Quantities and covariation: an inquiry into the reasoning of experts engaged in graphically representing dynamic situations
Hobson, Natalie Laura Fleischmann
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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.