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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 gauge the compute a  gain in student competency competency,  \begin{equation}  \label{eq:gain}  \langle g\rangle = \sum_{i=1}^{N} \left( \frac{S_{\mathrm{post}} - S_{\mathrm{pre}}}{S_{\mathrm{max}}-S_{\mathrm{pre}}}\right)_i,  \end{equation}  where $S_{\mathrm{pre}}$, $S_{\mathrm{post}}$,  and to evaluate how changes in $S_{\mathrm{max}}$ are  the course improve pre-test score, post-test score, and maximum score for  student learning. $i$.  The current pre-test is short---3 questions---and assesses knowledge of basic mechanics, spherical coordinates, and vector algebra. In subsequent editions of the course, we shall add questions on statistics (e.g., error in the mean, standard deviation of a population, and propagation of errors) and basic astronomy (e.g., inverse square law for flux, diffraction limit, and doppler effect).