An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth Through Covariation

Ellis A. B., Ozgur Z., Kulow T., Dogan M. F., Amidon J.

MATHEMATICAL THINKING AND LEARNING, vol.18, no.3, pp.151-181, 2016 (SSCI, Scopus)

Abstract

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students' conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students' progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.