CAREER: A Model for Describing Students

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This research will extend current theories describing how students'acquire an understanding of the function concept, the central concept ofthe undergraduate mathematics curriculum. The model that emerges willprovide a framework for the development of two research instruments tobroadly assess students' function knowledge. The Precalculus ConceptAssessment Instrument (PCA) and the Calculus Concept Assessment Instrument(CCA) will provide a consistent means of quantifying students' conceptdevelopment for two large-enrollment undergraduate courses. Investigations of students' problem solving behavior, usinginterviews, case studies and observations will attempt to identify majorbeliefs and behaviors that both promote and present obstacles to students'mathematical success and continued mathematical study. The results ofthese studies will form the basis for the development of a framework andinstrument to broadly define and assess undergraduate students' beliefsabout knowing and learning mathematics. The emergent instruments will provide objective means for examiningpatterns in students' function understandings and mathematical beliefs.The resultant investigations will provide insights for guiding thedevelopment of precalclulus and calculus level curriculum modules. Duringthe course of this project model workshops will also be offered todisseminate the newly developed instruments and curricular materials.