Quantities and covariation: an inquiry into the reasoning of experts engaged in graphically representing dynamic situations

Past researchers have illustrated students and teachers difficulties reasoning covariationally and have also claimed certain ways of thinking that are propitious for such reasoning abilities. In this thesis, I investigate two experts reasoning when tasked with drawing graphs that relate two varying quantities. By comparing each experts activities I argue that constructing and coordinating amounts of change and accumulations thereof afforded these experts the ability to interpret and graphically represent a dynamic situation covariationally. I present evidence that in some (but not all) cases these experts engaged in these ways of reasoning. I end by describing other strategies used by the experts while attempting to reason covariationally that I hypothesize may present barriers for one to successfully engage in such reasoning.