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Investigating Upper-Division Students' Interpretations of the Divergence Theorem
written by James A. Huffman, Michael Vignal, and Bethany R. Wilcox
The divergence theorem is an important mathematical tool used in many areas of physics, most notably, electricity and magnetism. Students have nominally encountered the divergence theorem in their math courses; however, its application in physics often differs meaningfully from its application in a pure math context. In this paper, we investigate physics students' understanding and interpretation of the divergence theorem through written responses to a brief two-part prompt which was designed to elicit separate responses for students' literal and qualitative interpretations of the divergence theorem. This differentiated between understanding the mathematical statement and being able to interpret its fundamental meaning. We found that students provided moderately successful literal interpretations but provided fewer meaningful qualitative interpretations. We also found that the ability to accurately translate the mathematical statement of the divergence theorem appeared to be a necessary, but not sufficient condition for being able to provide a meaningful
interpretation.
Physics Education Research Conference 2020
Part of the PER Conference series
Virtual Conference: July 22-23, 2020
Pages 222-227
Subjects Levels Resource Types
Education - Basic Research
- Alternative Conceptions
- Assessment
= Conceptual Assessment
Electricity & Magnetism
- Electric Fields and Potential
= Gauss' Law
Mathematical Tools
- Vector Calculus
= Divergence Theorem
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Researchers
- Professional/Practitioners
- Educators
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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.Huffman
Keyword:
PERC 2020
Record Creator:
Metadata instance created August 27, 2020 by Lyle Barbato
Record Updated:
August 29, 2020 by Lyle Barbato
Last Update
when Cataloged:
September 1, 2020
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Record Link
AIP Format
J. Huffman, M. Vignal, and B. Wilcox, presented at the Physics Education Research Conference 2020, Virtual Conference, 2020, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335).
AJP/PRST-PER
J. Huffman, M. Vignal, and B. Wilcox, Investigating Upper-Division Students' Interpretations of the Divergence Theorem, presented at the Physics Education Research Conference 2020, Virtual Conference, 2020, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335>.
APA Format
Huffman, J., Vignal, M., & Wilcox, B. (2020, July 22-23). Investigating Upper-Division Students' Interpretations of the Divergence Theorem. Paper presented at Physics Education Research Conference 2020, Virtual Conference. Retrieved February 26, 2021, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335
Chicago Format
Huffman, J, M. Vignal, and B. Wilcox. "Investigating Upper-Division Students' Interpretations of the Divergence Theorem." Paper presented at the Physics Education Research Conference 2020, Virtual Conference, July 22-23, 2020. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335 (accessed 26 February 2021).
MLA Format
Huffman, James A., Michael Vignal, and Bethany Wilcox. "Investigating Upper-Division Students' Interpretations of the Divergence Theorem." Physics Education Research Conference 2020. Virtual Conference: 2020. 222-227 of PER Conference. 26 Feb. 2021 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335>.
BibTeX Export Format
@inproceedings{ Author = "James A. Huffman and Michael Vignal and Bethany Wilcox", Title = {Investigating Upper-Division Students' Interpretations of the Divergence Theorem}, BookTitle = {Physics Education Research Conference 2020}, Pages = {222-227}, Address = {Virtual Conference}, Series = {PER Conference}, Month = {July 22-23}, Year = {2020} }
Refer Export Format

%A James A. Huffman
%A Michael Vignal
%A Bethany Wilcox
%T Investigating Upper-Division Students' Interpretations of the Divergence Theorem
%S PER Conference
%D July 22-23 2020
%P 222-227
%C Virtual Conference
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335
%O Physics Education Research Conference 2020
%O July 22-23
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Huffman, James A.
%A Vignal, Michael
%A Wilcox, Bethany
%D July 22-23 2020
%T Investigating Upper-Division Students' Interpretations of the Divergence Theorem
%B Physics Education Research Conference 2020
%C Virtual Conference
%P 222-227
%S PER Conference
%8 July 22-23
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=15487&DocID=5335


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