The notion of motion: covariational reasoning and the limit concept

Courtney Nagle, Tyler Tracy, Gregory Adams, Daniel Scutella

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.

Original languageEnglish (US)
Pages (from-to)573-586
Number of pages14
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number4
StatePublished - May 19 2017

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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