An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth Through Covariation. Issue 3 (2nd July 2016) - Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
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.