id: 06585954
dt: j
an: 2016d.00772
au: Jones, Steven R.
ti: The prevalence of area-under-a-curve and anti-derivative conceptions over
Riemann sum-based conceptions in studentsâ€™ explanations of definite
integrals.
so: Int. J. Math. Educ. Sci. Technol. 46, No. 5, 721-736 (2015).
py: 2015
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: I55
ut: calculus; definite integral; Riemann sum; area; anti-derivative
ci:
li: doi:10.1080/0020739X.2014.1001454
ab: Summary: This study aims to broadly examine how commonly various
conceptualizations of the definite integral are drawn on by students as
they attempt to explain the meaning of integral expressions. Previous
studies have shown that certain conceptualizations, such as the area
under a curve or the values of an anti-derivative, may be less
productive in making sense of contextualized integrals. On the other
hand, interpreting the integral using Riemann sum-based conceptions
proves much more productive for understanding contextualized integrals.
This study investigates how frequently students from a US calculus
population drew on these three conceptualizations (as well as others)
to interpret the meaning of definite integrals. The results were
achieved by asking a large sample of students from two US colleges
($n=150$) four open-ended questions regarding the underlying meaning of
definite integrals. Data from the student responses show a high
prevalence of area and anti-derivative ideas and a relatively low
occurrence of multiplicatively based summation ideas for interpreting
these integrals. Possible reasons for and implications of the results
are discussed.
rv: