  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. As part of research investigating student learning in
statistical physics, we are developing curriculum materials that guide students
through a derivation of the Boltzmann factor, using a Taylor series expansion
of entropy. Using results from written surveys, classroom observations, and
both individual think-aloud and teaching interviews, we present evidence that
many students can recognize and interpret series expansions, but they often
lack fluency with the Taylor series despite previous exposures in both calculus
and physics courses. We present students' successes and failures both using and
interpreting Taylor series expansions in a variety of contexts.
