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Abstract Title: Identifying and Addressing Partial Differentiation Difficulties in Calculus and Thermodynamics
Abstract: We have reported previously that upper-level thermodynamics students demonstrate an inability to correctly equate the mixed second-order partial derivatives of the state function of volume (nonzero quantities in general), arguing instead that these derivatives must identically equal zero.[1]  Here we document the presence of this difficulty among students enrolled in a multivariable calculus course.  Data were gathered via diagnostic questions structurally identical to those administered in the thermodynamics course, yet devoid of physical context.  We additionally present a guided-inquiry tutorial sequence that was specifically developed to address this and related student difficulties with partial derivatives encountered in our research.  The sequence uses a graphical interpretation of partial derivatives in the context of an ideal gas P-V-T surface to bridge the abstract mathematical concepts with concrete physical properties.  Preliminary results indicate that the sequence effectively addresses the above difficulty, and also positively impacts student performance on related topics.

Research supported in part by NSF Grants #PHY-0406764 and #REC-0633951, and by the Maine Academic Prominence Initiative
1 B.R. Bucy et al., 2006 Phys. Educ. Res. Proc. 883, 157 (2007).
Abstract Type: Contributed Poster

Author/Organizer Information

Primary Contact: Brandon R. Bucy
The University of Maine
5709 Bennett Hall
Orono, ME 04461
Phone: (207)581-1237
and Co-Presenter(s)
John R. Thompson, The University of Maine, Orono, ME, john.thompson -at- umit.maine.edu

Donald B. Mountcastle, The University of Maine, Orono, ME, thermostatprof -at- yahoo.com