The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of graphs in terms of value-thinking and location-thinking, which emerged from our data. These two ways of thinking were rooted in students' attention to different attributes of points on graphs we provided: either the input and output values represented by the points or the location of the points in space. Our findings indicate that students' thinking about aspects of graphs accounts for key differences in their understandings of mathematical statements. [For the complete proceedings, see ED606531.]