@inbook {MATHEDUC.06434205,
author = {Jones, Steven R.},
title = {The frequencies of various interpretations of the definite integral in a general student population.},
year = {2014},
booktitle = {Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education ``Mathematics education at the edge", PME 38 held jointly with the 36th conference of PME-NA, Vancouver, Canada, July 15--20, 2014, Vol. 3},
isbn = {978-0-86491-360-9},
pages = {401-408},
publisher = {[s. l.]: International Group for the Psychology of Mathematics Education},
abstract = {Summary: Student understanding of integration has become a topic of recent interest in calculus research. Studies have shown that certain interpretations of the definite integral, such as the area under a curve or the values of an anti-derivative, are less productive in making sense of contextualized integrals, while on the other hand understanding the integral as a Riemann sum or as ``adding up pieces" is highly productive for contextualized integrals. This report investigates the frequency of these three conceptualizations in a general calculus student population. Data from student responses show a high prevalence of area and anti-derivative ideas and a very low occurrence of summation ideas. This distribution held even for students whose calculus instructors focused on Riemann sums while introducing the definite integral.},
msc2010 = {I50xx},
identifier = {2015c.00820},
}