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Student difficulties in translating between mathematical and graphical representations in introductory physics

We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions.