Student representational competence, self-assessment, and problem solving in physics
Patrick B. Kohl and Noah D. Finkelstein
University of Colorado at Boulder

Abstract
Student problem-solving ability is related to the representational format of the problem. In a
study of two large-lecture algebra-based introductory university physics classes, we examine student
problem solving ability on homework problems given in four di¤erent representational formats
(mathematical, pictorial, graphical, verbal), with problems as close to isomorphic as possible.
In addition to the homeworks, we examine students assessment of representations by providing
follow-up quizzes in which they choose between various problem formats. Subsequently, we look
for factors that may influence their ability or choices. As a control, some parts of the classes
were assigned a random-format follow-up quiz. We find that there are statistically significant
performance differences between different representations of nearly isomorphic quiz and homework
problems. We also find that allowing students to choose which representational form they use
improves student performance under some circumstances and degrades it in others. We also
begin to characterize how and why students choose and make use of the different representations
available.