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How students describe infinitesimal sources and infinitesimal spaces in integrals
written by Gregory Mulder, Paul J. Emigh, and Elizabeth Gire
Many students who have completed a full year of calculus continue to demonstrate a weak understanding of the role of the infinitesimal in an integral. This lack of understanding has implications for learning in introductory calculus-based physics, where students must integrate contributions from spatially-distributed sources. Symbolically, a student who constructs such an integral in terms of small chunks of sources, like dm or dq, will need to relate their infinitesimal to a small chunk of space, like dx. In order to better understand how students use the integration infinitesimal, we collected and analyzed written solutions from 39 upperdivision physics majors who solved for the electric field at an asymmetric point in space above a homogeneously charged bar. We have identified several categories of ways students handled the infinitesimal when constructing an integral. We present evidence, supporting prior work, that a small segment understanding of the infinitesimal leads students to a correct translation from dq to dx.
Physics Education Research Conference 2018
Part of the PER Conference series
Washington, DC: August 1-2, 2018
Subjects Levels Resource Types
Education - Basic Research
- Alternative Conceptions
Electricity & Magnetism
- Electric Fields and Potential
= Electric Field
Mathematical Tools
- Calculus
= Integral
- Upper Undergraduate
- Reference Material
= Research study
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Format:
application/pdf
Mirror:
https://doi.org/10.1119/perc.2018…
Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 3.0 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.2018.pr.Mulder
Keyword:
PERC 2018
Record Creator:
Metadata instance created December 31, 2018 by Lyle Barbato
Record Updated:
December 31, 2018 by Lyle Barbato
Last Update
when Cataloged:
December 31, 2018
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AIP Format
G. Mulder, P. Emigh, and E. Gire, presented at the Physics Education Research Conference 2018, Washington, DC, 2018, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974).
AJP/PRST-PER
G. Mulder, P. Emigh, and E. Gire, How students describe infinitesimal sources and infinitesimal spaces in integrals, presented at the Physics Education Research Conference 2018, Washington, DC, 2018, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974>.
APA Format
Mulder, G., Emigh, P., & Gire, E. (2018, August 1-2). How students describe infinitesimal sources and infinitesimal spaces in integrals. Paper presented at Physics Education Research Conference 2018, Washington, DC. Retrieved September 27, 2021, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974
Chicago Format
Mulder, G, P. Emigh, and E. Gire. "How students describe infinitesimal sources and infinitesimal spaces in integrals." Paper presented at the Physics Education Research Conference 2018, Washington, DC, August 1-2, 2018. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974 (accessed 27 September 2021).
MLA Format
Mulder, Gregory, Paul Emigh, and Elizabeth Gire. "How students describe infinitesimal sources and infinitesimal spaces in integrals." Physics Education Research Conference 2018. Washington, DC: 2018. of PER Conference. 27 Sep. 2021 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974>.
BibTeX Export Format
@inproceedings{ Author = "Gregory Mulder and Paul Emigh and Elizabeth Gire", Title = {How students describe infinitesimal sources and infinitesimal spaces in integrals}, BookTitle = {Physics Education Research Conference 2018}, Address = {Washington, DC}, Series = {PER Conference}, Month = {August 1-2}, Year = {2018} }
Refer Export Format

%A Gregory Mulder %A Paul Emigh %A Elizabeth Gire %T How students describe infinitesimal sources and infinitesimal spaces in integrals %S PER Conference %D August 1-2 2018 %C Washington, DC %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974 %O Physics Education Research Conference 2018 %O August 1-2 %O application/pdf

EndNote Export Format

%0 Conference Proceedings %A Mulder, Gregory %A Emigh, Paul %A Gire, Elizabeth %D August 1-2 2018 %T How students describe infinitesimal sources and infinitesimal spaces in integrals %B Physics Education Research Conference 2018 %C Washington, DC %S PER Conference %8 August 1-2 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974


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