
06585954
j
2016d.00772
Jones, Steven R.
The prevalence of areaunderacurve and antiderivative conceptions over Riemann sumbased conceptions in students' explanations of definite integrals.
Int. J. Math. Educ. Sci. Technol. 46, No. 5, 721736 (2015).
2015
Taylor \& Francis, Abingdon, Oxfordshire
EN
I55
calculus
definite integral
Riemann sum
area
antiderivative
doi:10.1080/0020739X.2014.1001454
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 antiderivative, may be less productive in making sense of contextualized integrals. On the other hand, interpreting the integral using Riemann sumbased 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 openended questions regarding the underlying meaning of definite integrals. Data from the student responses show a high prevalence of area and antiderivative 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.