Scaffolding: integrating social and cognitive perspectives on children’s learning at home

Since the translation and cultural assimilation of Vygotsky’s (1978) ideas into the English-speaking academic community from the 1970s, through thinkers such as Wertsch (1984), Vygotsky’s ideas continue to have a powerful influence in psychology and education, as well as being enthusiastically appropriated in other fields such as technology-mediated education (Luckin, 2003). As academics working across these disciplines, we felt the time was right to reflect on the use of socio-cultural theory, and the concept of scaffolding in particular, in understanding parent-child tutoring interactions at home, with reference to children’s academic achievement at school. Thanks to funding from the British Psychological Society, we ran a series of three seminars, and this Special Issue arises from questions raised there

Fractional charge excitations in fermionic ladders

The system of interacting spinless fermions hopping on a two-leg ladder in the presence of an external magnetic field is shown to possess a long range order: the bond density wave or the staggered flux phase. In both cases the elementary excitations are $Z_2$ kinks and carry one half the charge of an electron.Comment: 4 pages, 3 figure

Mathematics, mastery and metacognition: how adding a creative approach can support children in maths

Background: Children who hold an incremental view of ability show greater perseverance, improved help-seeking skills and are better able to cope with unexpected challenges. Classroom instruction can influence how children view themselves as learners. Aim: To explore how mastery-orientated classroom instruction, collaborative learning and metacognitive reflection can foster learners’ attitudes to their task performance. We hypothesised that using a mastery-oriented approach within a mathematics curriculum encourages metacognition, improves motivation and helps children achieve an underlying understanding of mathematical concepts thus improving mathematics performance. Method: This paper reports an 11-week project aiming to embed problem-solving strategies within a mastery-oriented whole-class environment. Children completed pre- and post-task semi-structured interviews and maths problems in addition to the 11-week collaborative maths project. Participants were 24 children from a rural primary school in East Sussex, 12 boys and 12 girls (mean age 8 years and 9 months). The interviews are presented qualitatively and a repeated measures analysis of variance on mathematics motivation and performance was conducted. Findings: The learners showed increased metacognitive reflection on learning strategies as well as increases in girls’ motivation for mathematics. Limitations: This is a small sample size and, being conducted within a typical everyday classroom, there were several uncontrolled variables. Although change was evident in both attitude and maths scores, it was difficult to apportion added value to the different variables contributing to the change in maths scores. Conclusions: Challenging children’s perceptions of mathematics encouraged greater self-reflection and increased motivation for girls

The effect of a local perturbation in a fermionic ladder

We study the effect of a local external potential on a system of two parallel spin-polarized nanowires placed close to each other. For single channel nanowires with repulsive interaction we find that transport properties of the system are highly sensitive to the transverse gradient of the perturbation: the asymmetric part completely reflects the electrons leading to vanishing conductance at zero temperature, while the flat potential remains transparent. We envisage a possible application of this unusual property in the sensitive measurement of local potential field gradients.Comment: 4+ pages, 2 figures, typos correcte

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte

A new stall-onset criterion for low speed dynamic-stall

The Beddoes/Leishman dynamic-stall model has become one of the most popular for the provision of unsteady aerofoil data embedded in much larger codes. The underlying modeling philosophy was that it should be based on the best understanding, or description, of the associated physical phenomena. Even though the model was guided by the flow physics, it requires significant empirical inputs in the form of measured coefficients and constants. Beddoes provided these for a Mach number range of 0.3–0.8. This paper considers one such input for a Mach number of 0.12, where, from the Glasgow data, it is shown that the current stall-onset criterion, and subsequent adjustments, yield problematic results. A new stall criterion is proposed and developed in the best traditions of the model. It is shown to be very capable of reconstructing the Glasgow's data for stall onset both the ramp-up and oscillatory tests

The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure

A complete classification of spherically symmetric perfect fluid similarity solutions

We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such solutions are described by two parameters and they can be classified in terms of their behaviour at large and small distances from the origin; this usually corresponds to large and small values of z but (due to a coordinate anomaly) it may also correspond to finite z. We base our analysis on the demonstration that all similarity solutions must be asymptotic to solutions which depend on either powers of z or powers of lnz. We show that there are only three similarity solutions which have an exact power-law dependence on z: the flat Friedmann solution, a static solution and a Kantowski-Sachs solution (although the latter is probably only physical for a1/5, there are also two families of solutions which are asymptotically (but not exactly) Minkowski: the first is asymptotically Minkowski as z tends to infinity and is described by one parameter; the second is asymptotically Minkowski at a finite value of z and is described by two parameters. A complete analysis of the dust solutions is given, since these can be written down explicitly and elucidate the link between the z>0 and z<0 solutions. Solutions with pressure are then discussed in detail; these share many of the characteristics of the dust solutions but they also exhibit new features.Comment: 63 pages. To appear in Physical Review