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Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine
written by David J. Roundy, Eric Weber, Grant Sherer, and Corinne A. Manogue
We developed the Partial Derivative Machine (PDM) in response to difficulties we encountered in teaching students about mathematical concepts involving partial derivatives and total differentials that are needed in thermodynamics. The Partial Derivative Machine is a system that has four observable and controllable properties: two forces and two positions. However, of these four properties only two may be controlled independently. This context-dependence of independent and dependent variables enables the same sort of mathematical flexibility (and confusion) that is present in thermodynamics. Because the PDM is easy to use and understand, we hypothesized that it would allow us to explore the nature of experts' thinking about derivatives, even those unfamiliar with ideas in thermodynamics. In this paper, we present results from interviews with experts from several disciplines, as we explore how they understand partial derivatives when given an ambiguous prompt. The research question guiding this work is "How do experts think about partial derivatives?"
Physics Education Research Conference 2014
Part of the PER Conference series
Minneapolis, MN: July 30-31, 2014
Pages 227-230
Subjects Levels Resource Types
Education Foundations
- Problem Solving
= Expert-Novice Comparisons
Education Practices
- Technology
Mathematical Tools
- Multivariable Calculus
= Partial Derivative
- Upper Undergraduate
- Graduate/Professional
- Reference Material
= Research study
Intended Users Formats Ratings
- Researchers
- application/pdf
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Mirror:
http://dx.doi.org/10.1119/perc.20…
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.2014.pr.053
NSF Numbers:
0618877
0837829
1023120
1323800
PACSs:
01.40.Fk
01.40.G-
05.70.-a
Keywords:
PERC 2014, disciplinary differences, experiment, expert views, interview, thermodynamics
Record Creator:
Metadata instance created April 28, 2015 by Lyle Barbato
Record Updated:
May 26, 2015 by Bruce Mason
Last Update
when Cataloged:
April 28, 2015
Other Collections:

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Record Link
AIP Format
D. Roundy, E. Weber, G. Sherer, and C. Manogue, presented at the Physics Education Research Conference 2014, Minneapolis, MN, 2014, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088).
AJP/PRST-PER
D. Roundy, E. Weber, G. Sherer, and C. Manogue, Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine, presented at the Physics Education Research Conference 2014, Minneapolis, MN, 2014, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088>.
APA Format
Roundy, D., Weber, E., Sherer, G., & Manogue, C. (2014, July 30-31). Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine. Paper presented at Physics Education Research Conference 2014, Minneapolis, MN. Retrieved December 11, 2017, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088
Chicago Format
Roundy, D, E. Weber, G. Sherer, and C. Manogue. "Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine." Paper presented at the Physics Education Research Conference 2014, Minneapolis, MN, July 30-31, 2014. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088 (accessed 11 December 2017).
MLA Format
Roundy, David, Eric Weber, Grant Sherer, and Corinne Manogue. "Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine." Physics Education Research Conference 2014. Minneapolis, MN: 2014. 227-230 of PER Conference. 11 Dec. 2017 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088>.
BibTeX Export Format
@inproceedings{ Author = "David Roundy and Eric Weber and Grant Sherer and Corinne Manogue", Title = {Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine}, BookTitle = {Physics Education Research Conference 2014}, Pages = {227-230}, Address = {Minneapolis, MN}, Series = {PER Conference}, Month = {July 30-31}, Year = {2014} }
Refer Export Format

%A David Roundy
%A Eric Weber
%A Grant Sherer
%A Corinne Manogue
%T Experts' Understanding of Partial Derivatives Using the Partial   Derivative Machine
%S PER Conference
%D July 30-31 2014
%P 227-230
%C Minneapolis, MN
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088
%O Physics Education Research Conference 2014
%O July 30-31
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Roundy, David
%A Weber, Eric
%A Sherer, Grant
%A Manogue, Corinne
%D July 30-31 2014
%T Experts' Understanding of Partial Derivatives Using the Partial   Derivative Machine
%B Physics Education Research Conference 2014
%C Minneapolis, MN
%P 227-230
%S PER Conference
%8 July 30-31
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13493&DocID=4088


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