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

TL;DR

This study investigates how scaffolding influences students' ability to translate mathematical expressions into graphical representations in electrostatics, revealing that excessive support can sometimes hinder learning and understanding.

Contribution

It introduces a two-level scaffolding intervention for improving students' representational consistency in physics problems involving Gauss's law.

Findings

Scaffolding can improve students' graphing performance

Excessive scaffolding may hinder student understanding

Students often fail to see the relevance of additional support

Abstract

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.