PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Meta-representational competence with linear algebra in quantum mechanics
Page: 326
In this report we share analysis regarding students’ meta-representational competence (MRC) that is expressed as they engage in solving quantum mechanics problems that involve linear algebra concepts. The particular characteristic of MRC that is the focus of this analysis is students’ critiquing and comparing the adequacy of representations, specifically matrix notation and Dirac notation, and judging their suitability for various tasks (diSessa, 2004). With data from semi-structured individual interviews, we created categories of types of MRC elicited during students’ work on an expectation value problem. We provide detail on two students who serve as paradigmatic examples of a student’s power and flexibility in thinking in and using different notation systems. This work lends credence to and inspires our preliminary conjecture that strong meta-representational competence (MRC) is necessary not only to be fluent and proficient in the mathematics involved in solving quantum mechanics problems but also to develop a robust understanding of the quantum mechanics content.