Student Understanding of Taylor Series Expansions in Statistical Mechanics

TL;DR

This paper investigates how students understand Taylor series expansions in statistical physics, revealing that while students recognize series, they often lack fluency with Taylor series despite prior exposure.

Contribution

It develops curriculum materials that guide students through deriving the Boltzmann factor using Taylor series of entropy and provides evidence on student understanding and misconceptions.

Findings

Students can recognize and interpret series expansions.

Many students lack fluency with Taylor series despite prior exposure.

Students' successes and failures vary across contexts.

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. 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.