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Developing and making sense of quantitative models is a core practice ofphysics. Covariational reasoning -- considering how the changes in one quantityaffect changes in another, related quantity -- is an essential part of modelingquantitatively. Covariational reasoning has been studied widely in mathematicseducation research, but has only begun to be used in physics educationresearch. We present evidence from three studies of 25 individual interviewswith physics experts, in which the experts were asked to reason out loud whilegenerating graphical models. We analyze the studies through the lens ofcovariational reasoning frameworks from mathematics education research, anddetermine that the frameworks are useful but do not completely describe thecovariational reasoning of the physics experts we interviewed. From our data,we identified reasoning patterns that are not described in the mathematicseducation research that, together with the mathematics covariational reasoningframeworks, begin to characterize physics covariational reasoning.

Expert covariational reasoning resources in physics graphing tasks