The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

Conceptual approaches to contemporary physics topics pose many learning challenges. One factor influencing knowledge integration is a student's epistemological framing. Epistemic frames provide a context within which a particular situation is perceived, interpreted, and judged. The utility of an epistemic frame is context dependent, and the…

Assessments are an integral part of academic environments and can present opportunities for students to make sense of novel contexts using their existing ideas. Assessments also provide insights on students' learning and the efficacy of the pedagogical practices. Consequently, physics education research shares a storied history of developing…

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…

Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…

Quantum mechanical (QM) and molecular docking methods are used to probe systems of biological and synthetic interest. Probing interactions of nucleobases within proteins, and properly modeling said interactions toward novel nucleobase development, is extremely difficult, and of great utility in RNA interference (RNAi) therapeutics. The issues in…

Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively "realist" perspectives of introductory…