Believing in Infinity: Exploring Students’ Conceptions of Improper Integrals

Abstract

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of improper integrals that are compatible with the conventions of the discipline, and they are forced to wrestle with their underlying beliefs about infinity, limits, and areas of unbounded regions.

KEYWORDS:

• Improper integrals
• infinity
• calculus
• student conceptions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The three texts refer to these differently: Stewart uses “Type 1” and “Type 2,” Thomas uses “Type I” and “Type II,” and Larson refers to these as “Improper Integrals with Infinite Limits of Integration” and “Improper Integrals with Infinite Discontinuities.”

Additional information

Notes on contributors

Holly Zolt

Holly Zolt is a Mathematics Education PhD student at Texas State University. Her main interests involve learning about how students think and engage with mathematical topics, especially in abstract algebra. In her free time, she enjoys spending time with her friends, reading, and watching movies.

Elizabeth Wrightsman

Elizabeth Wrightsman is attending Texas State University earning her PhD in mathematics education. Her primary research interest involves a better understanding of teaching practices that result in equitable student outcomes in mathematics. Elizabeth also volunteers with MathHappens Foundation, a non-profit organization that aims to make math accessible for all. In her free time, she lifts weights, attempts to finish jigsaw puzzles, and enjoys spending time with friends and family.

Lucinda Ford

Lucinda Ford is a Mathematics Education PhD student at Texas State University with a focus on student thinking in undergraduate developmental mathematics courses. In her free time, she loves to spend time by the water.

Cody L. Patterson

Cody L. Patterson is an Assistant Professor of Mathematics at Texas State University. His research investigates students’ and teachers’ mathematical meanings for concepts and procedures in secondary and postsecondary mathematics, such as solving equations and graphing quantitative relationships. In his free time, he enjoys spending time with his bulldogs Rosie and Truman.