Student Profiling from Tutoring System Log Data: When do Multiple Graphical Representations Matter?

We analyze log-data generated by an experiment with Math-tutor, an intelligent tutoring system for fractions. The ex-periment compares the educational effectiveness of instruc-tion 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 con-dition and learning outcome are clearly associated b) ex-perimental condition and learning strategy are not, and c) almost all of the association between experimental condition and learning outcome is found among students implement-ing 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 char-acterize this group illuminate the mechanism underlying the effectiveness of multiple representations and suggest strate-gies for tailoring instruction to individual students. Our methodology can be implemented in an on-line tutoring sys-tem to dynamically tailor individualized instruction. 1