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.
LINK
This article introduces Gilles Deleuze and Félix Guattari’s concepts of smooth and striated space and couples these with the realms of art and technology. In doing so, and by analysing a case study, the dynamic natures and complex mixtures of art and technology are discussed. As a result, a perspective through which art and technology work together to enable new experiences opens up. The case study consists of Anja Hertenberger’s work entitled InBetween — an ongoing performance project in which she examines the reactions of people to her wearing an item of clothing which features a miniature camera on the front and a screen at the back. The article concludes by arguing that although Hertenberger’s performance concerns mediation, it mainly brings about immediate experiences that can be regarded as ‘imaginings’ rather than imaginations.
MULTIFILE
In this article I explore a perspective that the philosophical concepts of German phenomenologist Hermann Schmitz (*1928) may open up for thinking about the growing practice of wearing textile integrated electronics directly on the body. It is my contention that traditional conceptions of wearing (non-technological) clothing on the body fail to capture the changed situation and I hence suggest a paradigm shift is needed to think about the novel scope of affects that can be related to body-technology communication. Schmitz’s concepts of the perceptive felt body, corporeal communication and emotions as atmospheres perceived as outside, on or close to the ‘material’ body will be elaborated upon to investigate how they may enhance existing notions of bodily perception and human-technology relations. The case study used for this philosophical investigation is found in the Tactile Sleeve for Social Touch, a wearable created by Elitac, HvA and UTwente, which allows sensations of stroking, tapping and touching to be communicated from one person to another across a distance.
MULTIFILE
