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ACER: A Framework on the Use of Mathematics in Upper-division Physics
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.
Physics Education Research Conference 2012
Part of the PER Conference series Philadelphia, PA: August 1-2, 2012 Volume 1513, Pages 90-93
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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=17197">Caballero, M, B. Wilcox, R. Pepper, and S. Pollock. "ACER: A Framework on the Use of Mathematics in Upper-division Physics." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012.</a>
M. Caballero, B. Wilcox, R. Pepper, and S. Pollock, , presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119).
M. Caballero, B. Wilcox, R. Pepper, and S. Pollock, ACER: A Framework on the Use of Mathematics in Upper-division Physics, presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119>.
Caballero, M., Wilcox, B., Pepper, R., & Pollock, S. (2012, August 1-2). ACER: A Framework on the Use of Mathematics in Upper-division Physics. Paper presented at Physics Education Research Conference 2012, Philadelphia, PA. Retrieved November 8, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119
Caballero, M, B. Wilcox, R. Pepper, and S. Pollock. "ACER: A Framework on the Use of Mathematics in Upper-division Physics." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119 (accessed 8 November 2025).
Caballero, Marcos D., Bethany Wilcox, Rachel Pepper, and Steven Pollock. "ACER: A Framework on the Use of Mathematics in Upper-division Physics." Physics Education Research Conference 2012. Philadelphia, PA: 2012. 90-93 Vol. 1513 of PER Conference. 8 Nov. 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119>.
@inproceedings{
Author = "Marcos D. Caballero and Bethany Wilcox and Rachel Pepper and Steven Pollock",
Title = {ACER: A Framework on the Use of Mathematics in Upper-division Physics},
BookTitle = {Physics Education Research Conference 2012},
Pages = {90-93},
Address = {Philadelphia, PA},
Series = {PER Conference},
Volume = {1513},
Month = {August 1-2},
Year = {2012}
}
%A Marcos D. Caballero %A Bethany Wilcox %A Rachel Pepper %A Steven Pollock %T ACER: A Framework on the Use of Mathematics in Upper-division Physics %S PER Conference %V 1513 %D August 1-2 2012 %P 90-93 %C Philadelphia, PA %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119 %O Physics Education Research Conference 2012 %O August 1-2 %O application/pdf %0 Conference Proceedings %A Caballero, Marcos D. %A Wilcox, Bethany %A Pepper, Rachel %A Pollock, Steven %D August 1-2 2012 %T ACER: A Framework on the Use of Mathematics in Upper-division Physics %B Physics Education Research Conference 2012 %C Philadelphia, PA %V 1513 %P 90-93 %S PER Conference %8 August 1-2 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=17197&DocID=6119 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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