Designing an e-tutoring system for large classes: mixed-method research

This study aimed at assessing the perceptions of 167 teachers about the tutoring system adopted in an online training course involving teachers from 20 Schools of Sesimbra, Setúbal and Palmela counties. The course, called “Distributed Knowledge with Web 2.0”, was officially certified as a blended learning modality, with the duration of 50 hours, 41 of which occurred online in two editions, the first in February and the second in July of 2012, each one of them involving respectively 82 and 85 teachers, divided in four classes with about 20 trainees each. This blended learning course was designed at producing educational materials in digital format, and included autonomous and group activities, knowledge sharing and reflection. A learning environment, supported by the Ning platform, was set up. At the end of the course, the trainees answered to a pencil and paper survey, in order to evaluate the adopted online tutoring strategy. Additionally the trainees’ final reports contained evidence of how the trainees assessed the tutoring model component of the course; both the survey and the reports were the basis for this research. The results show that the teachers who attended the two course editions disclosed very positive perceptions about online learning, a modality they consider adequate to their current professional status and conditions. The trainees also showed their intention of, in the future, opting for blended training arrangements. Future developments of this study involve a content analysis of the tutor’s posts, in order to understand more accurately the tutor’s messages characteristics, in their social and cognitive dimensions

Boundary Conditions for Kerr-AdS Perturbations

The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.Comment: 33 pages, 6 figure

AdS nonlinear instability: moving beyond spherical symmetry

Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.Comment: 7 pages, no figures, 2 table