How Should Intelligent Tutoring Systems Sequence Multiple Graphical Representations of Fractions? A Multi-Methods Study

Abstract

Providing learners with multiple representations of learning content has been shown to enhance learning outcomes. When multiple representations are presented across consecutive problems, we have to decide in what sequence to present them. Prior research has demonstrated that interleaving tasks types (as opposed to blocking them) can foster learning. Do the same advantages apply to interleaving representations? We addressed this question using a variety of research methods. First, we conducted a classroom experiment with an intelligent tutoring system for fractions. We compared four practice schedules of multiple graphical representations: blocked, fully interleaved, moderately interleaved, and increasingly interleaved. Based on data from 230 4th and 5th-grade students, we found that interleaved practice leads to better learning outcomes than blocked practice on a number of measures. Second, we conducted a think-aloud study to gain insights into the learning mechanisms underlying the advantage of interleaved practice. Results show that students make connections between representations only when explicitly prompted to do so (and not spontaneously). This finding suggests that reactivation, rather than abstraction, is the main mechanism to account for the advantage of interleaved practice. Third, we used methods derived from Bayesian knowledge tracing to analyze tutor log data from the classroom experiment. Modeling latent measures of students’ learning rates, we find higher learning rates for interleaved practice than for blocked practice. This finding extends prior research on practice schedules, which shows that interleaved practice (compared to blocked practice) impairs students’ problem-solving performance during the practice phase when using raw performance measures such as error rates. Our findings have implications for the design of multi-representational learning materials and for research on adaptive practice schedules in intelligent tutoring systems.