This report discusses the results of semi-structured clinical interviews with ten prospective secondary mathematics teachers who were provided with dynamic images of Ferris wheels. We asked the students to graph the relationship between the distance a rider traveled around the Ferris wheel and the height of the rider from the ground. We focus on the different quantitative and non-quantitative ways of thinking in which students engaged to justify the curvature of their drawn graphs. We also discuss how these ways of thinking relate to reasoning covariationally about directional change and amounts of change. [For the complete proceedings, see ED583608.]