id: 06439997
dt: j
an: 2015d.00740
au: Johnson, Heather L.
ti: Together yet separate: studentsâ€™ associating amounts of change in
quantities involved in rate of change.
so: Educ. Stud. Math. 89, No. 1, 89-110 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: I23 M53
ut: quantitative reasoning; rate of change; quantity; covariational reasoning;
Cartesian graphs
ci:
li: doi:10.1007/s10649-014-9590-y
ab: Summary: This paper extends work about quantitative reasoning related to
covarying quantities involved in rate of change. It reports a multiple
case study of three studentsâ€™ reasoning about quantities involved in
rate of change when working on tasks incorporating multiple
representations of covarying quantities. When interpreting
relationships between associated amounts, students identified sections
(e.g., an interval on a graph) in which they could make comparisons
between amounts of change in quantities. Although such reasoning is
useful for interpreting a Cartesian graph as a representation of
covarying quantities, it does not foster attention to variation in the
intensity of change in covarying quantities (e.g., a decreasing
increase). Focusing on the kinds of relationships students make between
amounts of change in covarying quantities might provide further insight
into how students could develop a robust understanding of rate of
change.
rv: