PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Definite integrals versus indefinite integrals: How do students see them as the same or as different?
Page: 682
Much of the calculus education research on student understanding of integrals has been separated into definite-integral-focused studies and indefinite-integral-focused studies. This means that research may not be capturing how students might see these two types of integrals in relation to one another, as opposed to in isolation of each other. This study examines whether students see these two types of integrals as representing the same basic concept, distinct concepts, or as sharing some concepts while diverging in others. The results show that a large majority of students ascribe the exact same underlying conceptions to both types of integrals, even describing the indefinite integral as representing the area under a curve also. We relate what aspects of each type of conception students saw as common to both types of integrals, and what features of the conception the students saw as different between them.