Results from an investigation of student understanding of physical optics indicate that university students who have studied this topic at the introductory level and beyond often cannot account for the pattern produced on a screen when light is incident on a single or double slit. Many do not know whether to apply geometrical or physical optics to a given situation and may inappropriately combine elements of both. Some specific difficulties that were identified for single and double slits proved to be sufficiently serious to preclude students from acquiring even a qualitative understanding of the wave model for light. In addition, we found that students in advanced courses often had mistaken beliefs about photons, which they incorporated into their interpretation of the wave model for matter. A major objective of this investigation was to build a research base for the design of a curriculum to help students develop a functional understanding of introductory optics.

During an investigation of student understanding of physical optics, we found that some serious difficulties that students have with this topic may be due, at least in part, to a lack of understanding of the nature of light as an electromagnetic wave. We therefore decided to look carefully at how students interpret the diagrammatic and mathematical formalism commonly used to represent a plane EM wave. The results of this research have guided the development and modification of tutorials that address some of the difficulties that we identified. These instructional materials are an example of how, within a relatively short time allotment, a curriculum developed on the basis of research can help students relate the concepts and formal representations associated with EM waves to physical phenomena.

The conceptual understanding and reasoning skills of advanced undergraduates as they make the transition from a traditional sequence in introductory calculus-based physics to their first course in upper-level mechanics are probed. The results thus far are consistent with findings from other investigations in upper-division courses, which indicate that persistent difficulties with fundamental concepts can hinder meaningful learning of advanced topics. To address this problem, the tutorial approach developed at the University of Washington has been adapted and incorporated into the intermediate mechanics course at Grand Valley State University. This modification has produced promising results.

This paper reports on a study of student understanding of the wave nature of matter in the context of the pattern produced by the diffraction and interference of particles. Students in first-year, second-year, and third-year physics courses were asked to predict and explain how a single change in an experimental setup would affect the pattern produced when electrons or other particles are incident on a single slit, double slit, or crystal lattice. The errors made by students after standard instruction indicated the presence of similar conceptual and reasoning difficulties at all levels. Among the most serious was an inability to interpret diffraction and interference in terms of a basic wave model. Other errors revealed a lack of a functional understanding of the de Broglie wavelength. Students often treated it as a fixed property of a particle, not as a function of the momentum. An important goal of this investigation was to provide a research base for the design of instruction to help students develop and apply a basic wave model for matter.

The study of linear oscillations-including simple harmonic, damped, and driven oscillations-is not only fundamental in classical mechanics but lies at the heart of numerous applications in the engineering sciences. Results from research conducted in the context of junior-level mechanics courses suggest the presence of specific conceptual and reasoning difficulties, many of which seem to be based on fundamental concepts. Evidence from pretests (ungraded quizzes) will be presented to illustrate critical difficulties in understanding conceptual underpinnings, relating concepts to graphical representations {e.g., motion graphs), and connecting the physics to the relevant differential equations of motion. Preliminary results from the development of a tutorial approach to instruction, modeled after Tutorials in Introductory Physics by McDermott, et al,[1] suggest that such an approach can be effective in both physics and engineering courses. (Supported by NSF grants DUE-0441426 and DUE-0442388.).