id: 06477064
dt: j
an: 2015e.00770
au: McGee, Daniel Lee; Moore-Russo, Deborah
ti: Impact of explicit presentation of slopes in three dimensions on
studentsâ€™ understanding of derivatives in multivariable calculus.
so: Int. J. Sci. Math. Educ. 13, Suppl. 2, 357-384 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: I65 C35
ut: differentiation; multivariable calculus; representations; semiotic
registers; slopes
ci:
li: doi:10.1007/s10763-014-9542-0
ab: Summary: In two dimensions (2D), representations associated with slopes are
seen in numerous forms before representations associated with
derivatives are presented. These include the slope between two points
and the constant slope of a linear function of a single variable. In
almost all multivariable calculus textbooks, however, the first
discussion of slopes in three dimensions (3D) is seen with the
introduction of partial derivatives. The nature of the discussions
indicates that authors seem to assume that students are able to
naturally extend the concept of a 2D slope to 3D and correspondingly it
is not necessary to explicitly present slopes in 3D. This article
presents results comparing students that do not explicitly discuss
slopes in 3D with students that explicitly discuss slopes in 3D as a
precursor to discussing derivatives in 3D. The results indicate that
students may, in fact, have significant difficulty extending the
concept of a 2D slope to a 3D slope. And that the explicit presentation
of slopes in 3D as a precursor to the presentation of derivatives in 3D
may significantly improve student comprehension of topics of
differentiation in multivariable calculus.
rv: