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 this chapter, I look back at the implementation of W12-16, a major reform of mathematics education in the lower grades of general secondary education and pre-vocational secondary education in the Netherlands including all students aged 12–16. The nationwide implementation of W12-16 started in 1990 and envisioned a major change in what and how mathematics was taught and learned. The content was broadened from algebra and geometry to algebra, geometry and measurement, numeracy, and data processing and statistics. The learning trajectories and the instruction theory were based on the ideas of Realistic Mathematics Education (RME): the primary processes used in the classroom were to be guided re-invention and problem solving. ‘Ensuring usability’ in the title of this chapter refers to the aim of the content being useful and understandable for all students, but also to the involvement of all relevant stakeholders in the implementation project, including teachers, students, parents, editors, curriculum and assessment developers, teacher educators, publishers, media and policy makers. Finally, I reflect on the current state of affairs more than 20 years after the nationwide introduction. The main questions to be asked are: Have the goals been reached? Was the implementation successful?
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De impact van de coronaperiode blijft voelbaar, maar heeft onsook waardevolle inzichten opgeleverd. Studenten en docentenhebben hun veerkracht moeten tonen, en op verschillendegebieden is hard gewerkt om onderwijsachterstanden in te halendie tijdens de crisis zijn ontstaan.
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Fontys University of Applied Science’s Institute of Engineering, and the Dutch Institute for Fundamental Energy Research (DIFFER) are proposing to set up a professorship to develop novel sensors for fusion reactors. Sensors are a critical component to control and optimise the unstable plasma of Tokamak reactors. However, sensor systems are particularly challenging in fusion-plasma facing components, such as the divertor. The extreme conditions make it impossible to directly incorporate sensors. Furthermore, in advanced reactor concepts, such as DEMO, access to the plasma via ports will be extremely limited. Therefore, indirect or non-contact sensing modalities must be employed. The research group Distributed Sensor Systems (DSS) will develop microwave sensor systems for characterising the plasma in a tokamak’s divertor. DSS will take advantage of recent rapid developments in high frequency integrated circuits, found, for instance, in automotive radar systems, to develop digital reflectometers. Access through the divertor wall will be achieved via surface waveguide structures. The waveguide will be printed using 3D tungsten printing that has improved precision, and reduced roughness. These components will be tested for durability at DIFFER facilities. The performance of the microwave reflectometer, including waveguides, will be tested by using it to analyse the geometry and dynamics of the Magnum PSI plasma beam. The development of sensor-based systems is an important aspect in the integrated research and education program in Electrical Engineering, where DSS is based. The sensing requirements from DIFFER offers an interesting and highly relevant research theme to DSS and exciting projects for engineering students. Hence, this collaboration will strengthen both institutes and the educational offerings at the institute of engineering. Furthermore millimeter wave (mmWave) sensors have a wide range of potential applications, from plasma characterisation (as in this proposal) though to waste separation. Our research will be a step towards realising these broader application areas.
