id: 06261886
dt: j
an: 2014b.00707
au: Sealey, Vicki
ti: A framework for characterizing student understanding of Riemann sums and
definite integrals.
so: J. Math. Behav. 33, 230-245 (2014).
py: 2014
pu: Elsevier, New York, NY
la: EN
cc: I55 C35 M55 D55
ut: calculus; definite integral; Riemann sum; student learning; structuralism
ci:
li: doi:10.1016/j.jmathb.2013.12.002
ab: Summary: It has been shown in the literature that students can often
evaluate definite integrals by applying the fundamental theorem of
calculus or by interpreting an integral as an area under a curve.
However, students struggle to solve word problems involving definite
integrals, even when the context is quite familiar to the students.
This research examines the obstacles calculus students encounter and
the ways in which they overcome those obstacles when solving definite
integral problems without relating to area under a curve. A framework
for characterizing student understanding of Riemann sums and definite
integrals is presented and discussed. Results indicate that
conceptualizing the product of $f(x)$ and $Δx$ proves to be the most
complex part of the problem-solving process, despite the simplicity of
the mathematical operations required in this step.
rv: