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

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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.