Facets of Meta-Representational Competence in Quantum Mechanics Change of Basis Problems

Meta-Representational Competence (MRC) is a theoretical framework that is used to analyze how people create and interact with external representations. Within Quantum Mechanics, problems may be approached or perceived differently based on the notation used (either Dirac, Matrix, or Spinor notation) in the problem statement or by the person working on the problem. Semi-structured interviews were conducted to present physics students with change of basis content problems in the context of Quantum Mechanics. These content questions were used to ask students about MRC concepts directly. Student statements were coded to revise previously identified facets of MRC and as well as novel facets that came out of the data. Our analysis of three student interviews demonstrates an array of utility of MRC concepts, solidifies MRC as a useful lens for investigating student thinking and suggests that specific instruction on MRC concepts could be worthwhile for student skill development and conceptual understanding. We highlight specific codes that were prevalent in our data and our definitions of novel codes.