Building Mathematical Understanding Through Collective Property Noticing
Tóm tắt
In this article we explore the mechanisms through which one group of preservice teachers engage in Collective Property Noticing—a phenomenon in which group members integrate individual contributions such that the group, as a unit, notices mathematical properties of their collective image. Drawing on improvisational theory to help to illuminate these collaborative processes, we claim that Collective Property Noticing is a capacity that is vital for mathematical sense-making in collaborative groups and we propose several conditions under which it is appropriate for a teacher to intervene in students’ learning in a problem-solving setting in order to provoke Collective Property Noticing. Résumé: Dans cet article, nous nous penchons sur les mécanismes grâce auxquels un groupe de futurs enseignants participe à des activités d’observation des propriétés collectives, durant lesquelles les membres du groupe intègrent les contributions individuelles de chacun de façon à ce que le groupe en tant qu’équipe puisse observer les propriétés de son image collective. Sur la base d’une théorie de l’improvisation servant à éclairer ces processus de collaboration, nous postulons que l’observation des propriétés collectives constitue une habileté vitale pour la construction du sens mathématique dans les groupes de collaboration, et nous formulons plusieurs conditions dans lesquelles il est approprié que les enseignants interviennent dans l’apprentissage des étudiants, dans un contexte de résolution de problèmes, de façon à stimuler l’observation des propriétés collectives.
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