History   Help on query formulation   Quantifying exponential growth: three conceptual shifts in coordinating multiplicative and additive growth. (English)
J. Math. Behav. 39, 135-155 (2015).
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.
Classification: I23 M63