorize commonalities of their responses and actions. In the third phase, a search-back through the data was done for additional supporting evidence of the commonalities previously observed. This third phase allowed making a more general classification of the various behaviors observed. Participants were classified into five different stages in using mathematical definitions according to their behaviors when working with a particular definition. [For the complete proceedings, see ED583608.]