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\subsection{Evaluation of gains in competency}  We measure student gains \citep[see, e.g.,][]{hake1998interactive} by incorporating a pre-test and post-test into the course. We will ask questions from the pre-test again, either on in-class quizzes or on the final exam. This allows us to compute a mean  gain in student competency, \begin{equation}  \label{eqn:gain}  \langle g\rangle = \sum_{i=1}^{N} \left( \frac{S_{\mathrm{post}} - S_{\mathrm{pre}}}{S_{\mathrm{max}}-S_{\mathrm{pre}}}\right)_i,