Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study

The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation of high-performing second semester calculus students ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a functions dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a functions domain. However, students appeared to have difficulty forming images of continuously changing rate and were unable to accurately represent and interpret increasing and