Brave Forms of Mentoring Supported by Technology in Teacher Education

Indexación: Web of ScienceQuality education is undoubtedly a global concern, tied closely to preoccupations with economic and social development. Increasingly, the adoption and effective use of current technology tools are being recognized as visible signs of that quality. Scholars are providing increasing evidence of the kinds of empowered teacher identities that will adopt the effective use of technology tools in teaching. Less is being discussed about how technology can support the processes needed to mediate such identities. The context of Teacher Education is a strategic place to begin to initiate such processes. Our aim in this article is twofold: 1) to describe two recent examples of innovative, technology - supported mentoring processes that were conducted in the context of an EFL Teacher Education program in Chile; 2) to revisit the findings of these studies in light of new evidence from participants who have moved on in their careers. This evidence is viewed in the framework of recent scholarship on the responsibilities that Teacher Education plays in their development. The first 16-month study examined the influences of a guided reading program involving e-readers on the identities and literacy skills of pre-service teachers. The second was a student-conceived study. That inquiry sought to determine the influence of upper year students' peer mentoring, made available partly through a social media site (SMS), on the identities and investment in learning of 12 firs-year students in the pedagogy program. The initial evidence from ethnographic tools used in both studies indicated that the participants were struggling with confidence and doubting themselves as knowledgeable, effective future teachers - not predictive of a potential for quality teaching. Positive signs at the end of both studies and more recent reports from participants suggest that the mentoring had longitudinal benefits for some, although not uniformly. The potential of apprenticeship and mentoring in a technology-supported environment requires rethinking Teacher Education mandates if we are to empower emerging teachers to be quality teachers.http://www.ejel.org/issue/download.html?idArticle=48

Cylindrical gravitational waves in expanding universes: Models for waves from compact sources

New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where the waves have not reached and wave amplitudes fall off more rapidly than they do in Einstein-Rosen solutions, permitting a more regular null inifinity.Comment: Minor corrections to references. A note added in proo

Asymptotic Behavior of the T3×RT^3 \times R Gowdy Spacetimes

We present new evidence in support of the Penrose's strong cosmic censorship conjecture in the class of Gowdy spacetimes with $T^3$ spatial topology. Solving Einstein's equations perturbatively to all orders we show that asymptotically close to the boundary of the maximal Cauchy development the dominant term in the expansion gives rise to curvature singularity for almost all initial data. The dominant term, which we call the ``geodesic loop solution'', is a solution of the Einstein's equations with all space derivatives dropped. We also describe the extent to which our perturbative results can be rigorously justified.Comment: 30 page

Internal Time Formalism for Spacetimes with Two Killing Vectors

The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes, and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model canonical variables which can be used to identify points of space and instants of time, {\it i.e.}, internally defined spacetime coordinates, are identified. To do this it is necessary to extend the usual ADM phase space by a finite number of degrees of freedom. Canonical transformations are exhibited that identify each of these models with harmonic maps in the parametrized field theory formalism. The identifications made between the gravitational models and harmonic map field theories are completely gauge invariant, that is, no coordinate conditions are needed. The degree to which the problems of time are resolved in these models is discussed.Comment: 36 pages, Te

Cosmologies with Two-Dimensional Inhomogeneity

We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar field, or alternatively with perfect fluid, can be constructed using this algorithm. Some families of solutions and the applications of the algorithm are discussed.Comment: 9 pages, one postscript figur

Complete quantization of a diffeomorphism invariant field theory

In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not correspond to a subset of Einstein's gravity it has the advantage that the programme of canonical quantization can be carried out completely and explicitly, both, via the reduced phase space approach or along the lines of the algebraic quantization programme. This model stands in close correspondence to the frequently treated cylindrically symmetric waves. In contrast to other models that have been looked at up to now in terms of the new variables the reduced phase space is infinite dimensional while the scalar constraint is genuinely bilinear in the momenta. The infinite number of Dirac observables can be expressed in compact and explicit form in terms of the original phase space variables. They turn out, as expected, to be non-local and form naturally a set of countable cardinality.Comment: 32p, LATE

Numerical Investigation of Cosmological Singularities

Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te

The Gowdy T3 Cosmologies revisited

We have examined, repeated and extended earlier numerical calculations of Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological models. Our results are consistent with theirs and we support their claim that the models exhibit AVTD behaviour, even though spatial derivatives cannot be neglected. The behaviour of the curvature invariants and the formation of structure through evolution both backwards and forwards in time is discussed.Comment: 11 pages, LaTeX, 6 figures, results and conclusions revised and (considerably) expande

Gowdy waves as a test-bed for constraint-preserving boundary conditions

Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting 200

Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it local} Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the `geometric structures') of the models. In particular, we show a method of reduction to the natural reduced manifold, and analyze the equivalences at the reduced level of the models as dynamical models. Based on these fundamentals, we examine the influence of spatial topologies on dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear in CQ