378
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

The notion of motion: covariational reasoning and the limit concept

, , &
Pages 573-586 | Received 11 Aug 2016, Published online: 12 Dec 2016

References

  • Cetin N. The performance of undergraduate students in the limit concept. Int J Math Educ Sci Technol. 2009;40:323–330.
  • Cornu B. Limits. In: Tall DO, editor. Advanced mathematical thinking. Dordrecht: Kluwer; 1991. p. 25–41.
  • Ferrini-Mundy J, Graham, K. Research in calculus learning: understanding of limits, derivatives, and integrals. In: Kaput J, Dubinsky E, editors. Research issues in undergraduate mathematics learning. Washington (DC): MAA; 1994. p. 31–45.
  • Pettersson K, Scheja M. Algorithmic contexts and learning potentiality: a case study of students’ understanding of calculus. Int J Math Educ Sci Technol. 2008;39(6):767–784.
  • Scheja M, Pettersson K. Transformation and contextualisation: conceptualising students’ conceptual understandings of threshold concepts in calculus. High Educ. 2010;59(2):221–241.
  • Larson R, Edwards B. Calculus: early transcendental functions. 6th ed. Boston (MA): Cengage Learning; 2015.
  • Cottrill J, Dubinsky E, Nichols, D, et al. Understanding the limit concept: beginning with a coordinated process scheme. J Math Behav. 1996;15:167–192.
  • Güçler B. Examining the discourse on the limit concept in a beginning-level calculus classroom. Educ Stud Math. 2013;82(3):439–453.
  • Güçler B. The role of symbols in mathematical communication: the case of the limit notation. Res Math Educ. 2014;16(3):251–268.
  • Davis RB, Vinner S. The notion of limit: some seemingly unavoidable misconception stages. J Math Behav. 1986;5:281–303.
  • Monaghan J. Problems with the language of limits. For Learning Math. 1996;11(3):20–24.
  • Oehrtman MC. Strong and weak metaphors for limits. In: Pateman N, Dougherty B, Zillioz J, editors. Proceedings of the 27th Annual Meeting of the International Group for the Psychology of Mathematics Education; 2003 Jul 13–18. Honolulu (HI): PME-NA; 2003. Available from: http://files.eric.ed.gov/fulltext/ED500857.pdf
  • Oehrtman MC. Collapsing dimensions, physical limitation, and other student metaphors for limit concepts. J Res Math Educ. 2009;40:396–426.
  • Williams SR. Models of limit held by college calculus students. J Res Math Educ. 1991;22:219–236.
  • Przenioslo M. Images of the limit of function formed in the course of mathematical studies at the university. Educ Stud Math. 2004;55:103–132.
  • Juter K. Limits of functions as they developed through time and as students learn them today. Math Think Learning. 2006;8(4):407–431.
  • Nagle C. Transitioning from introductory calculus to formal limit conceptions. For Learning Math. 2013;33(2):2–10.
  • Boester T. Testing conceptual frameworks of limit: a classroom-based case study. Paper presented at: Conference on Research in Undergraduate Mathematics Education. 13th Annual Meeting; 2010 February 25–28; Raleigh, NC.
  • Williams SR. Predictions of the limit concept: an application of repertory grids. J Res Math Educ. 2001;32:341–367.
  • Lakoff G, Núñez RE. Where mathematics comes from: how the embodied mind brings mathematics into being. New York (NY): Basic Books; 2001.
  • Swinyard C. Reinventing the formal definition of limit: the case of Amy & Mike. J Math Behav. 2011;30:93–114.
  • Swinyard C, Larsen S. Coming to understand the formal definition of limit: insights gained from engaging students in reinvention. J Res Math Educ. 2012;43(4):465–493.
  • Kidron I. Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks. Educ Stud Math. 2008;69(3):197–216.
  • Barbé J, Bosch M, Espinoza L, et al. Didactic restrictions on the teacher's practice: the case of limits of functions in Spanish high schools. Educ Stud Math. 2005;59:235–268.
  • Tall D. The transition to formal thinking in mathematics. Math Educ Res J. 2008;20(2):5–24.
  • Nagle C. Using predictions to introduce limits and continuity. MathAMATYC Educator. 2013;1(1):24–28.
  • Patel RM, McCombs P, Zollman A. Metaphor clusters: characterizing instructor metaphorical reasoning on limit concepts in college calculus. Sch Sci Math. 2014;114(5):236–245.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.