id: 06468447
dt: j
an: 2015e.00580
au: Johnson, Heather Lynn
ti: Secondary students’ quantification of ratio and rate: a framework for
reasoning about change in covarying quantities.
so: Math. Think. Learn. 17, No. 1, 64-90 (2015).
py: 2015
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: F83
ut: quantitative reasoning; covariational reasoning; quantifiaction of ratio;
quantification of rate
ci: ME 2003f.05237
li: doi:10.1080/10986065.2015.981946
ab: Summary: Contributing to a growing body of research addressing secondary
students’ quantitative and covariational reasoning, the multiple case
study reported in this article investigated secondary students’
quantification of ratio and rate. This article reports results from a
study investigating students’ quantification of rate and ratio as
relationships between quantities and presents the Change in Covarying
Quantities Framework, which builds from {\it M. P. Carlson} et al.’s
Covariation Framework [J. Res. Math. Educ. 33, No. 5, 352‒378 (2002;
ME 2003f.05237)]. Each of the students in this study was consistent in
terms of the quantitative operation he or she used (comparison or
coordination) when quantifying both ratio and rate. Illustrating how
students can engage in different quantitative operations when
quantifying rate, the Change in Covarying Quantities Framework helps to
explain why students classified as operating at a particular level of
covariational reasoning appear to be using different mental actions.
Implications of this research include recommendations for designing
instructional tasks to foster students’ quantitative and
covariational reasoning.
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