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Physical Review Physics Education Research
written by Megan Wawro, Kevin Lee Watson, and Warren M. Christensen
This 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.
Physical Review Physics Education Research: Volume 16, Issue 2, Pages 020112
Subjects Levels Resource Types
Education - Applied Research
- Learning Environment
Education - Basic Research
- Cognition
= Cognition Development
- Communication
= Representations
- Learning Theory
= Representations
- Problem Solving
= Representational Use
- Student Characteristics
= Skills
General Physics
- Physics Education Research
- Scientific Reasoning
Other Sciences
- Mathematics
Quantum Physics
- General
- Upper Undergraduate
- Graduate/Professional
- Reference Material
= Research study
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Free access
License:
This material is released under a Creative Commons Attribution 4.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.16.020112
NSF Number:
DUE-1452889
Keyword:
visual representation
Record Creator:
Metadata instance created May 12, 2021 by Bruce Mason
Record Updated:
February 9, 2022 by Caroline Hall
Last Update
when Cataloged:
August 25, 2020
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AIP Format
M. Wawro, K. Watson, and W. Christensen, , Phys. Rev. Phys. Educ. Res. 16 (2), 020112 (2020), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.16.020112).
AJP/PRST-PER
M. Wawro, K. Watson, and W. Christensen, Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics, Phys. Rev. Phys. Educ. Res. 16 (2), 020112 (2020), <https://doi.org/10.1103/PhysRevPhysEducRes.16.020112>.
APA Format
Wawro, M., Watson, K., & Christensen, W. (2020, August 25). Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics. Phys. Rev. Phys. Educ. Res., 16(2), 020112. Retrieved May 20, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.16.020112
Chicago Format
Wawro, M, K. Watson, and W. Christensen. "Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics." Phys. Rev. Phys. Educ. Res. 16, no. 2, (August 25, 2020): 020112, https://doi.org/10.1103/PhysRevPhysEducRes.16.020112 (accessed 20 May 2024).
MLA Format
Wawro, Megan, Kevin Lee Watson, and Warren M. Christensen. "Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics." Phys. Rev. Phys. Educ. Res. 16.2 (2020): 020112. 20 May 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.16.020112>.
BibTeX Export Format
@article{ Author = "Megan Wawro and Kevin Lee Watson and Warren M. Christensen", Title = {Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {16}, Number = {2}, Pages = {020112}, Month = {August}, Year = {2020} }
Refer Export Format

%A Megan Wawro %A Kevin Lee Watson %A Warren M. Christensen %T Students' metarepresentational competence with matrix notation and Dirac notation in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %D August 25, 2020 %P 020112 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020112 %O application/pdf

EndNote Export Format

%0 Journal Article %A Wawro, Megan %A Watson, Kevin Lee %A Christensen, Warren M. %D August 25, 2020 %T Students' metarepresentational competence with matrix notation and Dirac notation in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %P 020112 %8 August 25, 2020 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020112


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