Investigating Student Mental Models at the Intersection of Mathematics and Physical Reasoning in Physics

A significant challenge in learning science and mathematics is coordinating different types of mental models, such as mathematical and physical mental models, that represent different aspects of a given phenomenon. This challenge is illustrated in the present study, in which we observed a small number of college students reasoning about forces as both physical and mathematical quantities as they reasoned about a physical system. Using video analysis of the students’ gesture and as they reasoned qualitatively and mathematically about the system, we documented the construction and coordination of participants’ mental models. We found that participants constructed mathematical mental models as imagined lines uniquely to physical mental models as imagined pulls. Moreover, students rarely exhibited the coordination of these two mental models. These findings suggest that instructors that they cannot assume that students generate models, even circumstances designed to support them