Examining the discourse on the limit concept in a beginninglevel calculus classroom
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Existing research on limits documents many difficulties students encounter when learning about the concept. There is also some research on teaching of limits but it is not yet as extensive as the research on student learning about limits. This study explores the discourse on limits in a beginninglevel undergraduate calculus classroom by focusing on one instructor’s and his students’ discourses through a communicational approach to cognition. The findings indicate that some of the limitrelated contexts in which students struggled coincided with those in which the instructor shifted his elements of discourse on limits. The instructor did not attend to the shifts in his discourse, making them implicit for the students. The study highlights that the discrepancies among participants’ discourses signal communicational breakages and suggests that future studies should examine whether teachers’ explicit attention to the elements of their discourse can enhance communication in the classrooms.
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 Bagni, G. T. (2005). The historical roots of the limit notion: Cognitive development and development of representation registers. Canadian Journal of Science, Mathematics, and Technology Education, 5(4), 453–468. CrossRef
 Bergsten, C. (2007). Investigating quality of undergraduate mathematics lectures. Mathematics Education Research Journal, 19(3), 48–72. CrossRef
 Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of firstyear students. International Journal of Mathematical Education in Science and Technology, 32(4), 487–500. CrossRef
 Cornu, B. (1991). Limits. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Dordrecht, The Netherlands: Kluwer Academic Publishers.
 Edwards, C. H. (1979). The historical development of the calculus. New York: Springer. CrossRef
 Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation: history as a method for learning metadiscursive rules in mathematics. Educational Studies in Mathematics, 80(3), 327–349. CrossRef
 Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.
 Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press. CrossRef
 Nardi, E. (2007). Amongst mathematicians: Teaching and learning mathematics at the university level. New York: Springer.
 Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5(2), 193–216. CrossRef
 Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. CrossRef
 Sfard, A. (1992). Operational origin of mathematical objects and the quandary of reification—the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59–84). Washington, DC: Mathematical Association of America.
 Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1/3), 13–57. CrossRef
 Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses and mathematizing. New York: Cambridge University Press. CrossRef
 Sfard, A., Forman, E., & Kieran, C. (2001). Guest editorial: Learning discourse: Sociocultural approaches to research in mathematics education. Educational Studies in Mathematics, 46(1/3), 1–12. CrossRef
 Sierpińska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18(4), 371–397. CrossRef
 Tall, D. (1980). Mathematical intuition, with special reference to limiting processes. In Proceedings of the fourth International Congress on Mathematics Education (Vol. 1, pp. 170–176). CA: Berkeley.
 Tall, D., & Schwarzenberger, R. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44–49.
 Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. CrossRef
 Williams, S. R. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22(3), 219–236. CrossRef
 Williams, S. R. (2001). Predications of the limit concept: An application of repertory grids. Journal for Research in Mathematics Education, 32(4), 343–367. CrossRef
 Title
 Examining the discourse on the limit concept in a beginninglevel calculus classroom
 Journal

Educational Studies in Mathematics
Volume 82, Issue 3 , pp 439453
 Cover Date
 20130301
 DOI
 10.1007/s1064901294382
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Limits
 Commognitive framework
 Teacher discourse
 Student discourse
 Industry Sectors
 Authors

 Beste Güçler ^{(1)}
 Author Affiliations

 1. Kaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth, 200 Mill Road, Suite 150B, Fairhaven, MA, 02719, USA