Virtual encounters: the murky and furtive world of mathematical inventiveness

Abstract

Based on Châtelet's insights into the nature of mathematical inventiveness, drawn from historical analyses, we propose a new way of framing creativity in the mathematics classroom. The approach we develop emphasizes the social and material nature of creative acts. Our analysis of creative acts in two case studies involving primary school classrooms also reveals the characteristic ways in which digital technologies can occasion such acts.

Recent research on geometry education: an ICME-13 survey team report

“…These findings are in line with those of Sinclair, de Freitas and Ferrara (2012), who examined first grade children's reasoning about intersecting lines that were displayed using a DGE. The dynamic diagram contained two lines that could be dragged on the screen.…”

Wabi-Sabi Mathematics

“…A true picture of doing mathematics as tinkering and bricolage (e.g. [3]) is remindful of what de Freitas and Sinclair [43] describe as the process through which a mathematical idea "becomes a highly animate concept made vibrant and creative through the indeterminacy buried in it" connected to a shift of attention "from an emphasis on logical necessity towards an opening for contingency, ambiguity and creativity" (page 466). We also get a strong sense of how what Roth [36] calls the "living/lived mathematical work" can be seen, in the spirit of wabi-sabi aesthetics, as a constellation of private, intuitive, relative experiences.…”

Interpréter la créativité du raisonnement dans les productions d’élèves en mathématiques d’une communauté d’apprentissages multidisciplinaires interactifs

“…Nos travaux sont donc cohérents avec ceux de Vygotsky (1978). Nos travaux permettent aussi d'entrevoir autrement le travail de Sinclair et al (2013) et ceux de Hitt (2004). L'une des forces du registre spontané par rapport aux autres registres est qu'il permet de gérer implicitement plusieurs contraintes, tout en soutenant les relations entre ces contraintes.…”

“…Ils correspondent à différentes représentations d'un même concept mathématique : représentation numérique (nombre), arithmétique (opérations d'addition, de multiplication…), algébrique (algèbre), géométrique (triangle, cube…) et graphique (plan cartésien, figure). Nous définissons le diagramme comme étant un dessin permettant d'actualiser les actions de l'élève, sur la base du potentiel du dessin, afin de matérialiser le possible selon le contexte du dessin (Sinclair et al, 2013).…”