Investigating Student Connections Between Mathematics and Thermal Physics

Details Investigating Student Connections Between Mathematics and Thermal Physics Investigating Student Connections Between Mathematics and Thermal Physics

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aas...20913502t&link_type=abstract

2007 AAS/AAPT Joint Meeting, American Astronomical Society Meeting 209, #135.02; Bulletin of the American Astronomical Society,

Computer Science

Learning

Scientific paper

As part of work on teaching and learning in upper-level undergraduate thermal physics courses, we are exploring student functional understanding of mathematical concepts required for productive reasoning about thermal and statistical physics. We find evidence that students do not make connections between the physical situations or processes under study and the mathematical concepts or algorithms needed for analysis of the physics.
Examples will be provided from integrals and path integrals in the context of P-V diagrams, and from partial derivatives in the context of material properties and the Maxwell relations. With integration, our results suggest that while students may indeed have difficulties associated with the physical concepts in question, mathematical difficulties compound the problem. In particular, some students lack a functional understanding of two fundamental concepts of integration: the Riemann sum and the Fundamental Theorem of Calculus, both of which strongly impact whether a given variable is a state function or not. With partial differentiation, we find that although students are able to take partial derivatives easily, many students have difficulty understanding the mathematical and/or physical significance of their differentiation, even after instruction. Results from research are being used to develop instructional materials to address specific difficulties.
Supported in part by NSF Grant #PHY-0406764.

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