The relation between mathematical object/mathematical name: Conceptual changes between designation, description, denomination and definition

Giorgio Bolondi 1, Federica Ferretti 1 * , Alessandro Gambini 2
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1 Department of Mathematics, Alma Mater Studiorum University of Bologna, Bologna, Italy
2 Department of Mathematics, University of Ferrara. Ferrara, Italy
* Corresponding Author
EUR J SCI MATH ED, Volume 2, Issue 2A, pp. 169-176.
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The actions of designation, description, denotation, denomination and definition are crucial in the didactic activity in the classroom (D'Amore and Fandiño Pinilla, 2012) since they embody different interplays between objects, representations, properties, names (in the sense of Duval (2008)). Switching from one action to the other may be the result of a conceptual change (diSessa, 2006). We present the result of a teaching experiment in classes of grades from 2 to 4 where the relation object/name is investigated in the case of the circle. The experiment makes use of a particular artefact, the Lénárt Spheres (Lénárt, 1996). Comparative geometry activities allow to deal with geometrical objects in a learning environment where the relations between objects, representations and properties are different from the usual ones, hence implying a restructuration of the interplays between them. As a result of the teaching experiment, as can be seen, in particular, from the comparison of initial and conclusive questionnaires, children started a change of their way of associating a name to an object. We argue that this is due also to a conceptual change and not only to “learning what was taught”.


Bolondi, G., Ferretti, F., & Gambini, A. (2014). The relation between mathematical object/mathematical name: Conceptual changes between designation, description, denomination and definition. European Journal of Science and Mathematics Education, 2(2A), 169-176.


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