Dissertation Abstract ROLE OF MULTIPLE REPRESENTATIONS IN PROBLEM SOLVING IN PHYSICS Improving studentsâ€™ problem solving skills is a central goal of introductory physics courses. The problem solving process is important in learning physics because it is the main modus through which introductory students make sense of physics concepts and improve their knowledge structure of physics. Representations play a major role in problem solving because they can help students focus on the conceptual aspects of physics. In addition, representing a problem in a diagrammatic form is an important initial step that helps initiate the key stage of conceptual planning and analysis and is therefore employed by experts engaged in problem solving. This thesis explores the role that multiple representations play in introductory studentsâ€™ problem solving performance in several investigations. Findings suggest that employing a diagrammatic approach to problem solving is the expert approach and that students who draw productive diagrams are more successful problem solvers even if their approach is primarily mathematical. In addition, students who were provided with a diagrammatic representation corresponding to the physical situation presented in a problem, sometimes exhibited deteriorated performance. Think-aloud interviews with individual students suggested that this deteriorated performance is in part due to the fact that students who are provided with diagrams can spend less time on the important initial stage of conceptual planning and sometimes even omit it altogether jumping in the implementation stage without ensuring that they understand the problem. Another study which investigated two interventions aimed at improving introductory students representational consistency between mathematical and graphical representations revealed that a lot of scaffolding which would be considered effective by most experts can have a detrimental effect. Interviews suggested that the detrimental effect could be in part due to the increased cognitive load brought on by the additional instructions, which, for some students, may have resulted in cognitive overload and caused significant difficulties to students engaged in problem solving. In addition, this investigation revealed that students who exhibited representational consistency also showed improved problem solving performance. The final investigation expounded in this thesis is centered on a problem solving task administered to first year physics graduate teaching assistants (TAs) designed to provide information about their pedagogical content knowledge (PCK). In particular, the graduate students identified what they considered to be the most common difficulties of introductory physics students related to graphical representations of kinematics concepts as they occur in the Test of Understanding Graphs in Kinematics (TUG-K). As an extension, the Force Concept Inventory (FCI) was also used to assess this aspect of PCK (knowledge of student difficulties) of both instructors and TAs. Several interesting results are discussed: when it comes to the performance in identifying common introductory student alternate conceptions and difficulties, teaching an independent course and recent teaching experience do not appear to correlate with this performance. In addition, American TAs did not perform any better than Chinese TAs or other foreign TAs in identifying common student alternate conceptions/difficulties both in the context of the TUG-K and in the context of the FCI. Finally, while both instructors and TAs performed better than random guessing, there were many common introductory student alternate conceptions and difficulties that were not identified by many instructors and TAs.