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.