When basic changes to a solution suggest meaningful differences in mathematics

Wittmann, Michael C.; Black, Katrina E.

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When basic changes to a solution suggest meaningful differences in mathematics

written by Michael C. Wittmann and Katrina E. Black

When solving two integrals arising from the separation of variables in a first order linear differential equation, students have multiple correct choices for how to proceed. They might set limits on both integrals or use integration constants on both or only one equation. In each case, the physical meaning of the mathematics is equivalent. But, how students choose to represent the mathematics can tell us much about what they are thinking. We observe students debating how to integrate the quantity dt. One student seeks a general function that works for everyone, and does not wish to specify the value of the integration constant. Another student seeks a function consistent with the specific physics problem. They compromise by using a constant, undefined in value for one student, zero in value for the other.

Physics Education Research Conference 2011
Part of the PER Conference Invited Paper series
Omaha, Nebraska: August 3-4, 2011
Volume 1413, Pages 93-96

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Published: February 6, 2012

Subjects	Levels	Resource Types
Mathematical Tools - Calculus	- Lower Undergraduate - Graduate/Professional	- Reference Material = Article

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Mirror:: https://doi.org/10.1063/1.3680002
Access Rights:: Free access and
Available for purchase; A preprint of the work is available. A hard copy of the PERC 2011 proceedings is available for purchase from the AIP.
Restriction:: © 2011 American Institute of Physics
DOI:: 10.1063/1.3680002
NSF Numbers:: 0441426; 0442388; 0633951; 0962805.
PACSs:: 01.40.Fk; 01.40.Ha
Keywords:: embodied cognition, PERC 2011, wave propagation
Record Cloner:: Metadata instance created April 24, 2012 by Lyle Barbato
Record Updated:: May 15, 2012 by Vince Kuo
Last Update when Cataloged:: February 6, 2012
Other Collections:: The PER-Central

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Record Link

<a href="https://www.compadre.org/portal/items/detail.cfm?ID=11821">Wittmann, Michael, and Katrina E. Black. "When basic changes to a solution suggest meaningful differences in mathematics." Paper presented at the Physics Education Research Conference 2011, Omaha, Nebraska, August 3-4, 2011.</a>

AIP Format

M. Wittmann and K. Black, , presented at the Physics Education Research Conference 2011, Omaha, Nebraska, 2011, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671).

AJP/PRST-PER

M. Wittmann and K. Black, When basic changes to a solution suggest meaningful differences in mathematics, presented at the Physics Education Research Conference 2011, Omaha, Nebraska, 2011, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671>.

APA Format

Wittmann, M., & Black, K. (2011, August 3-4). When basic changes to a solution suggest meaningful differences in mathematics. Paper presented at Physics Education Research Conference 2011, Omaha, Nebraska. Retrieved November 1, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671

Chicago Format

Wittmann, Michael, and Katrina E. Black. "When basic changes to a solution suggest meaningful differences in mathematics." Paper presented at the Physics Education Research Conference 2011, Omaha, Nebraska, August 3-4, 2011. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671 (accessed 1 November 2024).

MLA Format

Wittmann, Michael, and Katrina E. Black. "When basic changes to a solution suggest meaningful differences in mathematics." Physics Education Research Conference 2011. Omaha, Nebraska: 2011. 93-96 Vol. 1413 of PER Conference Invited Paper. 1 Nov. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671>.

BibTeX Export Format

@inproceedings{ Author = "Michael Wittmann and Katrina E. Black", Title = {When basic changes to a solution suggest meaningful differences in mathematics}, BookTitle = {Physics Education Research Conference 2011}, Pages = {93-96}, Address = {Omaha, Nebraska}, Series = {PER Conference Invited Paper}, Volume = {1413}, Month = {August 3-4}, Year = {2011} }

Refer Export Format

%A Michael Wittmann %A Katrina E. Black %T When basic changes to a solution suggest meaningful differences in mathematics %S PER Conference Invited Paper %V 1413 %D August 3-4 2011 %P 93-96 %C Omaha, Nebraska %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671 %O Physics Education Research Conference 2011 %O August 3-4 %O application/pdf

EndNote Export Format

%0 Conference Proceedings %A Wittmann, Michael %A Black, Katrina E. %D August 3-4 2011 %T When basic changes to a solution suggest meaningful differences in mathematics %B Physics Education Research Conference 2011 %C Omaha, Nebraska %V 1413 %P 93-96 %S PER Conference Invited Paper %8 August 3-4 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=11821&DocID=2671

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