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…

The study examined whether embedding the linear equations and ratio and proportion strategies used to solve percent problems in the higher-order structures of proportional logic and group properties would aid achievement. Thus, it examined the interaction in differences in understanding fundamental structures in mathematics, and instruction…