The relationship between mathematics preparation and conceptual learning gains in physics: A possible "hidden variable" in diagnostic pretest scores

There have been many investigations into the factors that underlie variations in individual student performance in college physics courses. Numerous studies report a positive correlation between students' mathematical skills and their exam grades in college physics. However, few studies have examined students' learning gain resulting from physics instruction, particularly with regard to qualitative, conceptual understanding. We report on the results of our investigation into some of the factors, including mathematical skill, that might be associated with variations in students' ability to achieve conceptual learning gains in a physics course that employs interactive-engagement methods. It was found that students' normalized learning gains are not significantly correlated with their pretest scores on a physics concept test. In contrast, in three of the four sample populations studied it was found that there is a significant correlation between normalized learning gain and students' preinstruction mathematics skill. In two of the samples, both males and females independently exhibited the correlation between learning gain and mathematics skill. These results suggest that students' initial level of physics concept knowledge might be largely unrelated to their ability to make learning gains in an interactive-engagement course; students' preinstruction algebra skills might be associated with their facility at acquiring physics conceptual knowledge in such a course; and between-class differences in normalized learning gain may reflect not only differences in instructional method, but student population differences ("hidden variables") as well.