  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.
