
06079393
j
2012e.00693
Johnson, Heather L.
Reasoning about variation in the intensity of change in covarying quantities involved in rate of change.
J. Math. Behav. 31, No. 3, 313330 (2012).
2012
Elsevier, New York, NY
EN
I44
C34
E44
calculus
quantitative reasoning
rate of change
covariational reasoning
transformational reasoning
secondary school mathematics
secondary school students
cognitive processes
mathematical concepts
interviews
educational research
doi:10.1016/j.jmathb.2012.01.001
Summary: This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratiobased. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change.