Theories and practical perspectives on fostering embodied abstraction in primary school geometry education - Boonstra, Karel; Kool, Marjolein; Shvarts, Anna; Drijvers, Paul (Frontiers in Education, 2023)
In this paper we align theoretical perspectives on embodied learning related to abstraction in geometry, with practical perspectives from in-service teachers. Our aim is to inform on suggestions for teacher education based on the alignment of these two perspectives. We focus on the teaching and learning of realistic geometry. Not only because this domain is apt for sensori-motor action investigations, but also because abstraction in realistic geometry is under researched in relation to other domains of mathematics. Furthermore, teachers knowledge of geometry and also confidence in teaching geometry lacks behind. The research question that will be addressed reads: how does a theoretical embodied perspective on abstraction in geometry education in the higher grades of primary school align with current teacher practices? Two studies are performed, 1) a synthesizing literature study, and 2) and an interview study (n=6). The theoretical study led to the following definition of embodied abstraction in geometry: abstraction is a process of reflecting on sensory-motor actions that structure the experienced world in a new way and describing and explaining the actions and the emergent structures using mathematical artifacts. The interview study, where this definition was presented, shows that teachers are potentially prepared for using certain aspects of embodied learning (e.g. manipulatives), but are not aware of the dimensions of enactment that could lead students towards abstraction. In order to be able to foster students abstraction process in geometry, theories on embodiment and abstraction do not suffice. Instead, knowledge of embodied abstraction in geometry, and how to foster this, grows with experience in enactment, with the discovery that cognition is in service of action.