'Recast' in a new light: insights for practice from typical language studies

This article reviews the nature and function of RECASTS, a well-documented way of responding to young children. Recasts have featured in intervention programmes for children with language delay (LD), but with mixed success. The aim of the current review is to provide a theoretically-motivated account of just those recasts that are likely to benefit LD children. To this end, the Contrast theory of corrective input is invoked, where the focus is on adult models that are directly contingent on child errors (Saxton, 1997). Both theoretical and empirical evidence suggests that this kind of input can facilitate the acquisition of adult-like grammatical competenc

Supersaturation for hereditary properties

Let $\mathcal{F}$ be a collection of $r$-uniform hypergraphs, and let $0 < p < 1$. It is known that there exists $c = c(p,\mathcal{F})$ such that the probability of a random $r$-graph in $G(n,p)$ not containing an induced subgraph from $\mathcal{F}$ is $2^{(-c+o(1)){n \choose r}}$. Let each graph in $\mathcal{F}$ have at least $t$ vertices. We show that in fact for every $\epsilon > 0$, there exists $\delta = \delta (\epsilon, p,\mathcal{F}) > 0$ such that the probability of a random $r$-graph in $G(n,p)$ containing less than $\delta n^t$ induced subgraphs each lying in $\mathcal{F}$ is at most $2^{(-c+\epsilon){n \choose r}}$. This statement is an analogue for hereditary properties of the supersaturation theorem of Erd\H{o}s and Simonovits. In our applications we answer a question of Bollob\'as and Nikiforov.Comment: 5 pages, submitted to European Journal of Combinatoric

What's in a name? Coming to terms with the child's linguistic environment

This article reviews the proliferation of terms that have been coined to denote the language environment of the young child. It is argued that terms are often deployed by researchers without due consideration of their appropriateness for particular empirical studies. It is further suggested that just three of the dozen or more available terms meet the needs of child language researchers in most instances: Child Directed Speech, Infant Directed Speech and exposure language. The phenomena denoted by these terms are then considered. The term register is generally borrowed for this purpose from sociolinguistics. However, close inspection of this concept reveals that the notion of register needs to be constrained, in specified ways, in order to be of any real value within the field of child language research

Strictly monotonic multidimensional sequences and stable sets in pillage games

Let $S \subset \mathbb{R}^n$ have size $|S| > \ell^{2^n-1}$. We show that there are distinct points $\{x^1,..., x^{\ell+1}\} \subset S$ such that for each $i \in [n]$, the coordinate sequence $(x^j_i)_{j=1}^{\ell+1}$ is strictly increasing, strictly decreasing, or constant, and that this bound on $|S|$ is best possible. This is analogous to the \erdos-Szekeres theorem on monotonic sequences in $\real$. We apply these results to bound the size of a stable set in a pillage game. We also prove a theorem of independent combinatorial interest. Suppose $\{a^1,b^1,...,a^t,b^t\}$ is a set of $2t$ points in $\real^n$ such that the set of pairs of points not sharing a coordinate is precisely $\{\{a^1,b^1\},...,\{a^t,b^t\}\}$. We show that $t \leq 2^{n-1}$, and that this bound is best possible

Aspire Public Schools: Building the Organizational Capacity for Healthy Growth

Two years into an aggressive expansion plan, Aspire Public Schools was on track in terms of school openings but behind on its goals to add a layer of management. The schools were performing well, but the nonprofit's leaders were stretched paper thin and concerned about the organization's ability to perform in the face of more growth. Determined to build an organization that could support their expansion plans, the Aspire team took swift action. Their initiatives included:Articulating criteria for "healthy growth" that they would use to assess expansion opportunities, thereby incorporating organizational sustainability into any future decisions about growth;Addressing a profound anxiety about hiring "outsiders" and delegating responsibilities to an increasingly larger team;Defining the boundaries of accountability for each of the organization's leadership positions;Clarifying decision-making authority at a broad level, and making explicit the roles and responsibilities associated with specific and potentially contentious decisions

Stability analysis of two-temperature radiative shocks; formulation, eigenfunctions, luminosity response and boundary conditions

We present a general formulation for stability analyses of radiative shocks with multiple cooling processes, longitudinal and transverse perturbations, and unequal electron and ion temperatures. Using the accretion shocks of magnetic cataclysmic variables as an illustrative application, we investigate the shock instabilities by examining the eigenfunctions of the perturbed hydrodynamic variables. We also investigate the effects of varying the condition at the lower boundary of the post-shock flow from a zero-velocity fixed wall to several alternative types of boundaries involving the perturbed hydrodynamic variables, and the variations of the emission from the post-shock flow under different modes of oscillations. We found that the stability properties for flow with a stationary-wall lower boundary are not significantly affected by perturbing the lower boundary condition, and they are determined mainly by the energy-transport processes. Moreover, there is no obvious correlation between the amplitude or phase of the luminosity response and the stability properties of the system. Stability of the system can, however, be modified in the presence of transverse perturbation. The luminosity responses are also altered by transverse perturbation