The relation between mathematical object/mathematical name: conceptual changes among designation, description, denotation, denomination and definition.
Abstract
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”.
Collections
Related items
Showing items related by title, author, creator and subject.

From individual interactions to collective patterns: A mathematical approach
Bertotti, ML (2011)A mathematical approach is here discussed, addressed to try and explain the emergence of collective properties of socioeconomic systems with a large number of individuals, based on the knowledge of pairwise individual ... 
An εlagrange multiplier rule for a mathematical programming problem on Banach spaces
Hamel, AH (2001)The aim of this paper is to extend the multiplier rule due to Clarke for a nondifferentiable mathematical programming problem on a Banach space to eminimal (suboptimal) solutions of the problem. This seems to be useful ... 
On the qualitative analysis of the solutions of a mathematical model of social dynamics
Bertotti, ML; Delitala, M (Elsevier, 2006)This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods ...