ACER: A Framework on the Use of Mathematics in
Upper-division Physics
Marcos D. Caballero, Bethany R. Wilcox, and Steven J. Pollock
Department of Physics, University of Colorado Boulder, Boulder, CO 80309
Rachel E. Pepper
Department of Integrative Biology, University of California, Berkeley, CA, 94720
Abstract
At the University of Colorado Boulder, as part of our broader e orts to transform middle- and
upper-division physics courses, we research students' di culties with particular concepts, meth-
ods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly,
a number of di culties 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
uently in introductory physics (e.g., mapping meaning onto mathematical
symbols). We have developed a theoretical framework to facilitate connecting students' di culties
to challenges with speci c 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.
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