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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We present a fully working prototype of NOOT, an interactive tangible system which supports (sharing of) moments of reflection during brainstorms. We discuss the iterative design process, informed by embodied situated cognition theory and by user studies in context using various versions of the prototype. Apart from a potentially useful product, NOOT served as a research-tool showing how physical materials and social interactions scaffold people’s sense-making efforts, and how technology might fit in to support this process.
In this paper we explore the influence of the physical and social environment (the design space) son the formation of shared understanding in multidisciplinary design teams. We concentrate on the creative design meeting as a microenvironment for studying processes of design communication. Our applied research context entails the design of mixed physical–digital interactive systems supporting design meetings. Informed by theories of embodiment that have recently gained interest in cognitive science, we focus on the role of interactive “traces,” representational artifacts both created and used by participants as scaffolds for creating shared understanding. Our research through design approach resulted in two prototypes that form two concrete proposals of how the environment may scaffold shared understanding in design meetings. In several user studies we observed users working with our systems in natural contexts. Our analysis reveals how an ensemble of ongoing social as well as physical interactions, scaffolded by the interactive environment, grounds the formation of shared understanding in teams. We discuss implications for designing collaborative tools and for design communication theory in general.
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