2 research outputs found
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.Comment: 10 pages, 1 figures, 2 tables, accepted to the 2012 PERC Proceeding
Analytic Framework for Students' Use of Mathematics in Upper-Division Physics
Many students in upper-division physics courses struggle with the
mathematically sophisticated tools and techniques that are required for
advanced physics content. We have developed an analytical framework to assist
instructors and researchers in characterizing students' difficulties with
specific mathematical tools when solving the long and complex problems that are
characteristic of upper-division. In this paper, we present this framework,
including its motivation and development. We also describe an application of
the framework to investigations of student difficulties with direct integration
in electricity and magnetism (i.e., Coulomb's Law) and approximation methods in
classical mechanics (i.e., Taylor series). These investigations provide
examples of the types of difficulties encountered by advanced physics students,
as well as the utility of the framework for both researchers and instructors.Comment: 17 pages, 4 figures, 3 tables, in Phys. Rev. - PE