Who makes better use of technology for learning in D&T? Schools or university?

University teacher training departments have many functions in their role as Schools for Initial Teacher Education (ITE), these include accrediting qualified teacher status, teaching subject knowledge and pedagogy, and influencing change in a school subject's content and pedagogy. This paper discusses this latter area. It can be easy for teacher training in universities to become ivory towers, modelling new ideas for curriculum delivery and content in a 'bubble' away from the real world of the school classroom. A centre of design and technology (D&T) education at an English university has undertaken research-led developments in the use of web 2.0 technologies and technology enhanced learning (TEL), modelling how they can be used in the classroom. The research examined in this paper is the next stage of the centre's curriculum development to ensure the relevance of the university curriculum content and practices. Anecdotal evidence suggests that the use of TEL in secondary schools is inconsistent and sporadic with D&T teachers using TEL, with minimal awareness of research available, which could inform their practice. This impacts on the centre's trainee teachers as they begin teaching in schools during their final year of the course, with a possible unrealistic expectation of how TEL is used in schools, based on their university experiences

3D APIs in Interactive Real-Time Systems: Comparison of OpenGL, Direct3D and Java3D.

Since the first display of a few computer-generated lines on a Cathode-ray tube (CRT) over 40 years ago, graphics has progressed rapidly towards the computer generation of detailed images and interactive environments in real time (Angel, 1997). In the last twenty years a number of Application Programmer's Interfaces (APIs) have been developed to provide access to three-dimensional graphics systems. Currently, there are numerous APIs used for many different types of applications. This paper will look at three of these: OpenGL, Direct3D, and one of the newest entrants, Java3D. They will be discussed in relation to their level of versatility, programability, and how innovative they are in introducing new features and furthering the development of 3D-interactive programming

A Bayesian conjugate gradient method (with Discussion)

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about the numerical error. In this paper we propose a novel statistical model for this numerical error set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging

Radiative transfer as a Bayesian linear regression problem

Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their implementation, realistic radiative transfer models remain very computationally expensive, such that one often has to resort to approximate descriptions. The complexity of these models makes it difficult to assess the validity of any approximation and to quantify uncertainties on the model results. This impedes scientific rigour, in particular, when comparing models to observations, or when using their results as input for other models. We present a probabilistic numerical approach to address these issues by treating radiative transfer as a Bayesian linear regression problem. This allows us to model uncertainties on the input and output of the model with the variances of the associated probability distributions. Furthermore, this approach naturally allows us to create reduced-order radiative transfer models with a quantifiable accuracy. These are approximate solutions to exact radiative transfer models, in contrast to the exact solutions to approximate models that are often used. As a first demonstration, we derive a probabilistic version of the method of characteristics, a commonly-used technique to solve radiative transfer problems

Vertices contained in all or in no minimum total dominating set of a tree

AbstractA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree

Testing whether a Learning Procedure is Calibrated

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution, representing uncertainty about $\theta$ after seeing the dataset. Bayesian inference is a prime example of such a procedure but one can also construct other learning procedures that return distributional output. This paper studies conditions for a learning procedure to be considered calibrated, in the sense that the true data-generating parameters are plausible as samples from its distributional output. A learning procedure that is calibrated need not be statistically efficient and vice versa. A hypothesis-testing framework is developed in order to assess, using simulation, whether a learning procedure is calibrated. Finally, we exploit our framework to test the calibration of some learning procedures that are motivated as being approximations to Bayesian inference but are nevertheless widely used