\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015c.00820}
\itemau{Jones, Steven R.}
\itemti{The frequencies of various interpretations of the definite integral in a general student population.}
\itemso{Oesterle, Susan (ed.) et al., 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. [s. l.]: International Group for the Psychology of Mathematics Education (ISBN 978-0-86491-360-9/set; 978-0-86491-363-0/v.3). 401-408 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{I50}
\itemut{definite integral; interpretations; area under a curve; values of an anti-derivative; Riemann sum}
\itemli{}
\end