Students' metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

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dc.contributor.authorWawro, Meganen
dc.contributor.authorWatson, Kevinen
dc.contributor.authorChristensen, Warrenen
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-10-05T13:49:40Zen
dc.date.available2020-10-05T13:49:40Zen
dc.date.issued2020-08-25en
dc.description.abstractThis article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves 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. With data of students' work during semistructured individual interviews, components of students' MRC were analyzed and categorized according to value-based preferences, problem-based preferences, and purpose and utility awareness. Detail is provided on two students who serve as paradigmatic examples of students' power and flexibility within different notation systems, and detail of a third student is given as a point of contrast. In addition to adapting MRC as a helpful construct for characterizing student understanding at the intersection of undergraduate mathematics and physics, we aim to demonstrate how students' rich understanding of linear algebra and quantum mechanics includes and is aided by their understanding and flexible use of different notational systems. For example, the problem-based preference aspects of MRC highlight that any particular problem-solving approach is itself intrinsically tied to a notational system. We suggest that any instruction with the goal of helping students develop a deep understanding of quantum mechanics and linear algebra should provide opportunities for students to use and improve their MRC.en
dc.description.notesThis material is based upon work supported by the National Science Foundation under Grant No. DUE-1452889. The authors thank Andrea diSessa, Jeffrey Rabin, Michael Wittmann, and Michelle Zandieh for their insights on the data. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. We are thankful for Kevin Watson's integral involvement with this research, which included contributions to study design and data collection, theoretical and methodological framing, data analysis, and writing.en
dc.description.sponsorshipNational Science FoundationNational Science Foundation (NSF) [DUE-1452889]en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1103/PhysRevPhysEducRes.16.020112en
dc.identifier.issn2469-9896en
dc.identifier.issue2en
dc.identifier.other20112en
dc.identifier.urihttp://hdl.handle.net/10919/100166en
dc.identifier.volume16en
dc.language.isoenen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleStudents' metarepresentational competence with matrix notation and Dirac notation in quantum mechanicsen
dc.title.serialPhysical Review Physics Education Researchen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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