Graphing calculators are mainstay in the U.S. high school mathematics curriculum and because of that considerable research has been done on the effect of graphing calculators in the math classroom. Until recently most of the research on graphing calculator use in mathematics education has either been quantitative in nature, focusing on student achievement and attitude, or qualitative focusing on the teaching and learning of a particular mathematical topic (Choi-Koh, 2003; Ellington, 2003; Forester & Mueller, 2002; Smith & Shotsberger, 1997, for example). In addition, there is a growing body of research on how students are adapting graphing calculator technology to their mathematical learning (Artigue, 2002; Drijvers, 2000; Guinn and Trouche, 1999). However, none of this work addresses how students use the graphing calculator when they are working in independent situations or their perceptions of how the graphing calculator impacts their mathematical experience. My work aims to attend to this gap in the research. This dissertation reports on a mixed methods study with data consisting of survey data (n = 111) and in-depth interview data compiled from six case studies. The case study students participated in a task based interview and a stimulated response reflection interview. Particular attention was paid to both the affective and mathematical aspects of graphing calculator use. The data indicates that AP Calculus students value the ability to change the cognitive demand of tasks, the ability to engage in mathematical play, to check their written solutions, and to manage time effectively when doing mathematics. All of the students reported that using the graphing calculator in each of these ways provides them with both a mathematical and affective pay-off. Most surprising is that the ways in which the students value using their graphing calculators to solve problems does not coincide with their perceptions of what it means to 'do math' in a school setting. This result suggests that in the continuing discussion of how and if graphing calculators should be incorporated into school mathematics and assessment it is important to address this inconsistency.