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1
An Investigation of the Visual-Mental Capability of Pre- and In-Service Mathematics Teachers: A Tale of Two Cones and One Cube

( Barkai Ruthi ),( Patkin Dorit ) 한국수학교육학회 2014 수학교육연구 Vol.18 No.1
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This study investigated the visual-mental capabilityof pre-service and in-service mathematics teachers as well as academicians making a career change to mathematics teachers with regard to manipulations of two geometric shapes (from 2- to 3-dimensional). Moreover, it investigated whether there are differences between the visual-mental capabilityof these participant groups. Findings illustrate that most of the participants demonstrate an adequate visual capability relating to the task dealing with a cube. Conversely, very low percentage of participants manifested a visual-mental capability in a task requiring the identification of a solid resulting from rotation of a square page, whose diagonal serves as the rotation axis. The study indicates that learners` high visual view should be developed in order to enhancetheir visual-mental capability.
2
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

Metzler, Ralf,Jeon, Jae-Hyung,Cherstvy, Andrey G.,Barkai, Eli The Royal Society of Chemistry 2014 Physical chemistry chemical physics Vol.16 No.44
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Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion. Graphic AbstractThis Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=c4cp03465a'>