Abstract

Although learning from multiple representations has been shown to be effective in a variety of domains, little is known about the mechanisms by which it occurs. We analyzed log data on error-rate, hint-use, and time-spent obtained from two experiments with a Cognitive Tutor for fractions. The goal of the experiments was to compare learning from multiple graphical representations of fractions to learning from a single graphical representation. Finding that a simple statistical model did not fit data from either experiment, we searched over all possible mediation models consistent with background knowledge, finding several that fit the data well. We also searched over alternative measures of student error-rate, hint-use, and time-spent to see if our data were better modeled with simple monotonic or u-shaped non-monotonic relationships. We found no evidence for non-monotonicity. No matter what measures we used, time-spent was irrelevant, and hint-use was only occasionally relevant. Although the total effect of multiple representations on learning was positive, they also had a negative effect on learning, mediated by a higher error-rate. Our evidence suggests that multiple representations increase error-rate, which in turn inhibits learning. The mechanisms by which multiple representations improve learning are as yet unmodeled