Exploratory Research on Student Understanding of ExponentialFunctions: Instruction Using Multiple-Representational Systems

本项目将对学生指数函数概念的发展进行研究。这些首席研究员选择了指数函数，这是一组特别丰富和有用的概念，因为它容易产生误解，并且在数学、科学和工程中有着广泛而重要的应用。通过临床访谈和教学实验，这些研究者将检查学生的概念，他们的非正式和正式知识之间的关系，他们的感叹词和概念在各种语境中的使用，以及这些概念在应用中的元认知策略的发展。该项目将探索多代表性（激光光盘）教学系统的设计和使用，探索使用其巨大的内存存储来跟踪学生解决问题的策略和学生对教学的控制。因此，这些研究者希望显著地促进我们对学生概念发展的理解，并为高中和大学学生的微积分预科课程创建指数函数的原型单元。

This project will conduct research on the development of students' conceptions of exponential functions. These Principal Investigators have selected exponential functions, a particularly rich and useful set of concepts, because of its propensity for misconceptions and its widespread and significant, applications in mathematics, the sciences and engineering. Through, the use of clinical interviews and the teaching experiment, these investigators will examine students' conceptions, the relationships between their informal and formal knowledge, their interjections and use of concepts across a variety of contexts and the development of metacognitive strategies in the application of these concepts. The project will explore the design and use of a multi-representatival (Laser Disc) instructional systems, to explore options for using its vast memory storage for tracking student problem-solving strategies and student control of instruction. Thus, these investigators hope to significantly advance our understanding of the development of student concepts and create a prototype unit in exponential functions for a precalculus course for high school and college students.