  Prior research suggest that introductory physics students have difficulty
with graphing and interpreting graphs. Here, we discuss an investigation of
student difficulties in translating between mathematical and graphical
representations for a problem in electrostatics and the effect of increasing
levels of scaffolding on students' representational consistency. Students in
calculus-based introductory physics were given a typical problem that can be
solved using Gauss's law involving a spherically symmetric charge distribution
in which they were asked to write a mathematical expression for the electric
field in various regions and then plot the electric field. In study 1, we found
that students had great difficulty in plotting the electric field as a function
of the distance from the center of the sphere consistent with the mathematical
expressions in various regions, and interviews with students suggested possible
reasons which may account for this difficulty. Therefore, in study 2, we
designed two scaffolding interventions with levels of support which built on
each other (i.e., the second scaffolding level built on the first) in order to
help students plot their expressions consistently and compared the performance
of students provided with scaffolding with a comparison group which was not
given any scaffolding support. Analysis of student performance with different
levels of scaffolding reveals that scaffolding from an expert perspective
beyond a certain level may sometimes hinder student performance and students
may not even discern the relevance of the additional support. We provide
possible interpretations for these findings based on in-depth, think-aloud
interviews.
