id: 06440671
dt: j
an: 2015d.00785
au: Jones, Steven R.
ti: Areas, anti-derivatives, and adding up pieces: definite integrals in pure
mathematics and applied science contexts.
so: J. Math. Behav. 38, 9-28 (2015).
py: 2015
pu: Elsevier, New York, NY
la: EN
cc: I55 M55
ut: calculus; definite integral; Riemann sum; area; anti-derivative; physics
and engineering
ci:
li: doi:10.1016/j.jmathb.2015.01.001
ab: Summary: Research in mathematics and science education reveals a disconnect
for students as they attempt to apply their mathematical knowledge to
science and engineering. With this conclusion in mind, this paper
investigates a particular calculus topic that is used frequently in
science and engineering: the definite integral. The results of this
study demonstrate that certain conceptualizations of the definite
integral, including the area under a curve and the values of an
anti-derivative, are limited in their ability to help students make
sense of contextualized integrals. In contrast, the Riemann sum-based
“adding up pieces" conception of the definite integral (renamed in
this paper as the “multiplicatively-based summation" conception) is
helpful and useful in making sense of a variety of applied integral
expressions and equations. Implications for curriculum and instruction
are discussed.
rv: