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

Marilyn Carlson, Sally Jacobs, Edward Coe, Sean Larsen, Eric Hsu 

November 2002, Volume 33, Issue 5, Page 352

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 2nd-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 function’s 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 function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest  that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.

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