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Finding Derivatives from an Equipotential Graph
written by Paul J. Emigh and Corinne A. Manogue
We examine how upper-division physics students find derivatives from an equipotential graph in an individual interview setting.  We focus specifically on identifying the different kinds of behavior that students engage in when finding a derivative from an equipotential graph, and also on the representational elements that students use or introduce during their work.  We find that the students were able to find the derivative successfully using a ratio-of-small-changes approach.  Students engaged in behavior like sketching straight lines or arrows on the given graph as a way to choose points for calculating a ratio and to keep one variable constant for the derivative.  We also saw students make sense of the equipotential graph and reinterpret the derivative they found using those representations using two other graphical representations: cross-sections and three-dimensional plastic surfaces.  We find these results encouraging because the students had studied equipotential graphs and derivatives as ratios-of-small-changes as part of their junior-level electrostatics, suggesting that such a course is effective at helping students develop representational fluency for working with multivariable derivatives.
Physics Education Research Conference 2022
Part of the PER Conference series
Grand Rapids, MI: July 13-14, 2022
Pages 163-169
Subjects Levels Resource Types
Education - Basic Research
- Assessment
- Problem Solving
= Processes
= Representational Use
- Student Characteristics
= Skills
Mathematical Tools
- Multivariable Calculus
= Partial Derivative
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Professional/Practitioners
- Researchers
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Format:
application/pdf
Mirror:
https://doi.org/10.1119/perc.2022…
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.2022.pr.Emigh
NSF Numbers:
1323800
1836604
Keyword:
PERC 2022
Record Creator:
Metadata instance created September 7, 2022 by Lyle Barbato
Record Updated:
September 14, 2022 by Lyle Barbato
Last Update
when Cataloged:
September 15, 2022
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Record Link
AIP Format
P. Emigh and C. Manogue, , presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595).
AJP/PRST-PER
P. Emigh and C. Manogue, Finding Derivatives from an Equipotential Graph, presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595>.
APA Format
Emigh, P., & Manogue, C. (2022, July 13-14). Finding Derivatives from an Equipotential Graph. Paper presented at Physics Education Research Conference 2022, Grand Rapids, MI. Retrieved April 15, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595
Chicago Format
Emigh, Paul, and Corinne Manogue. "Finding Derivatives from an Equipotential Graph." Paper presented at the Physics Education Research Conference 2022, Grand Rapids, MI, July 13-14, 2022. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595 (accessed 15 April 2024).
MLA Format
Emigh, Paul, and Corinne Manogue. "Finding Derivatives from an Equipotential Graph." Physics Education Research Conference 2022. Grand Rapids, MI: 2022. 163-169 of PER Conference. 15 Apr. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595>.
BibTeX Export Format
@inproceedings{ Author = "Paul Emigh and Corinne Manogue", Title = {Finding Derivatives from an Equipotential Graph}, BookTitle = {Physics Education Research Conference 2022}, Pages = {163-169}, Address = {Grand Rapids, MI}, Series = {PER Conference}, Month = {July 13-14}, Year = {2022} }
Refer Export Format

%A Paul Emigh %A Corinne Manogue %T Finding Derivatives from an Equipotential Graph %S PER Conference %D July 13-14 2022 %P 163-169 %C Grand Rapids, MI %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595 %O Physics Education Research Conference 2022 %O July 13-14 %O application/pdf

EndNote Export Format

%0 Conference Proceedings %A Emigh, Paul %A Manogue, Corinne %D July 13-14 2022 %T Finding Derivatives from an Equipotential Graph %B Physics Education Research Conference 2022 %C Grand Rapids, MI %P 163-169 %S PER Conference %8 July 13-14 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16226&DocID=5595


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