2,672 research outputs found

    ‘Balancing’ the ‘live’ use of resources towards the introduction of the iterative numerical method

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    This paper draws on the Knowledge Quartet (Rowland, Huckstep, & Thwaites, 2005) to analyse an introductory to the Iterative Numerical Method Year 13 lesson of a secondary mathematics teacher who uses a range of paper based and electronic resources including Autograph, a mathematics-education software. Data were collected during one lesson observation and a follow up interview with the teacher. Analysis identifies the different aspects of the Knowledge Quartet dimensions: foundation, transformation, connection and contingency, in relation to the introduction to the Iterative method and to the teaching of Year 13 students. Findings demonstrate how the teacher used students’ contributions as resource for his teaching; how he balanced his use of resources; and how he created connections between these resources while he remained attentive to exam requirement

    Anisotropic Transport Properties of Ferromagnetic-Superconducting Bilayers

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    We study the transport properties of vortex matter in a superconducting thin film separated by a thin insulator layer from a ferromagnetic layer. We assume an alternating stripe structure for both FM and SC layers as found in [7]. We calculate the periodic pinning force in the stripe structure resulting from a highly inhomogeneous distribution of the vortices and antivortices. We show that the transport properties in FM-SC bilayer are highly anisotropic. In the absence of random pinning it displays a finite resistance for the current perpendicular to stripes and is superconducting for the current parallel to stripes. The average vortex velocity, electric field due to the vortex motion, Josephson frequency and higher harmonics of the vortex oscillatory motion are calculated.Comment: 4 pages, 2figures, Submitted to PR

    Hysteresis of Finite Arrays of Magnetic nano Dots

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    Hysteresis curves for finite arrays of N×NN\times N ferromagnetic nano dots subject to the dipole-dipole interaction are investigated for N=2...13N=2... 13. Spin arrangements up to N=6 are presented, which indicate the onset of bulk-like behavior associated with odd (N=5) and even (N=6) systems. The effect of field misalignment on the hysteresis loops is also studied for N=3...6N=3... 6. The area ANA_N of the hysteresis loop is studied as a function of NN. We find that ANAA_N-A_\infty approximately scales as N3/2N^{-{3/2}} for NN odd and as N2N^{-2} for NN even.Comment: 6 pages, 8 figures, Submitted to PR

    Ferromagnetic Annulus And Superconducting Vortices

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    The screening currents induced in a superconducting film by a magnetic annulus whose magnetization is perpendicular to the superconductor are calculated. We show that close to the superconductor transition temperature TcT_c particular values of the magnetization and radii of the annulus make the creation of superconducting vortices energy favorable. We also show that the magnetic annulus offers an alternative tool for vortex pinning in the superconductor. Statistical mechanical properties of this system are discussed.Comment: 4 pages, 2 figures, submitted to PR

    Teachers' use of resources for mathematics teaching: The case of teaching trigonometry.

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    This paper draws on the documentational approach and knowledge quartet to analyse a trigonometry Year 13 lesson of a secondary mathematics teacher who uses a range of paper based and electronic resources. Data were collected during one lesson observation and a follow-up interview with the teacher. Analysis identifies the resources and schemes of use of these resources: aims of the teaching activity, rules of actions, operational invariants and inferences in relation to the trigonometry lesson but also in relation to Year 13 teaching, especially towards student preparation for the exams. It also explores this teacher’s work in the class by using the different dimensions of the knowledge quartet: foundation, transformation, connection and contingency. The findings explore teacher’s use of resources and the potencies of using the knowledge quartet in tandem with the documentational approach

    Micro-evolution of documentational work in the teaching of the volume of revolution

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    In this paper, we draw on the documentational approach to analyse the evolution of one experienced secondary teacher’s work towards the teaching of the topic of “volume of revolution”. He used a range of paper and computer based resources in- cluding the software Autograph. Data were collected in observations of three lessons on this topic taught to two different groups of 16-18 years old students and a follow up interview with the teacher where he was asked to reflect on his choices in these lessons. The findings illustrate teacher’s documentational work with the used resources, and his schemes of use – aims, rules of actions, operational invariants and inferences – and identify the micro-evolution, namely the small changes and the rationale behind these changes, of these schemes across the lessons
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