The danger of being overly attached to the concrete: the case of division by zero

Authors

  • Caroline Lajoie
  • Roberta Mura

DOI:

https://doi.org/10.7146/nomad.v6i1.146497

Abstract

In this article, we use the example of division by zero to illustrate how reliance on concrete representations of mathematical concepts can become an obstacle to understanding. We describe some difficulties encountered by prospective elementary teachers in dealing with division by zero and we show how these difficulties could be explained by the students' desire for a (non-existent) physical interpretation of the mathematical problem.

References

Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144. https://doi.org/10.2307/749140

Clements, D. H. & S. Mc Millen (1996). Rethinking "concrete" manipulatives. Teaching Children Mathematics, 2(5), 270-279. https://doi.org/10.5951/TCM.2.5.0270

Fischbein, E., M. Deri, M. Nello & M. Marino (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17. https://doi.org/10.2307/748969

Graeber, A. O., D. Tirosh & R. Glover (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102. https://doi.org/10.5951/jresematheduc.20.1.0095

Nantais, N., M. Francavilla & D. Biron (1994). Réflexion didactique sur le rôle et l'importance des représentations utilisées pour l'enseignement de la multiplication å l'intérieur des manuels scolaires du primaire.Instantanés mathématiques, 31(1), 12-17.

Pallascio, R. (1991). Puissance et limite des modèles : Deux exemples appliqués aux propriétés multiplicatives et à la notion de dimension ! Instantanés mathématiques, 27(3), 9-13.

Pimm, D. (1995). Symbols and Meanings in School Mathematics. New York: Routledge.

Simon, M. A. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254. https://doi.org/10.2307/749346

Wheeler, M. M. & I. Feghali (1983). Much ado about nothing: Preservice elementary teachers' concept of zero. Journal for Research in Mathematics Education, 14(3), 147-155. https://doi.org/10.2307/748378

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Published

1998-03-01

How to Cite

Lajoie, C., & Mura, R. (1998). The danger of being overly attached to the concrete: the case of division by zero. NOMAD Nordic Studies in Mathematics Education, 6(1), 7–21. https://doi.org/10.7146/nomad.v6i1.146497

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Section

Articles