@article {MATHEDUC.06476343,
author = {Ellis, Amy B. and \"Ozg\"ur, Zekiye and Kulow, Torrey and Williams, Caroline C. and Amidon, Joel},
title = {Quantifying exponential growth: three conceptual shifts in coordinating multiplicative and additive growth.},
year = {2015},
journal = {The Journal of Mathematical Behavior},
volume = {39},
issn = {0732-3123},
pages = {135-155},
publisher = {Elsevier, New York, NY},
doi = {10.1016/j.jmathb.2015.06.004},
abstract = {Summary: This article presents the results of a teaching experiment with middle school students who explored exponential growth by reasoning with the quantities height ($y$) and time ($x$) as they explored the growth of a plant. Three major conceptual shifts occurred during the course of the teaching experiment: (1) from repeated multiplication to initial coordination of multiplicative growth in $y$ with additive growth in $x$; (2) from coordinating growth in $y$ with growth in $x$ to coordinated constant ratios (determining the ratio of $f(x_{2})$ to $f(x_{1})$ for corresponding intervals of time for $(x_{2}-x_{1})\geq 1$), and (3) from coordinated constant ratios to within-units coordination for corresponding intervals of time for $(x_{2}-x_{1})<1$. Each of the three shifts is explored along with a discussion of the ways in which students' mathematical activity supported movement from one stage of understanding to the next. These findings suggest that emphasizing a coordination of multiplicative and additive growth for exponentiation may support students' abilities to flexibly move between the covariation and correspondence views of function.},
msc2010 = {I23xx (M63xx)},
identifier = {2015e.00740},
}