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EPISTEMOLOGICAL OBSTACLES IN COMING TO UNDERSTAND THE LIMIT OF A FUNCTION AT UNDERGRADUATE LEVEL: A CASE FROM THE NATIONAL UNIVERSITY OF LESOTHO

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An Erratum to this article was published on 17 June 2009

Abstract

This article reports on part of a doctoral study in which epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit of functions in different modes of representation were investigated. A group of mathematics students at undergraduate level at the National University of Lesotho was the sample for the study. Empirical data were collected using questionnaires and interviews.

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References

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Cornu, B. (1991). Limits. In D.O. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Cottrill, J., Dubinsky, E., Nichols, D., Schwingendorf, K., Thomas, K. & Vidakovic, D. (1996). Understanding the limit concept: beginning with a coordinated process schema. Journal of Mathematical Behavior, 15, 167–192.

    Article  Google Scholar 

  • Davis, R.B. & Vinner, S. (1986). The notion of limit: some seemingly unavoidable misconception stages. Journal of Mathematical Behavior, 5, 281–303.

    Google Scholar 

  • Dubinsky, E. & Harel, G. (1992). The nature of the process conception of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: aspects of epistemology and pedagogy, MAA Notes (pp. 85–106). Washington, DC: MAA.

    Google Scholar 

  • Ferrini-Mundy, J. & Gaudard, M. (1992). Secondary school calculus: preparation or pitfall in the study of college calculus. Journal for Research in Mathematics Education, 1(23), 56–71.

    Article  Google Scholar 

  • Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38, 11–50.

    Article  Google Scholar 

  • Fischbein, E. (2001). Tacit models of infinity. Educational Studies in Mathematics, 48, 309–329.

    Article  Google Scholar 

  • Fischbein, E., Tirosh, D. & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement? Educational Studies in Mathematics, 12, 491–512.

    Article  Google Scholar 

  • Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 60–86). Reston, V: Lawrence Erlbaum for NCTM.

    Google Scholar 

  • Kannemeyer, L. D. (2003). The development of a reference framework for measuring students’ understanding in a first year calculus course. Unpublished doctoral thesis. Cape Town: University of the Western Cape.

  • Monaghan, J. (1991). Problems with language of limits. For the Learning of Mathematics, 11(3), 20–24.

    Google Scholar 

  • Moru, E.K. (2006). Epistemological obstacles in coming to understand the limit concept at undergraduate level: a case of the National University of Lesotho. Unpublished doctoral thesis. Cape Town: University of the Western Cape.

  • Moru, E.K. (2007). Talking with the literature on epistemological obstacles. For the Learning of Mathematics, 27(3), 34–37.

    Google Scholar 

  • Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371–397.

    Article  Google Scholar 

  • Taback, S. (1975). The child’s concept of limit. In M.F. Rosskopf (Ed.), Children’s mathematical concepts (pp. 111–144). New York: Teachers College Press.

    Google Scholar 

  • Tall, D.O. (1991). Reflections. In D.O. Tall (Ed.), Advanced mathematical thinking (pp. 251–259). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Tall, D.O. (1996). Functions and Calculus. In A.J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 289–311). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Tall, D.O. & Schwarzenberger, R.L.E. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44–49.

    Google Scholar 

  • Tall, D.O., Thomas, M., Davis, G., Gray, E. & Simpson, E. (2000). What is the object of encapsulation of a process. Journal of Mathematical Behavior, 18(2), 223–241.

    Article  Google Scholar 

  • Tirosh, D. & Stavy, R. (1996). Intuitive rules in science and mathematics: the case of ‘everything can be divided by two’. International Journal of Science Education, 18(6), 669–683.

    Article  Google Scholar 

  • Williams, S.R. (1991). Models of limit held by college calculus students. Journal for research in Mathematics Education, 22(3), 219–236.

    Article  Google Scholar 

  • Winsløw, C. (2000). Semiotics as an analytic tool for the didactics of mathematics. Retrieved November 13, 2004 from: http://wwww.naturdidak.ku.dk/winslow/NOMADICME10.pdf.

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Correspondence to Eunice Kolitsoe Moru.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10763-009-9168-9.

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Moru, E.K. EPISTEMOLOGICAL OBSTACLES IN COMING TO UNDERSTAND THE LIMIT OF A FUNCTION AT UNDERGRADUATE LEVEL: A CASE FROM THE NATIONAL UNIVERSITY OF LESOTHO. Int J of Sci and Math Educ 7, 431–454 (2009). https://doi.org/10.1007/s10763-008-9143-x

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  • DOI: https://doi.org/10.1007/s10763-008-9143-x

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