Student Reasoning about Linear Algebra in Quantum Physics
Talk by Dr. Megan Wawro (Mathematics Dept, Virginia Tech)
9/30/2019 Wilson Hall 1-144 4:10-5:00pm
In the research project An Interdisciplinary Study of Learning: Student Understanding of Linear Algebra in Physics (NSF 1452889), I investigate students’ understanding, symbolization, and interpretation of eigentheory and related ideas from linear algebra in quantum mechanics. In my talk, I will share results from two ongoing research threads of this project. One thread involves analyzing students’ meta- representational competence (MRC) as they solve a quantum mechanical expectation value problem during semi-structured individual interviews. The particular characteristic of MRC that I focus on is students’ critiquing and comparing the adequacy of representations, specifically matrix notation and Dirac notation, to judge their suitability for various tasks (diSessa, 2004). I will share examples from the data and explore the relationship between MRC and conceptual understanding in this setting. The second thread investigates students' language for eigentheory across mathematics and quantum physics contexts. Using interview data, I present students' interpretations of a canonical mathematical 2x2 eigenequation, a spin-½ operator eigenequation, and a spin-½ operator equation in which the operation "flips" the spin state. Using discourse analysis, results characterize students' nuanced imagery for the equations and highlight instances of synergistic and potentially incompatible interpretations. I hope the research findings will help facilitate a conversation about the relationship between what is taught in linear algebra courses and quantum mechanics courses, and what experiencing and making sense of both courses might be like for students.