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Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space
written by Emily Marshman and Chandralekha Singh
Dirac notation is a compact and elegant notation taught to students in advanced quantum mechanics courses. However, students struggle to master Dirac notation and have difficulty translating between the Dirac notation and representations of the same quantum mechanical entity in different situations. We discuss an investigation of student difficulties with Dirac notation in the context of a three-dimensional vector space and the development, validation and evaluation of a Quantum Interactive Learning Tutorial (QuILT) that uses analogical reasoning to improve student understanding of this notation. The QuILT uses analogical reasoning and builds on students' prior knowledge of three-dimensional vectors in the familiar context of introductory mechanicsto help students build a coherent understanding of Dirac notation before transitioning to the quantum mechanical context. We summarize the development and validation of the QuILT and findings from the inclass evaluation.
Physics Education Research Conference 2020
Part of the PER Conference series
Virtual Conference: July 22-23, 2020
Pages 309-314
Subjects Levels Resource Types
Education - Applied Research
- Instructional Material Design
= Tutorial
- Pedagogy
= Analogies
- Technology
= Multimedia
Mathematical Tools
- Vector Calculus
Quantum Physics
- Foundations and Measurements
= Hilbert Space
= Projection Operators
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Researchers
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Format:
application/pdf
Mirror:
https://doi.org/10.1119/perc.2020…
Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 4.0 license. Further distribution of this work must maintain attribution to the published article's author(s), title, proceedings citation, and DOI.
Rights Holder:
American Association of Physics Teachers
DOI:
10.1119/perc.2020.pr.Marshman
NSF Number:
1806691
Keyword:
PERC 2020
Record Creator:
Metadata instance created August 27, 2020 by Lyle Barbato
Record Updated:
August 31, 2020 by Bruce Mason
Last Update
when Cataloged:
September 1, 2020
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
E. Marshman and C. Singh, presented at the Physics Education Research Conference 2020, Virtual Conference, 2020, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349).
AJP/PRST-PER
E. Marshman and C. Singh, Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space, presented at the Physics Education Research Conference 2020, Virtual Conference, 2020, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349>.
APA Format
Marshman, E., & Singh, C. (2020, July 22-23). Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space. Paper presented at Physics Education Research Conference 2020, Virtual Conference. Retrieved June 13, 2021, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349
Chicago Format
Marshman, Emily, and Chandralekha Singh. "Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space." Paper presented at the Physics Education Research Conference 2020, Virtual Conference, July 22-23, 2020. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349 (accessed 13 June 2021).
MLA Format
Marshman, Emily, and Chandralekha Singh. "Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space." Physics Education Research Conference 2020. Virtual Conference: 2020. 309-314 of PER Conference. 13 June 2021 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349>.
BibTeX Export Format
@inproceedings{ Author = "Emily Marshman and Chandralekha Singh", Title = {Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space}, BookTitle = {Physics Education Research Conference 2020}, Pages = {309-314}, Address = {Virtual Conference}, Series = {PER Conference}, Month = {July 22-23}, Year = {2020} }
Refer Export Format

%A Emily Marshman
%A Chandralekha Singh
%T Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space
%S PER Conference
%D July 22-23 2020
%P 309-314
%C Virtual Conference
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349
%O Physics Education Research Conference 2020
%O July 22-23
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Marshman, Emily
%A Singh, Chandralekha
%D July 22-23 2020
%T Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space
%B Physics Education Research Conference 2020
%C Virtual Conference
%P 309-314
%S PER Conference
%8 July 22-23
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15501&DocID=5349


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Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space:


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