This dissertation presents results from research and curriculum development related to student understanding of the principle of superposition in introductory optics and upper-division quantum mechanics courses. The focus is on the extent to which students are able to relate the mathematical formalism used in physics to real-world phenomena. In particular, the investigation involves three topics: (1) student ability to determine quantum probabilities for discrete and continuous cases and to recognize similarities between the procedures, (2) student ability to recognize the measurable effects of relative phase in superposition states, and (3) student ability to apply superposition to the interference of classical waves. In each case, specific difficulties that students encounter when reasoning about superposition are presented, together with a discussion of how curriculum was developed to promote student learning and to address common errors. The process through which the curriculum is developed and its impact on student understanding of superposition are discussed explicitly. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]