| In the past three decades, physics education research has primarily focused on student conceptual understanding; little work has been conducted to investigate student difficulties in problem solving. In cognitive science and psychology, however, extensive studies have explored the differences in problem solving between experts and naive students. A major finding indicates that experts often apply qualitative representations in problem solving, but that novices use an equation-centered method. This dissertation describes investigations into the use of multiple representations and visualizations in student understanding and problem solving with the concepts of work and energy.;A multiple-representation strategy was developed to help students acquire expertise in solving work-energy problems. In this approach, a typical work-energy problem is considered as a physical process. The process is first described in words---the verbal representation of the process. Next, a sketch or a picture, called a pictorial representation, is used to represent the process. This is followed by work-energy bar charts---a physical representation of the same processes. Finally, this process is represented mathematically by using a generalized work-energy equation. In terms of the multiple representations, the goal of solving a work-energy problem is to represent the physical process in different ways---words, sketches, bar charts, and equations. The abstract verbal description is linked to the abstract mathematical representation by the more intuitive pictorial and diagrammatic physical representations. Ongoing assessment of student learning indicates that this multiple-representation technique is more effective than standard instruction methods in student problem solving.;Internal energy is an abstract concept in work and energy. To help students visualize this difficult-to-understand concept, a guided-inquiry learning activity using a pair of model carts and an experiment problem using a sandbag were developed. Assessment results have shown that these research-based materials are effective in helping students visualize this concept and give a pictorial idea of "where the kinetic energy goes" during inelastic collisions.;The research and curriculum development was conducted in the context of the introductory calculus-based physics course. Investigations were carried out using common physics education research tools, including open-ended surveys, written test questions, and individual student interviews. |
