id: 06356584
dt: j
an: 2014f.00754
au: Weber, Eric; Thompson, Patrick W.
ti: Studentsâ€™ images of two-variable functions and their graphs.
so: Educ. Stud. Math. 87, No. 1, 67-85 (2014).
py: 2014
pu: Springer Netherlands, Dordrecht
la: EN
cc: I60
ut: two-variable functions; three dimensions; calculus; quantitative reasoning;
covariational reasoning; conceptualization
ci:
li: doi:10.1007/s10649-014-9548-0
ab: Summary: This paper presents a conceptual analysis for studentsâ€™ images
of graphs and their extension to graphs of two-variable functions. We
use the conceptual analysis, based on quantitative and covariational
reasoning, to construct a hypothetical learning trajectory (HLT) for
how students might generalize their understanding of graphs of
one-variable functions to graphs of two-variable functions. To evaluate
the viability of this learning trajectory, we use data from two
teaching experiments based on tasks intended to support development of
the schemes in the HLT. We focus on the schemes that two students
developed in these teaching experiments and discuss their relationship
to the original HLT. We close by considering the role of covariational
reasoning in generalization, consider other ways in which students
might come to conceptualize graphs of two-variable functions, and
discuss implications for instruction.
rv: