id: 06170980
dt: j
an: 2013c.00683
au: Jones, Steven R.
ti: Understanding the integral: studentsâ€™ symbolic forms.
so: J. Math. Behav. 32, No. 2, 122-141 (2013).
py: 2013
pu: Elsevier, New York, NY
la: EN
cc: I55 C35
ut: calculus; integral; understanding; mathematical concepts; cognitive
processes; problem solving; concept formation
ci:
li: doi:10.1016/j.jmathb.2012.12.004
ab: Summary: Researchers are currently investigating how calculus students
understand the basic concepts of first-year calculus, including the
integral. However, much is still unknown regarding the cognitive
resources (i.e., stable cognitive units that can be accessed by an
individual) that students hold and draw on when thinking about the
integral. This paper presents cognitive resources of the integral that
a sample of experienced calculus students drew on while working on pure
mathematics and applied physics problems. This research provides
evidence that students hold a variety of productive cognitive resources
that can be employed in problem solving, though some of the resources
prove more productive than others, depending on the context. In
particular, conceptualizations of the integral as an addition over many
pieces seem especially useful in multivariate and physics contexts.
rv: