No abstract

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on both time and motion-hence, on physical interpretations of mathematical abstractions-which are dimensions of thinking that are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide an essential mediating role between the two.

The complementary use of the theories of instrumental genesis and shifts of attention enabled me to obtain insights into students' understandings of the concepts of eigenvector and eigenvalue. My analysis suggests that the use of different dragging modalities can provide evidence of shifts in structure of a student's attention and consequently can reveal processes involved in her understanding of the concepts. Inversely, shifts in structure of her attention can result in her use of different dragging modalities. I also identified a new dragging modality-intentionally dragging-that is, to drag a point with the intention of producing a certain configuration.Résumé: L'utilisation complémentaire des théories de la genèse instrumentale et du déplacement de l'attention m'ont permis d'avoir un aperçu de la façon dont lesétudiants appréhendent les concepts de valeur propre et de vecteur propre. Mon analyse suggère que l'utilisation de différentes modalités de glissement indique un changement dans la structure de l'attention desétudiants et par conséquent révèle les processus impliqués dans leur compréhension des concepts. Inversement, les changements dans la structure de leur attention peuvent entrainer une utilisation de modalités de glissement différentes. J'aiégalement observé une nouvelle modalité de glissement-le glissement intentionnel-soit le glissement d'un point avec l'intention délibérée de produire une certaine configuration.