Connecting mathematics teaching with vocational learning

For many vocational students in England, mathematics is now a compulsory part of their programme, yet the inclusion of an academic subject within a vocational course presents challenges. In this paper, an analysis of a series of case studies of vocational student groups in Further Education colleges in England shows how contrasting practices in ‘functional mathematics’ and vocational classes reinforce perceptions that mathematics is an isolated and irrelevant subject. Some mathematics teachers made contextual connections by embedding mathematical problems in vocationally-related scenarios but distinctive socio-cultural features of vocational learning situations were often absent from mathematics classes. Addressing this disconnection requires a pedagogical approach and classroom culture that links mathematics learning with vocational values. The findings suggest that adopting mathematics classroom practices that reflect the surrounding vocational culture creates greater coherence for students and has positive effects on their engagement with mathematics learning

Connecting mathematics teaching with vocational learning

For many vocational students in England, mathematics is now a compulsory part of their programme, yet the inclusion of an academic subject within a vocational course presents challenges. In this paper, an analysis of a series of case studies of vocational student groups in Further Education colleges in England shows how contrasting practices in ‘functional mathematics’ and vocational classes reinforce perceptions that mathematics is an isolated and irrelevant subject. Some mathematics teachers made contextual connections by embedding mathematical problems in vocationally-related scenarios but distinctive socio-cultural features of vocational learning situations were often absent from mathematics classes. Addressing this disconnection requires a pedagogical approach and classroom culture that links mathematics learning with vocational values. The findings suggest that adopting mathematics classroom practices that reflect the surrounding vocational culture creates greater coherence for students and has positive effects on their engagement with mathematics learning

A Computer Model of Drafting Effects on Collective Behavior in Elite 10,000 m Runners

Purpose Drafting in cycling influences collective behaviour of pelotons. Whilst evidence for collective behaviour in competitive running events exists, it is not clear if this results from energetic savings conferred by drafting. This study modelled the effects of drafting on behavior in elite 10,000 m runners. Methods Using performance data from a men’s elite 10,000 m track running event, computer simulations were constructed using Netlogo 5.1 to test the effects of three different drafting quantities on collective behaviour: no drafting, drafting to 3m behind with up to ~8% energy savings (a realistic running draft); and drafting up to 3m behind with up to 38% energy savings (a realistic cycling draft). Three measures of collective behaviour were analysed in each condition; mean speed, mean group stretch (distance between first and last placed runner), and Runner Convergence Ratio (RCR) which represents the degree of drafting benefit obtained by the follower in a pair of coupled runners. Results Mean speeds were 6.32±0.28m.s-1, 5.57±0.18 m.s-1, and 5.51±0.13 m.s-1 in the cycling draft, runner draft, and no draft conditions respectively (all P<0.001). RCR was lower in the cycling draft condition, but did not differ between the other two. Mean stretch did not differ between conditions. Conclusions Collective behaviours observed in running events cannot be fully explained through energetic savings conferred by realistic drafting benefits. They may therefore result from other, possibly psychological, processes. The benefits or otherwise of engaging in such behavior are, as yet, unclear

A Matrix Model for AdS2

A matrix quantum mechanics with potential $V={q^2 \over r^2}$ and an SL(2,R) conformal symmetry is conjectured to be dual to two-dimensional type 0A string theory on AdS$_2$ with $q$ units of RR flux.Comment: 12 page

`NMR Crystallization': in-situ NMR techniques for time-resolved monitoring of crystallization processes

Solid-state NMR spectroscopy is a well-established and versatile technique for studying structural and dynamic properties of solids, and there is considerable potential to exploit the power and versatility of solid-state NMR for in-situ studies of chemical processes. However, a number of technical challenges are associated with adapting this technique for in-situ studies, depending on the process of interest. Recently, an in-situ solid-state NMR strategy for monitoring the evolution of crystallization processes has been developed and has proven to be a promising approach for identifying the sequence of distinct solid forms present as a function of time during crystallization from solution, and for the discovery of new polymorphs. The latest development of this technique, called “CLASSIC” NMR, allows simultaneous measurement of both liquid-state and solid-state NMR spectra as a function of time, thus yielding complementary information on the evolution of both the liquid phase and the solid phase during crystallization from solution. This article gives an overview of the range of NMR strategies that are currently available for in-situ studies of crystallization processes, with examples of applications that highlight the potential of these strategies to deepen our understanding of crystallization phenomena

The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.Comment: 14 pages, 5 figures, REVTeX4, submitted to PRB; clarification of the diagrammatic technique added, one figure update

Physical restraint in residential child care : the experiences of young people and residential workers

There have long been concerns about the use of physical restraint in residential care. This paper presents the findings of a qualitative study which explores the experiences of children, young people and residential workers about physical restraint. The research identifies the dilemmas and ambiguities for both staff and young people, and participants discuss the situations where they feel physical restraint is appropriate as well as their concerns about unjustified or painful restraints. They describe the negative emotions involved in restraint but also those situations where, through positive relationships and trust, restraint can help young people through unsafe situations

Black Hole Production at LHC: String Balls and Black Holes from pp and Lead-lead Collisions

If the fundamental planck scale is near a TeV, then parton collisions with high enough center-of-mass energy should produce black holes. The production rate for such black holes at LHC has been extensively studied for the case of a proton-proton collision. In this paper, we extend this analysis to a lead-lead collision at LHC. We find that the cross section for small black holes which may in principle be produced in such a collision is either enhanced or suppressed, depending upon the black hole mass. For example, for black holes with a mass around 3 TeV we find that the differential black hole production cross section, d\sigma/dM, in a typical lead-lead collision is up to 90 times larger than that for black holes produced in a typical proton-proton collision. We also discuss the cross-sections for `string ball' production in these collisions. For string balls of mass about 1 (2) TeV, we find that the differential production cross section in a typical lead-lead collision may be enhanced by a factor up to 3300 (850) times that of a proton-proton collision at LHC.Comment: Added some discussion, final version to appear in Phys. Rev. D (rapid communications

Quantum Fields in a Big Crunch/Big Bang Spacetime

We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We discuss a formal correspondence between our construction and quantum field theory on de Sitter spacetime.Comment: 30 pages, RevTex file, five postscript figure file