
06476343
j
2015e.00740
Ellis, Amy B.
\"Ozg\"ur, Zekiye
Kulow, Torrey
Williams, Caroline C.
Amidon, Joel
Quantifying exponential growth: three conceptual shifts in coordinating multiplicative and additive growth.
J. Math. Behav. 39, 135155 (2015).
2015
Elsevier, New York, NY
EN
I23
M63
algebra
exponential growth
functions
reasoning
doi:10.1016/j.jmathb.2015.06.004
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 withinunits 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.