CAREER: A Model for Describing Students

本研究将扩展现有的理论，描述学生如何获得对函数概念的理解，函数概念是本科数学课程的核心概念。所产生的模型将为两种研究工具的发展提供框架，以广泛评估学生的功能知识。微积分概念评估工具（PCA）和微积分概念评估工具（CCA）将为两个大规模招生的本科课程提供量化学生概念发展的一致手段。通过访谈、案例研究和观察，对学生解决问题的行为进行调查，将试图找出促进和阻碍学生数学成功和继续数学学习的主要信念和行为。这些研究的结果将构成一个框架和工具的基础，以广泛地定义和评估本科生的认识和学习数学的信念。这些新兴的工具将提供客观的手段来检查学生对函数的理解和数学信念的模式。由此产生的调查将为指导微积分前期和微积分水平课程模块的发展提供见解。在这个项目的过程中，还将提供示范讲习班，以传播新开发的仪器和课程材料。

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.