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The Role of Quantitative Reasoning in Solving Applied Precalculus Problems


In response to the continued difficulty of students constructing and modeling function relationships, we conducted an investigation of undergraduate precalculus students' developing quantitative and covariational reasoning abilities. Specifically, this investigation focused on a detailed examination of possible factors that contribute to or hinder the ability of a student to reason about quantities in a dynamic situation. It was the intention of this investigation to gain insights about the quantities that students do construct and the influence of these conceptions on reasoning about functions and covariational situations. This involved an attempt to identify various mental actions in the process of identifying quantities and the relation of these mental actions to a student's ability to conceive of functional relationships and reason covariationally with regards to these relationships.