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2011 AAPT Summer Meeting
July 30-August 3, 2011
Omaha, Nebraska

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Student Difficulties with a Taylor Series Expansion in Statistical Mechanics
  Location: HC 3023 & 3023A
  Date: Tuesday, Aug.2
  Time: 2:45 PM -2:55 PM
  Author: Trevor Smith, University of Maine
  Co-Author(s): John R. Thompson , Donald B. Mountcastle
  Abstract: One goal of physics instruction is to have students learn to make physical meaning of specific mathematical ideas, concepts and procedures, in different physical settings. We have reported on student difficulties with these connections in the contexts of integrals, total differentials, and partial derivatives in upper-division thermal and statistical physics. As part of research investigating student understanding and use of the Boltzmann factor, we are developing materials that guide students through a derivation of the Boltzmann factor that includes a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and individual think-aloud and teaching interviews, we present evidence that while some students can recognize familiar expressions as Taylor expansions, students lack fluency with Taylor expansions at the level one might expect of advanced undergraduates, despite previous exposure to Taylor series expansions in both calculus and physics courses.
  Footnotes: None
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