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Response time on math skills and its association with math skills accuracy and physics course grades
Accuracy on assessments is commonly studied in education research but response time (RT) is relatively less investigated even though decades of research in cognitive sciences indicate that time can be an important dimension for understanding student learning. To better understand RT and the potentially important relations between accuracy and RT in physics education, we conducted an exploratory investigation by collecting and analyzing both accuracy and RT data on physics-relevant math skills on low-stakes pre and posttests as well as course exam scores in algebra-based and calculus-based introductory physics courses over two semesters for a total of participants. Overall, we found a high level of variation in response times revealing weak but consistent patterns of associations between RT and accuracy on skills and exam scores. First, we found a nonlinear relationship between RT and accuracy on the pretest and on the post-test, which may indicate a variety of strategies and engagement among students on these participation-credit-only tests. Second, the results indicate that while RT alone does not predict course grade, when controlling for accuracy on pre or posttest math skills, students with lower RT on these skills are more likely to get better grades. Therefore, both pre or posttest accuracy and speed predicted course grades, though accuracy explained a substantial amount of variance ( ) while pretest RT explained a much smaller amount of variance ( ). Third, controlling for both pretest accuracy and pretest RT, we found that students who sped up from pre to posttest were likely to get higher exam scores; however, students who slowed down were on average likely to have a higher post-test score. Fourth, since systemic inequities in STEM education have been documented via measured mean differences between some demographic groups for exam scores and accuracy on math skills, we compared RTs by sex, race, first-generation status, and citizenship to potentially gain more insight into these inequities. We found no consistent or conclusive evidence of demographic differences, though in multiple comparisons, Black, Hispanic, Native American, and Pacific Islander students had larger RTs on average, and in one comparison they were slightly faster. We found that RT was not a mediator of demographic differences in physics grades, though, as expected, accuracy on math skills was a mediator. We briefly discuss how our results relate to various cognitive models such as cognitive ability, speed-accuracy trade-offs, fluency and cognitive load, dual-process theories, and student psychological factors like self-efficacy, anxiety, and motivation. We argue that, based on which (if any) of the above mechanisms are at play, valuing speed in physics may have benefits, such as improving fluency to reduce cognitive load and drawbacks, such as unintentionally using speed as a proxy for achievement or inducing excessive stress that may interfere with performance and student well-being.
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