A case study of a secondary mathematics teacher's understanding of exponential function: An emerging theoretical framework

This dissertation study describes a case study investigating a secondary mathematics teacher's ways of thinking as he worked through a collection of activities related to the concept of exponential function. The research instruments were designed to explore his ability to reason multiplicatively in the context of exponential behavior. Although previous research studies have examined students' multiplicative reasoning abilities, there have been no reported findings on secondary teachers' thinking about exponential behavior from a multiplicative perspective. Furthermore, the current body of research is devoid of a framework for knowing and learning exponential function. The study addresses this research gap by providing an account of one teacher's thinking through the lens of a developed exponential function framework.; Answers to the following research questions were sought: (a) What conceptions does a secondary mathematic teacher hold about exponential growth and decay?; (b) How effective are the current attributes of the developed exponential function framework in explaining the ways of thinking about exponential function?; and, (c) How does an instructional unit---focused on the concept of exponential function with an emphasis on multiplicative reasoning---facilitate the development of an understanding of exponential function? These research questions were approached using a cognitive constructivist perspective through teaching experiment methodology and semi-structured interview techniques.; Analysis of the data yielded varying ability levels for quantitatively representing and qualitatively describing exponential behavior. The ability to reason through exponential situations requires a mature understanding of constant percent.