id: 06079393
dt: j
an: 2012e.00693
au: Johnson, Heather L.
ti: Reasoning about variation in the intensity of change in covarying
quantities involved in rate of change.
so: J. Math. Behav. 31, No. 3, 313-330 (2012).
py: 2012
pu: Elsevier, New York, NY
la: EN
cc: I44 C34 E44
ut: calculus; quantitative reasoning; rate of change; covariational reasoning;
transformational reasoning; secondary school mathematics; secondary
school students; cognitive processes; mathematical concepts;
interviews; educational research
ci:
li: doi:10.1016/j.jmathb.2012.01.001
ab: 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 ratio-based. I discuss how
coordinating covariational and transformational reasoning supports
attending to variation in the intensity of change in quantities
involved in rate of change.
rv: