To reach for abstraction is a major but challenging goal in mathematics education: teachers struggle with finding ways how to foster abstraction in their classes. To shed light on this issue for the case of geometry education, we align theoretical perspectives on embodied learning and abstraction with practical perspectives from in-service teachers. 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, and teachers’ knowledge of geometry and confidence in teaching it lag behind. The following research question will be addressed: how can a theoretical embodied perspective on abstraction in geometry education in the higher grades of primary school inform current teacher practices? To answer this question, we carried out a literature study and an interview study with in-service teachers (n = 6). As a result of the literature study, we consider embodied abstraction in geometry as a process of reflecting on, describing, explaining, and structuring of sensory-motor actions in the experienced world through developing and using mathematical artifacts. The results from the interview study show that teachers are potentially prepared for using aspects of embodied learning (e.g., manipulatives), but are not aware of the different aspects of enactment that may invite students’ abstraction. We conclude that theories on embodiment and abstraction do not suffice to foster students’ abstraction process in geometry. Instead, teachers’ knowledge of embodied abstraction in geometry and how to foster this grows with experience in enactment, and with the discovery that cognition emerges to serve action.
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The purpose of the design-based research reported here is to show – as a proof of principle – how the idea of scaffolding can be used to support primary teachers in a professional development programme (PDP) to design and enact language-oriented science lessons. The PDP consisted of six sessions of 2.5 h each in which twelve primary school teachers took part over a period of six months. It centralised the language support that pupils need to reason during science lessons. In line with the idea of scaffolding, the structure of the PDP targeted teachers' gradual independence in designing lessons. The first research question is how scaffolding was enacted during the PDP. The analysis of video recordings, field notes, researcher and teacher logs, and teacher design assignments focused on the enactment of three scaffolding characteristics: diagnosis, responsiveness and handover to independence. The second research question concerns what teachers learned from the participation in the PDP that followed a scaffolding approach. The data analysis illustrates that these teachers had learned much in terms of designing and enacting language-oriented science lessons. In terms of diagnosis and responsiveness, our PDP approach was successful, but we problematise the ideal of scaffolding approaches focused on handover to independence.
This article examines how the human perception of knowledge is structured in the empirical world. It is often argued by scientists that facts in this empirical world can be perceived, which makes us believe that this world is an objective world. However, the human way of making sense of the world is individual and embodied, which causes the creation of an individual world for every human: a body-world. The empirical world is in this case a shared space for multiple bodies that agree on the causality of certain events and objects in that space. Every body-world therefore has its own partial perspective on the knowledge in this shared space, which is formed by the physiology of the body, the cultural background, and the identity of the person. The theater has the power, through the techniques of re-enactment and disruption, to give its audience insight in other situated knowledges from different partial perspectives. It can therefore connect different situated knowledges and create ecological knowledge: the awareness of the connected network of knowledges that is produced in various body-worlds on what is happening in the shared space. Only then can we emancipate knowledge and embrace the various partial perspectives that this shared space of body-worlds has to offer.
