id: 06581481
dt: j
an: 2016c.00862
au: McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael
ti: Making implicit multivariable calculus representations explicit: a clinical
study.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 25, No. 6, 529-541
(2015).
py: 2015
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: I65 I45 I55
ut: multivariable calculus; representations; derivatives; integrals; slope;
three dimensions
ci:
li: doi:10.1080/10511970.2015.1038858
ab: Summary: Reviewing numerous textbooks, we found that in both differential
and integral calculus textbooks the authors commonly assume that: (i)
students can generalize associations between representations in two
dimensions to associations between representations of the same
mathematical concept in three dimensions on their own; and (ii)
explicit discussions of these representations are not necessary. For
example, in the presentation of partial derivatives, textbook
presentations assume that students will understand the slope in a
specified direction in $\mathbb{R}^3$ without it ever being explicitly
presented. Our preliminary interviews indicated that such assumptions
may be erroneous, so we created and tested materials that explicitly
use representations commonly omitted in textbook presentations of the
differential and integral calculus of functions of two and three
variables. This paper discusses the classroom activities that were
created to include these missing representations, as well as the
results when they were implemented in classroom instruction.
rv: