  We have studied the impact of incoming preparation and demographic variables
on student performance on the final exam in physics 1, the standard
introductory, calculus-based mechanics course This was done at three different
institutions using multivariable regression analysis to determine the extent to
which exam scores can be predicted by a variety of variables that are available
to most faculty and departments. We have found that the results are
surprisingly consistent across the institutions, with the only two variables
that have predictive power being math SAT/ACT scores and concept inventory
pre-scores. The importance of both variables is comparable and fairly similar
across the institutions. They explain 20 - 30 percent of the variation in
students' performance on the final exam. Most notably, the demographic
variables (gender, under-represented minority, first generation to attend
college) are not significant. In all cases, although there appear to be gaps in
exam performance if one considers only the demographic variable, once these two
proxies of incoming preparation are included in the model, there is no longer a
demographic gap. There is only a preparation gap that applies equally across
the entire student population. This work shows that to properly understand
differences in student performance across a diverse population, and hence to
design more effective instruction, it is important to do statistical analyses
that take multiple variables into account. It also illustrates the importance
of having measures that are sensitive to both subject specific and more general
preparation. The results suggest that better matching of the course design and
teaching to the incoming student preparation will likely be the most effective
way to eliminate observed performance gaps across demographic groups while also
improving the success of all students.
