Exponential functions are important topic in school algebra and in higher mathematics, but research on students’ thinking suggests that understanding exponential growth remains an instructional challenge. This paper reports the results of a small-scale teaching experiment with students who explored exponential functions in the context of two continuously covarying quantities, height and time. We present two major conceptual paths that occurred in the development of an understanding of exponential growth, the covariation view and the correspondence view, and discuss the influence of each perspective on the growth of students’ understanding.
Ellis, A.B., Ozgur, Z., Kulow, T., Dogan, M.F., Williams, C.C., & Amidon, J. (2013, November). Correspondence and covariation: Quantities changing together. In M.V. Martinez & A.C. Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 119-126). Chicago, IL: University of Illinois at Chicago.