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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Objectives: Participation is considerably restricted in children and adolescents with acquired brain injury (ABI) as compared to their healthy peers. This systematic review aims to identify which factors are associated with participation in children and adolescents with ABI. Methods: A systematic search in Medline and various other electronic databases from January 2001–November 2014 was performed. All clinical studies describing determinants of participation at least 1 year after the diagnosis of ABI by means of one or more pre-defined instruments in patients up to 18 years of age were included. Extracted data included study characteristics, patient characteristics, participation outcome and determinants of participation (categorized into: health conditions (including characteristics of ABI), body functions and structures, activities, personal factors and environmental factors). The methodological quality of the studies was evaluated based on three quality aspects (selection, information and statistical analysis bias) and scored as low, moderate or high. Results: Eight studies using an explicit participation outcome measure were selected after review, including a total of 1863 patients, with a follow-up ranging from 1 up to 288 months. Three studies included patients with a traumatic or a non-traumatic brain injury (TBI or NTBI) and five studies with only TBI patients. Factors consistently found to be associated with more participation restrictions were: greater severity of ABI, impaired motor, cognitive, behavioural and/or sensory functioning, limited accessibility of the physical environmentand worse family functioning. Fewer participation problems were associated with a supportive/nurturing parenting style, higher household income, acceptance and support in the community and availability of special programmes. The overall methodological quality of the included studies was high in two and moderate in six studies. Conclusion: This systematic review shows that only a few, moderate quality, studies on the determinants of participation after paediatric ABI using recommended explicit measurement instruments are available. Various components of the ICF model: health condition, body functions and structures and environmental factors were consistently found to be associated with participation. More methodologically sound studies, using the recommended explicit outcome measures, a standardized set of potential determinants and longterm follow-up are suggested to increase the knowledge on participation in children and youth with ABI.
Functional Magnetic Resonance Imaging (fMRI) was used to study the activation of cerebral motor networks during auditory perception of music in professional keyboard musicians (n=12). The activation paradigm implied that subjects listened to two-part polyphonic music, while either critically appraising the performance or imagining they were performing themselves. Two-part polyphonic audition and bimanual motor imagery circumvented a hemisphere bias associated with the convention of playing the melody with the right hand. Both tasks activated ventral premotor and auditory cortices, bilaterally, and the right anterior parietal cortex, when contrasted to 12 musically unskilled controls. Although left ventral premotor activation was increased during imagery (compared to judgment), bilateral dorsal premotor and right posterior-superior parietal activations were quite unique to motor imagery. The latter suggests that musicians not only recruited their manual motor repertoire but also performed a spatial transformation from the vertically perceived pitch axis (high and low sound) to the horizontal axis of the keyboard. Imagery-specific activations in controls were seen in left dorsal parietal-premotor and supplementary motor cortices. Although these activations were less strong compared to musicians, this overlapping distribution indicated the recruitment of a general 'mirror-neuron' circuitry. These two levels of sensori-motor transformations point towards common principles by which the brain organizes audition-driven music performance and visually guided task performance.
