Starting from Toulmin’s analysis of impossibility and through the study of some cases, I investigate argumentations supporting mathematical impossibilities. In particular, I discuss issues related to the notions of impossibility, as the contradictoriness, the criteria and the implications of an impossibility, and the Toulmin’ pattern of argumentations produced to state that something is impossible. I show the use of this model to analyse students argumentations, to identify the specific aspects of these argumentations, to describe the differences and the analogies between argumentations and proofs that support impossibilities.
A model to analyse argumentations supporting impossibilities in mathematics / Antonini Samuele. - In: PROCEEDINGS OF THE PME CONFERENCE. - ISSN 0771-100X. - STAMPA. - 2:(2010), pp. 153-160. (Intervento presentato al convegno 34th Conference of the International Group for the Psychology of Mathematics Education tenutosi a Belo Horizonte, Brazil nel 18-23 July, 2010).
A model to analyse argumentations supporting impossibilities in mathematics
Antonini Samuele
2010
Abstract
Starting from Toulmin’s analysis of impossibility and through the study of some cases, I investigate argumentations supporting mathematical impossibilities. In particular, I discuss issues related to the notions of impossibility, as the contradictoriness, the criteria and the implications of an impossibility, and the Toulmin’ pattern of argumentations produced to state that something is impossible. I show the use of this model to analyse students argumentations, to identify the specific aspects of these argumentations, to describe the differences and the analogies between argumentations and proofs that support impossibilities.
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