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“Rules without a Reason”: ODEs in a concept image framework
written by Andy Fung and Michael E. Loverude
Elementary ODEs are seen as prerequisite knowledge gained from the introductory calculus sequence for any physics student entering the upper division. In this paper, we provide evidence that while students might be well-versed in the rules and notations of ODEs, this does not necessarily translate to the application of these "rules without a reason" to novel physics tasks. Using the mathematics education researchers Tall and Vinner's concept image framework, we propose that the body of knowledge or concept image a student brings to an upper division physics environment regarding ODEs is restricted. We present, via four student interviews, three potential signals of this "restricted concept image": mathematical processes that are formally taught in introductory calculus courses but are not reliably evoked when faced with a novel physics task. Our goal for this paper, as part of a larger project exploring student difficulties regarding ODEs, is to create a "proof of concept" that can be used in future work to more definitively identify the presence of a restricted ODE concept image.
Physics Education Research Conference 2022
Part of the PER Conference series
Grand Rapids, MI: July 13-14, 2022
Pages 188-193
Subjects Levels Resource Types
Education - Basic Research
- Alternative Conceptions
- Cognition
- Learning Theory
= Cognitive Modeling
- Student Characteristics
= Skills
Mathematical Tools
- Differential Equations
- Graduate/Professional
- Upper Undergraduate
- Reference Material
= Research study
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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.Fung
NSF Number:
1912660
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
A. Fung and M. Loverude, , presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16230&DocID=5599).
AJP/PRST-PER
A. Fung and M. Loverude, “Rules without a Reason”: ODEs in a concept image framework, presented at the Physics Education Research Conference 2022, Grand Rapids, MI, 2022, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16230&DocID=5599>.
APA Format
Fung, A., & Loverude, M. (2022, July 13-14). “Rules without a Reason”: ODEs in a concept image framework. 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=16230&DocID=5599
Chicago Format
Fung, Andy, and Michael Loverude. "“Rules without a Reason”: ODEs in a concept image framework." 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=16230&DocID=5599 (accessed 15 April 2024).
MLA Format
Fung, Andy, and Michael Loverude. "“Rules without a Reason”: ODEs in a concept image framework." Physics Education Research Conference 2022. Grand Rapids, MI: 2022. 188-193 of PER Conference. 15 Apr. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16230&DocID=5599>.
BibTeX Export Format
@inproceedings{ Author = "Andy Fung and Michael Loverude", Title = {“Rules without a Reason”: ODEs in a concept image framework}, BookTitle = {Physics Education Research Conference 2022}, Pages = {188-193}, Address = {Grand Rapids, MI}, Series = {PER Conference}, Month = {July 13-14}, Year = {2022} }
Refer Export Format

%A Andy Fung %A Michael Loverude %T "Rules without a Reason": ODEs in a concept image framework %S PER Conference %D July 13-14 2022 %P 188-193 %C Grand Rapids, MI %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16230&DocID=5599 %O Physics Education Research Conference 2022 %O July 13-14 %O application/pdf

EndNote Export Format

%0 Conference Proceedings %A Fung, Andy %A Loverude, Michael %D July 13-14 2022 %T "Rules without a Reason": ODEs in a concept image framework %B Physics Education Research Conference 2022 %C Grand Rapids, MI %P 188-193 %S PER Conference %8 July 13-14 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16230&DocID=5599


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