Past studies have shown that students struggle with main concepts of potential energy, such as reading graphs, understanding that potential energy can be negative, and, most pertinent to this research project, connecting potential energy to force. I designed an activity to help introductory physics students address these struggles. The activity required students to draw graphs of both gravitational potential energy (GPE) and gravitational force, which enabled them to see that GPE was completely negative, and to make mathematical and graphical connections between GPE and force. The activity took place during a weekly recitation, during which students worked in groups of 2-3 and used a plastic 3D surface manipulative and accompanying contour map to assist in answering the prompts. The surface and contour map were both representative of the GPE of an Earth-object system. I filmed 3 groups as they worked on the activity and examined the ways in which the students interacted with the surface and what purpose each interaction served.
I found that students most often interacted with the surface by pointing to or tracing components of the surface, showing that the students were unfamiliar with the surface and less comfortable with moving, turning, grabbing, and drawing on the surface. The students most often used the surface to examine the functional behavior of both GPE and force, discuss the rate of change of GPE, and to compare values, slopes, or signs (+ or -) between different locations. One group even discovered that they could use a pen to act as the tangent to the surface (specifically the tangent pointing only in the radial direction), a physical representation of force. In future surfaces activities, it might benefit students to do a small activity as an entire class. This would allow the students to watch how the instructor manipulates the surface in different ways and apply those strategies to subsequent activities. I found that all the students still struggled with one or more aspect of GPE, but both students and TA frequently used the surface to explain that aspect to the struggling student(s) and to make sense of their own difficulties.