Abstract
Analysing the various misconceptions held by students with regard to the mathematical set concept, the authors hypothesized that these misunderstandings may be explained by the initial ‘collection’ model. Even after learning the formal properties of a set in the mathematical sense, the students are still influenced in their reactions by the collection representation, which acts ‘from behind the scenes’ as a tacit model. If the mathematical concept is not continually reinforced through systematic use, it is the initial figural interpretation which will replace, as an effect of time, the formal one. The findings confirmed this hypothesis.
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REFERENCES
Bell, A., Grimison, L., Greer, B. and Mangan, C.: 1987, Multiplicative word problems. A classification scheme and its validation (internal report), Nottingham: Shen Centre for Mathematical Education, University of Nottingham, and Belfast: Department of Psychology, Queens University.
English, L. D. (ed.): 1997, Mathematical reasoning: Analogies, metaphors and images, Mahwah, NJ, Erlbaum.
Fischbein, E., Deri, M., Nello, M. S. and Marino, M. S.: 1985, 'The role of implicit models in solving verbal problems in multiplication and division', Journal for Research in Mathematics Education 16 (1), 3–17.
Harel, G., Post, T. H. and Behr, M.: 1988, 'On the textual and the semantic structure of mapping rule and multiplication compare problems', Proceedings of the 12th International Conference, Psychology of Mathematics Education, Vol. 11, Vezprem, Hungary, pp. 372–379.
Lakoff, G. and Núñez, R. E.: 1997, 'The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics', in L.D. English (ed.), Mathematical reasoning: Analogies, metaphors and images, Mahwah, NJ, Erlbaum.
Linchevski, L. and Vinner, Sh.: 1988, 'The naive concept of sets in elementary teachers', Proceedings of the 12th International Conference, Psychology of Mathematics Education, Vol. 11, Vezprem, Hungary, pp. 471–478.
Mangan, C. (1986), Choice of operation in multiplication and division word problems, Unpublished doctoral dissertation, Belfast, Queens University.
Tirosh, D., Graeber, A. D. and Glover, R. M.: 1986, 'Preservice teachers' choice of operation for multiplication and division word problems', Proceedings of the 10th International Conference, Psychology of Mathematics Education. London, England.
Verschaffel, L., De Corte, E. and Van Coillie: 1988, 'Specifying the multiplier effect on children's solutions of simple multiplication word problems', Proceedings of the 12th International Conference, Psychology of Mathematics Education, Vol. 11, Vezprem, Hungary, pp. 617–624.
Wilder, L.R.: 1965, Introduction to the foundations of mathematics, New York, John Wiley & Sons.
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Fischbein, E., Baltsan, M. The Mathematical Concept of set and the 'Collection' Model. Educational Studies in Mathematics 37, 1–22 (1998). https://doi.org/10.1023/A:1003421206945
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DOI: https://doi.org/10.1023/A:1003421206945