TY - JOUR

T1 - The notion of motion

T2 - covariational reasoning and the limit concept

AU - Nagle, Courtney

AU - Tracy, Tyler

AU - Adams, Gregory

AU - Scutella, Daniel

N1 - Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2017/5/19

Y1 - 2017/5/19

N2 - 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.

AB - 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.

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U2 - 10.1080/0020739X.2016.1262469

DO - 10.1080/0020739X.2016.1262469

M3 - Article

AN - SCOPUS:85003899061

SN - 0020-739X

VL - 48

SP - 573

EP - 586

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

IS - 4

ER -