The potential role of algebraic fluency on physics exam scores

Our recent study has documented that repeated mastery practice of basic algebra skills relevant for introductory physics may lead to improved exam scores for students who score well on an algebra pretest, but has no observed effect for students who score low on the algebra pretest. The results also indicate that, controlling for pretest score, the benefits of practice appear only for exam items that require algebraic operations beyond simple arithmetic. We propose that mastery practice increases algebraic fluency, measured by both algebraic accuracy and speed, and this lowers cognitive load for solving the mathematical aspects of the physics problems, which in turn improves physics exam performance. We further propose that this benefit only occurs for students with high prescores because only those students have reached a sufficient level of accuracy to also sufficiently increase in speed and thus attain a substantial level of fluency. To support this hypothesis, we have established in related studies that students become faster and more accurate with mastery practice, and that, controlling for accuracy, speed on algebra skills is positively correlated with exam scores. We describe our next step which is to employ a control-treatment design with algebra practice and measurements of speed to better determine whether the benefit of algebra practice on physics exam scores is replicated and, if so, whether improvements in algebra fluency help to explain the gains in exam performance.