This qualitative study investigated the nature of mathematical thinking in learning the function concept among three college students with Attention Deficit Hyperactivity Disorder (ADHD). The theoretical framework for this study combined ideas from Social Cognitive Theory (Bandura, 2001), Barkley's Unifying Theory of ADHD (1997) and work on covariational reasoning by (Carlson, Jacobs, Coe, Larson, & Hsu, 2002). Primary data were tutoring sessions in mathematics with three ADHD college students at two western universities over the course of one semester. The results presented here give a picture of these students' cognition around the concept of function. In addition, I compared ADHD and non—ADHD college students' thinking during a problem solving situation calling for the generation of a graph of height as a function of volume. Two ADHD college student participants, two college student participants without ADHD, and two instructors of mathematics completed the same task, the Bottle Problem as used by Carlson and colleagues (2002). I analyzed their responses and compared them to reported responses of participants in Carlson et al.

The results of the tutoring sessions and the bottle problem interviews indicate that there are similarities and differences between the difficulties ADHD college mathematics students encounter and those outlined in published literature for all college students learning mathematics. Similarities include sparse concept image of what constitutes a function and difficulty making connections among graphical, tabular, symbolic, and verbal representations of functions. However, there are differences in the types of representations each group works with most flexibly. The literature reports that college students, in general, express a preference for symbolic representations over graphical ones. In contrast, the results of this study suggest that working with visually rich representations, particularly graphical and tabular ones, may be a strength for ADHD college students. Moreover, a theory-building results of the dissertation is a refinement I made to the concept-level model introduced by Carlson et al. in the context of the bottle problem. I expanded the applicability of this model by connecting it to a larger cognitive framework for mathematical problem solving based on Barkley's (1998) unified theory of ADHD.