How high school learners of Spanish respond to a flipped classroom : an analysis of performance & involvement

Although many studies have examined “flipped classrooms” (essentially the inversion of presentational and practice learning spaces, Bergman & Sams, 2012; Bledsoe 2015; Bretzman, 2013; Lockwood & Folse, 2014; Pasisis, 2014; Plunkett & Beckerman, 2014), few have examined flipping foreign language classes and even fewer have examined the practice in high schools (Huang & Hong, 2016; Hao 2016). In addition, although a large number of blogs, teacher forums and online help pages address flipped language classrooms, few empirical studies have appeared in peer-reviewed journals. Consequently, the efficacy of the flipped classroom approach in the foreign language high-school classroom has not been adequately assessed. The purpose of this study was to better understand learning interactions and outcomes of secondary Spanish 2 students within a flipped classroom environment. The nine -week action research project assessed the flipped classroom approach for two high-school Spanish classes. The study investigated the process of learning second year Spanish at a private high school through a collection of questionnaires, teaching artifacts, and assessment data. Involvement with the flipped materials and student performance on daily quizzes proved to explain most of the variation in grades and other outcome measures. Data analysis showed students to be classified into four groups: high-performance high-involvement, low-performance high-involvement, high-performance low-involvement, and low-performance low-involvement. The study found that effective learners reported a range of learning strategies which they used to select the best methods to practice the target language concepts. A variety of learning strategies in addition to efficient choice of time and investment corresponded with increased performance in the Spanish class. The flipped classroom was an effective approach to teaching Spanish for secondary students in this study. The study also found that some learners needed support in selecting learning strategies, managing time, and remaining accountable. Teachers who want to implement flipped high school Spanish classrooms should pay attention to individual student involvement and performance for this approach to achieve maximal effect.Foreign Language Educatio

Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels, Garcke, and Gr\"un for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter.Comment: 33 page

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Expansion in SL_d(Z/qZ), q arbitrary

Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G) with respect to the generating set pi_q(S) form a family of expanders, where pi_q is the projection map Z->Z/qZ

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Maximal regularity for non-autonomous equations with measurable dependence on time

In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the $L^p$-boundedness of a class of vector-valued singular integrals which does not rely on H\"ormander conditions in the time variable. This is then used to develop an abstract operator-theoretic approach to maximal regularity. The results are applied to the case of $m$-th order elliptic operators $A$ with time and space-dependent coefficients. Here the highest order coefficients are assumed to be measurable in time and continuous in the space variables. This results in an $L^p(L^q)$-theory for such equations for $p,q\in (1, \infty)$. In the final section we extend a well-posedness result for quasilinear equations to the time-dependent setting. Here we give an example of a nonlinear parabolic PDE to which the result can be applied.Comment: Application to a quasilinear equation added. Accepted for publication in Potential Analysi