In this paper, we analyze processes of conjecture generation in the context of open problems proposed in a dynamic geometry environment, when a particular dragging modality, maintaining dragging, is used. This involves dragging points while maintaining certain properties, controlling the movement of the figures. Our results suggest that the pragmatic need of physically controlling the simultaneous movements of the different parts of figures can foster the production of two chains of successive properties, hinged together by an invariant that we will call pivot invariant. Moreover, we show how the production of these chains is tied to the production of conjectures and to the processes of argumentation through which they are generated.
Maintaining dragging and the pivot invariant in processes of conjecture generation / Antonini Samuele; Baccaglini-Frank Anna. - STAMPA. - 2:(2016), pp. 19-26. (Intervento presentato al convegno 40th Conference of the International Group for the Psychology of Mathematics Education tenutosi a Szeged, Hungary nel August 3-7, 2016).
Maintaining dragging and the pivot invariant in processes of conjecture generation
Antonini Samuele;
2016
Abstract
In this paper, we analyze processes of conjecture generation in the context of open problems proposed in a dynamic geometry environment, when a particular dragging modality, maintaining dragging, is used. This involves dragging points while maintaining certain properties, controlling the movement of the figures. Our results suggest that the pragmatic need of physically controlling the simultaneous movements of the different parts of figures can foster the production of two chains of successive properties, hinged together by an invariant that we will call pivot invariant. Moreover, we show how the production of these chains is tied to the production of conjectures and to the processes of argumentation through which they are generated.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.