Tracking and mixed-ability grouping in secondary school mathematics classrooms: a case study

This paper reports the findings of a retrospective study of ‘tracked’ grouping in a mathematics department in a co-educational comprehensive school in Greater London. Tracking consisted here of just two tracks, a 'fast track' for the top 25-30% of a cohort, and 'mixed tracks' for the remainder. The paper outlines the reasons for introducing tracking and explores the effects of this through analysis of interviews with teachers and data on the progress of students from age 14 to age 16. The teachers reported that tracking impacted differently on different students, and this is borne out by the quantitative data. It was not possible to provide for ‘setting’ across all the mathematics classrooms in the focal cohort, and one mixedability class was created. The use of analysis of covariance (ANCOVA) models shows that fast-track students were not significantly advantaged by their placement in these tracks, but the progress of students in the mixed-ability group showed a significant interaction between progress and prior attainment, with placement in the mixed-ability group conferring a significant advantage on lower-attaining students, while the disadvantage to higher attaining students was much smaller

Evolution of twist-shear and dip-shear in Faring active region NOAA 10930

We study the evolution of magnetic shear angle in a flare productive active region NOAA 10930. The magnetic shear angle is defined as the deviation in the orientation of the observed magnetic field vector with respect to the potential field vector. The shear angle is measured in horizontal as well as vertical plane. The former is computed by taking the difference between the azimuth angles of the observed and potential field and is called the twist-shear, while the latter is computed by taking the difference between the inclination angles of the observed and potential field and is called the dip-shear. The evolution of the two shear angles is then tracked over a small region located over the sheared penumbra of the delta sunspot in NOAA 10930. We find that, while the twist-shear shows an increasing trend after the flare the dip-shear shows a significant drop after the flare.Comment: 4 pages, Proceedings of IAU Symposium 273 "Physics of Sun and Starspots" Eds. D.P. Choudhary and K.G. Strassmeie

Density Measurements in the Base Flow Region of HRV Afterbody-Nozzle Configuration

A preliminary study to document the mean density field using Background Oriented Schlieren (BOS) has been carried out on a 1:10 scaled model of HSTDV afterbodynozzle configuration system at a freestream Mach number of 3.5 with unit Reynolds number of 38x106 per meter. The results show that the mean density field is quite adequately captured with the BOS technique with the derived Schlieren results matching well with conventional Schlieren images and with density data derived from pressure measurements on the ramp. While the data at nozzle exit is not reliable due to strong asymmetric 3D effects, presumably due to the flow expansion on the cowl lip influencing the flow field in the vicinity, the results show that flow field variable like density shows local effects better (e.g. local effect of the cowl extension) and this has been captured by the BOS whereas the wall static pressures do not show this effect. Streamwise variation of the density along the jet centerline and parallel to the ramp are presented showing that useful quantitative information can be extracted through this technique. The results would be useful for CFD code

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes

Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect ratio AR = Δy/Δx < < 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed

Convolutional Dictionary Regularizers for Tomographic Inversion

There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a regularizer. The key contribution is the use of a data-dependent weighting scheme for the l1 regularization to construct an effective denoising method that is integrated into the inversion using the Plug-and-Play reconstruction framework. Using simulated data sets we demonstrate that our approach can improve performance over traditional regularizers based on a Markov random field model and a patch-based sparse representation model for sparse and limited-view tomographic data sets