Examining the discourse on the limit concept in a beginning-level calculus classroom
- Beste Güçler
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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 beginning-level 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 limit-related 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.
- 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 first-year 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 meta-discursive 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
- Examining the discourse on the limit concept in a beginning-level calculus classroom
Educational Studies in Mathematics
Volume 82, Issue 3 , pp 439-453
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Commognitive framework
- Teacher discourse
- Student discourse
- 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