53 research outputs found

    Validation of Solutions of Construction Problems in Dynamic Geometry Environments

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    This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’ in DGEs and the use of only straightedge and compass in classic Euclidean geometry. We then demonstrate that the drag test criterion may permit constructions created using measurement tools to be considered valid; however, these constructions prove inconsistent with classical geometry. This inconsistency raises the question of whether dragging is an adequate test of validity, and the issue of measurement versus straightedge-and-compass. Without claiming that the inconsistency between what counts as valid solution of a construction problem in the two geometry worlds is necessarily problematic, we examine what would constitute the analogue of the straightedge-and-compass criterion in the domain of DGEs. Discovery of this analogue would enrich our understanding of DGEs with a mathematical idea that has been the distinguishing feature of Euclidean geometry since its genesis. To advance our goal, we introduce the compatibility criterion , a new but not necessarily superior criterion to the drag test criterion of validation of solutions of construction problems in DGEs. The discussion of the two criteria anatomizes the complexity characteristic of the relationship between DGEs and the paper-and-pencil Euclidean geometry environment, advances our understanding of the notion of geometrical constructions in DGEs, and raises the issue of validation practice maintaining the pace of ever-changing software.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42932/1/10758_2004_Article_6999.pd

    Forming conjectures within a spreadsheet environment

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    This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures

    Self-Help in Mathematics

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    Anatomically constrained tractography facilitates biologically plausible fiber reconstruction of the optic radiation in multiple sclerosis

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    Diffusion-weighted magnetic resonance imaging (dMRI) enables the microstructural characterization and reconstruction of white matter pathways in vivo non-invasively. However, dMRI only provides information on the orientation of potential fibers but not on their anatomical plausibility. To that end, recent methodological advances facilitate the effective use of anatomical priors in the process of fiber reconstruction, thus improving the accuracy of the results. Here, we investigated the potential of anatomically constrained tracking (ACT), a modular addition to the tractography software package MRtrix3, to accurately reconstruct the optic radiation, a commonly affected pathway in multiple sclerosis (MS). Diffusion MRI data were acquired from 28 MS patients and 22 age- and sex-matched healthy controls. For each participant, the optic radiation was segmented based on the fiber reconstruction obtained using ACT. When implementing ACT in MS, it proved essential to incorporate lesion maps to avoid incorrect reconstructions due to tissue-type misclassifications in lesional areas. The ACT-based results were compared with those obtained using two commonly used probabilistic fiber tracking procedures, based on FSL (FMRIB Software Library) and MRtrix3 without ACT. All three procedures enabled a reliable localization of the optic radiation in both MS patients and controls. However, for FSL and MRtrix3 without ACT it was necessary to place an additional waypoint halfway between the lateral geniculate nucleus and the primary visual cortex to filter out anatomically implausible tracks. In the case of ACT, the results with and without an additional waypoint were virtually identical, presumably because the employed anatomical constraints already prevented the occurrence of the most implausible tracks. Irrespective of the employed tractography procedure, increased diffusivity and decreased anisotropy were found in the optic radiation of the MS patients compared to the controls. Keywords: Magnetic resonance imaging, Multiple sclerosis, Fiber tracking, Probabilistic tractography, Diffusion MRI, Optic radiation, AC

    Upregulation of vascular endothelial growth factor in ischemic and non-ischemic human and experimental retinal disease

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    Vascular endothelial growth factor (VEGF) is induced by hypoxia and it has been implicated in the development of iris and retinal neovascularization (NV) in ischemic retinopathies in which it has been suggested that Müller cells are responsible for increased VEGF production. VEGF, however, is also known to be a potent mediator of vascular permeability in other tissues and may perform this function in retina. Immunohistochemical staining for VEGF was performed on a variety of human and experimental ischemic and non-ischemic ocular disorders in which blood retinal barrier (BRB) breakdown is known to occur to determine if there is an upregulation of VEGF in these conditions. We found increased VEGF immunoreactivity in ganglion cells of rats with oxygen-induced ischemic retinopathy and in ganglion cells, the inner plexiform layer, and some cells in the inner nuclear layer of rats with experimental autoimmune uveoretinitis (EAU), in which there was no identifiable ischemia or NV. In rats with EAU, VEGF staining intensity increased from 8 to 11 days after immunization, coincident with BRB failure. These results were confirmed using two distinct anti-VEGF antibodies and by immunoblot and the immunohistochemical staining was eliminated by pre-incubating the antibodies with VEGF peptide. VEGF staining was also increased in the retina and iris of patients with ischemic retinopathies, such as diabetic retinopathy and retinal vascular occlusive disease, and in patients with disorders in which retinal ischemia does not play a major role, such as aphakicl pseudophakic cystoid macular edema, retinoblastoma, ocular inflammatory disease or infection, and choroidal melanoma. VEGF was primarily localized within retinal neurons and retinal pigmented epithelial cells in these cases. In addition or in association with its role of inducing NV, VEGF may contribute to BRB breakdown in a variety of ocular disorders and blockage of VEGF signaling may help to reduce some types of macular edema

    Pour une approche sereine de la culture sportive

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    The clinical safety, use and pharmacokinetics of a new needle-free device for delivery of growth hormone (GH) were compared with those of conventional needle injection devices. In an open-label, randomized, 4-period crossover study, 18 healthy adults received single subcutaneous injections of Genotropin administered by the Genotropin ZipTip needle-free device and by conventional injection. Bioequivalence was established between the devices. In a separate open-label, randomized, multicenter, 2-period crossover study, pediatric patients underwent 2-weeks Genotropin treatment administered by the Genotropin ZipTip and by a fine-gauge needle device (>95% used the Genotropin Pen). In total, 128/133 patients who were treated completed the study. Genotropin ZipTip was well tolerated and >50% of patients found no difference between the devices for all parameters assessed. After study completion, >20% patients preferred to continue using Genotropin ZipTip. Although statistical analyses demonstrated superiority of the Genotropin Pen versus Genotropin ZipTip for bleeding, pain, soreness, and bruising, Genotropin ZipTip was considered to provide a safe and bioequivalent alternative to needle injection

    Conceptions of Atmospheric Carbon Budgets: Undergraduate Students' Perceptions of Mass Balance

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    With recent U.S. government efforts to develop policy procedures for addressing climate change, public understanding of basic aspects of climate change is imperative in order for people to understand such policy. However, widespread misconceptions of basic atmospheric principles exist among the public. In this study, we document levels of misunderstanding that undergraduate students at a large U.S. research institution have with respect to atmospheric carbon budgets and factors that may account for variability in their understanding. Students enrolled in an introductory geology course (n = 947) completed a survey on atmospheric carbon budgets in two sequential semesters. Results indicated that most students did not have a basic understanding of mass-balance problems and that their misunderstanding varied according to gender and their interest in science but not according to factors, such as students' opinions of the seriousness of climate change. Students also tended to exhibit poor graphical interpretation skills when examining mass-balance graphs.This article is from Journal of Geoscience Education 62 (2014): 460, doi:10.5408/13-052.1. Posted with permission.</p
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