Challenges in designing appropriate scaffolding to improve students’ representational consistency: The case of a Gauss’s law problem

Prior research suggests 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 student interviews.

Figure 1

Problem diagram.

Figure 2

Coordinate axes provided to all students for plotting the electric field in part (b).

Figure 3

Reproduction of a plot by a student in region $b<r<c$. His plots in other regions have been excluded for clarity.

Figure 4

Electric field plotted by Alex (an interviewed student).

Figure 5

Electric field plotted by Charles (an interviewed student).

Figure 6

Electric field plotted by Yara (an interviewed student).

Figure 7

Electric field plotted by Mike (an interviewed student).