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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A quantitative study of teachers' beliefs and practices regarding fair classroom differentiation
A regular short physical activity break in the classroom may improve classroom behavior. The current study reports on the results of the implementation of a daily 10-min Just Dance break in the classroom. A total of 31 Dutch primary school teachers agreed to participate in the study. We collected data on the frequency of the use of the Just Dance breaks via an online registration system. Data on the long-term barriers and facilitators of the implementation were collected using two online questionnaires. In addition, we held five interviews with teachers to elucidate data on barriers and facilitators. The results show that none of the teachers maintained the Just Dance breaks on a daily basis, and only 19% (n = 6) of the teachers on a weekly basis (i.e., one to three times a week). According to all participating teachers, a lack of time was the primary barrier to implement Just Dance breaks on a daily basis. Teachers who did not maintain Just Dance breaks on a weekly basis also experienced difficulties in 1) keeping all pupils engaged during the full 10-min Just Dance break or 2) getting the pupils focused again after the Just Dance break. Teachers who maintained the Just Dance breaks on a weekly basis provided several practical recommendations for a more sustainable implementation process. This study shows that the implementation process of daily Just Dance breaks is challenging. We recommend providing teachers with professional support when implementing physical activity breaks in their daily program.
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