@article {MATHEDUC.06440671,
    author       = {Jones, Steven R.},
    title        = {Areas, anti-derivatives, and adding up pieces: definite integrals in pure mathematics and applied science contexts.},
    year         = {2015},
    journal      = {The Journal of Mathematical Behavior},
    volume       = {38},
    issn         = {0732-3123},
    pages        = {9-28},
    publisher    = {Elsevier, New York, NY},
    doi          = {10.1016/j.jmathb.2015.01.001},
    abstract     = {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.},
    msc2010      = {I55xx (M55xx)},
    identifier   = {2015d.00785},
}