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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In organisations, learning is generally seen as a dynamic, collective and often conscious process that occurs by reflecting on real work experiences. In this article, we discuss these assumptions about learning in the context of work by presenting a case study in the care for older people. The case illustrates that learning in and through work is predominantly an embodied and responsive phenomenon that usually occurs implicitly while acting. We argue that a learning perspective grounded in the worldview of enactivism encapsulates this pragmatic and embodied character of learning and at the same time provides a reality and language helpful in encouraging a critical attitude towards assumptions about learning in organisations. Understanding learning from an enactive point of view carries consequences for studying and organising learning within organisations. These are outlined within this article to challenge managers’ meanings of learning in health care and comparable settings and to encourage further dialogue on this issue.
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The potential impact of urban (re)development on the well-being of residents has been recognized in literature (Butcher & Dickens, 2016; Brummet and Reed, 2019), underscoring the need to critically examine one’s approach to studying the so called ‘urban peripheries’. This paper proposes the practice of mapping alternative city imaginaries, together with local partners, to promote inclusive and 'a more diverse and sustainable perspective on [city] prosperity' (Arbonés Aran, Petkova and Moodey, 2023).We present a case study of the living lab ‘Cities and Visitors’ (Amsterdam School of International Business) based in Amsterdam Southeast (Zuidoost). The study employs a mixed methods to capture and map 'alternative imaginaries' of 'urban peripheries' together with local partners, students, and inter-city collaborators. As urban developments continue to comply with technocratic systems and strategies (Pries, 2022), it becomes important to deepen our understanding, engagement, exploration, and preservation of city spaces, particularly in the so called urban ‘peripheries’ that are often subjected to the dynamics of de/reconstruction and rejuvenation brought by external actors.The paper also advocates for a reflective and ethical research methodology, as the participants engage in thoughtful and (self) reflective research practices. We see this as an intervention in the business curriculum, often criticized for producing 'neoliberal agents' (Orta, 2019), whereas students must also cultivate competences in 'sustainability' (UNESCO 2014, 2017). Embracing the perspectives of affect (Thrift, 2008) and standpoint theory (Harding, 2008), as well as critical counter-mapping with digital methods (Rogers, 2013), we intend to nurture the emotional intelligence and literacy in students, facilitating transformative pedagogies (Mezirov 1990; Maiese 2017).
