
06170980
j
2013c.00683
Jones, Steven R.
Understanding the integral: students' symbolic forms.
J. Math. Behav. 32, No. 2, 122141 (2013).
2013
Elsevier, New York, NY
EN
I55
C35
calculus
integral
understanding
mathematical concepts
cognitive processes
problem solving
concept formation
doi:10.1016/j.jmathb.2012.12.004
Summary: Researchers are currently investigating how calculus students understand the basic concepts of firstyear 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.