
06440671
j
2015d.00785
Jones, Steven R.
Areas, antiderivatives, and adding up pieces: definite integrals in pure mathematics and applied science contexts.
J. Math. Behav. 38, 928 (2015).
2015
Elsevier, New York, NY
EN
I55
M55
calculus
definite integral
Riemann sum
area
antiderivative
physics and engineering
doi:10.1016/j.jmathb.2015.01.001
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 antiderivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sumbased ``adding up pieces" conception of the definite integral (renamed in this paper as the ``multiplicativelybased 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.