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，这是本科数学课程的中心概念。该模型的出现将提供一个框架，两个研究工具的发展，以广泛评估学生的功能知识。该Precalculus概念评估工具（PCA）和微积分概念评估工具（CCA）将提供一个一致的方法来量化学生的概念发展的两个大招生本科课程。 通过访谈、个案研究和观察，对学生的问题解决行为进行调查，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。 这些研究的结果将形成一个框架的发展基础，并有助于广泛地定义和评估本科生对了解和学习数学的信念。 本研究将提供一种客观的方法来考察学生的函数理解和数学信念模式，并为微积分前课程和微积分课程模块的开发提供指导。 在该项目实施过程中，还将举办示范讲习班，以传播新开发的工具和教材。

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.