9,272 research outputs found

    On the integration of digital technologies into mathematics classrooms

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    Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics

    Modeling Evolutionary Dynamics of Lurking in Social Networks

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    Lurking is a complex user-behavioral phenomenon that occurs in all large-scale online communities and social networks. It generally refers to the behavior characterizing users that benefit from the information produced by others in the community without actively contributing back to the production of social content. The amount and evolution of lurkers may strongly affect an online social environment, therefore understanding the lurking dynamics and identifying strategies to curb this trend are relevant problems. In this regard, we introduce the Lurker Game, i.e., a model for analyzing the transitions from a lurking to a non-lurking (i.e., active) user role, and vice versa, in terms of evolutionary game theory. We evaluate the proposed Lurker Game by arranging agents on complex networks and analyzing the system evolution, seeking relations between the network topology and the final equilibrium of the game. Results suggest that the Lurker Game is suitable to model the lurking dynamics, showing how the adoption of rewarding mechanisms combined with the modeling of hypothetical heterogeneity of users' interests may lead users in an online community towards a cooperative behavior.Comment: 13 pages, 5 figures. Accepted at CompleNet 201

    Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size

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    Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods are exposed to performance breakdown, as the sample covariance matrix can largely deviate from the true covariance matrix. In this paper, the problem of DOA estimation performance breakdown is investigated. We consider the structure of the sample covariance matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, the subspace leakage is theoretically derived. We also propose a two-step method which improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced. Furthermore, we introduce a phenomenon named as root-swap which occurs in the root-MUSIC algorithm in the low sample size region and degrades the performance of the DOA estimation. A new method is then proposed to alleviate this problem. Numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods. Moreover, the proposed algorithms are combined with the pseudo-noise resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal Processing in July 201

    Soft thought (in architecture and choreography)

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    This article is an introduction to and exploration of the concept of ‘soft thought’. What we want to propose through the definition of this concept is an aesthetic of digital code that does not necessarily presuppose a relation with the generative aspects of coding, nor with its sensorial perception and evaluation. Numbers do not have to produce something, and do not need to be transduced into colours and sounds, in order to be considered as aesthetic objects. Starting from this assumption, our main aim will be to reconnect the numerical aesthetic of code with a more ‘abstract’ kind of feeling, the feeling of numbers indirectly felt as conceptual contagions’, that are ‘conceptually felt but not directly sensed. The following pages will be dedicated to the explication and exemplification of this particular mode of feeling, and to its possible definition as ‘soft thought’
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