Abstract

We analyze log-data generated by an experiment with Mathtutor, an intelligent tutoring system for fractions. The experiment compares the educational effectiveness of instruction with single and multiple graphical representations. We extract the error-making and hint-seeking behaviors of each student to characterize their learning strategy. Using an expectation-maximization approach, we cluster the students by their strategic profile. We find that a) experimental condition and learning outcome are clearly associated b) experimental condition and learning strategy are not, and c) almost all of the association between experimental condition and learning outcome is found among students implementing just one of the learning strategies we identify. This class of students is characterized by relatively high rates of error as well as a marked reluctance to seek help. They also show the greatest educational gains from instruction with multiple rather than single representations. The behaviors that characterize this group illuminate the mechanism underlying the effectiveness of multiple representations and suggest strategies for tailoring instruction to individual students. Our methodology can be implemented in an on-line tutoring system to dynamically tailor individualized instruction