Skill with different representations and multiple representations is highly valued in physics, and prior work has shown that novice physics students can struggle with the representations typically used in solving physics problems. There exists work in PER examining student use of representations and multiple representations, but there have been no comprehensive attempts to understand what factors influence how introductory students succeed or fail in using representations in physics. This thesis is such an attempt, and is organized around four main goals and results. First, we establish that representation is a major factor in student performance, and uncover some of the mechanisms by which representation can affect performance, including representation-dependent cueing. Second, we study the effect of different instructional environments on student learning of multiple representation use during problem solving, and find that courses that are rich in representations can have significant impacts on student skills. Third, we evaluate the role of meta- representational skills in solving physics problems at the introductory level, and find that the meta-representational abilities that we test for in our studies are poorly developed in introductory students. Fourth, we characterize the differences in representation use between expert and novice physics problem solvers, and note that the major differences appear not to lie in whether representations are used, but in how they are used.

With these results in hand, we introduce a model of student use of representations during physics problem solving. This model consists of a set of practical heuristics plus an analysis framework adapted from cultural-constructivist theory. We demonstrate that this model can be useful in understanding and synthesizing our results, and we discuss the instructional implications of our findings.