Emerging covariational reasoning student resources in physics lab courses

Abstract

Students and experts engage in a plethora of sophisticated ways of thinking during modeling tasks, blending between mathematical and physical reasoning. This integrated way of reasoning about quantities and how they are related is ubiquitous to “thinking like a physicist.” One facet of this process is covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity. In laboratory courses that engage students in experimental design, students commonly use covariational reasoning as they model changing quantities and the relationships between them. However, those without strong mathematical reasoning skills may unintentionally be perceived as also having less nuanced physics reasoning skills. To investigate the multifaceted ways students model in physics lab courses, we examined student discussions during remote, student-designed labs in which students interact with physical, but fictitious, matter in a virtual reality (VR) simulation. The VR environment allows for students to observe and measure novel situations for which the “answer,” in this case a mathematical model about the particles’ behavior, is not known. Using a conceptual blend analysis, we examine two lab groups that take different approaches to the task, despite beginning with the same observations and reporting on the same final model. One group demonstrates expert-like mathematical reasoning that is typically rewarded in physics courses, while the other engages in early signs of expert-like physics reasoning. Our analysis suggests that there are productive ideas emerging in both groups, and that of the less mathematically rigorous may be going unnoticed. We suggest that characterizing these features of physics covariational reasoning may provide an opportunity to move beyond data analysis techniques in lab courses towards incorporating more physics expert-like techniques. In doing so, instructors may recognize hidden strengths that may otherwise go undetected.