Does Representational Understanding Enhance Fluency - Or Vice Versa? Searching for Mediation Models

Conceptual understanding of representations and fluency in using representations are important aspects of expertise. However, little is known about how these competencies interact: does representational understanding facilitate learning of fluency (understandingfirst hypothesis), or does fluency enhance learning of representational understanding (fluency-first hypothesis)? We analyze log data obtained from an experiment that investigates the effects of intelligent tutoring systems (ITS) support for understanding and fluency in connection-making between fractions representations. The experiment shows that instructional support for both representational understanding and fluency are needed for students to benefit from the ITS. In analyzing the ITS log data, we contrast the understanding-first hypothesis and the fluency-first hypothesis, testing whether errors made during the learning phase mediate the effect of experimental condition. Finding that a simple statistical model does not the fit data, we searched over all plausible causal path analysis models. Our results support the understanding-first hypothesis but not the fluency-first hypothesis.