Quantifying exponential growth: Three conceptual shifts in coordinating multiplicative and additive growth

Abstract 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 ) ≥ 1), and (3) from coordinated constant ratios to within-units coordination for corresponding intervals of time for ( x 2  −  x 1 )