THE INFLUENCE OF TEACHERS’ PRESENTATIONS ON PUPILS’ MENTAL REPRESENTATIONS

Teachers use a variety of external representations to communicate mathematical ideas to their pupils. This paper reports a preliminary study of the internal mental representations that 6- and 7- year-old pupils form as a result of their interactions with the teacher's verbal, written, pictorial and concrete material representations, involving two-digit numbers and operations on them. The results presented here concern the picture-like mental representations that pupils use in performing two-digit calculations mentally. The evidence suggests that pupils seldom spontaneously visualise teachers’ representations or attempt mental manipulation of visual images to help with calculation. Pupils can, however, have mental representations which reproduce some aspects of the teachers’ representations.     

Locating starting points in differential equations: a realistic mathematics education approach

The paper reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the learning and teaching of collegiate mathematics, using differential equations as a specific case. This report focuses on the RME design heuristic of guided reinvention as a means to locate a starting point for an instructional sequence for first-order differential equations and highlights the cyclical process instructional design and analysis of student learning. The instance of starting with a rate of change equation as an experientially real mathematical context is taken as a case for illustrating how university students might experience the creation of mathematical ideas. In particular, it is shown how three students came to reason conceptually about rate and in the process, develop their own informal Euler method for approximating solution functions to differential equations.     

Integrated distribution and loading planning via a compact metaheuristic algorithm

The present article examines a vehicle routing problem integrated with two-dimensional loading constraints, called 2L-CVRP. The problem is aimed at generating the optimal route set for satisfying customer demand. In addition, feasible loading arrangements have to be determined for the transported products. To solve 2L-CVRP, we propose a metaheuristic solution approach. The basic advantage of our approach lies at its compact structure, as in total, only two parameters affect the algorithmic performance. To optimize the routing aspects, we propose a local-search method equipped with an effective diversification component based on the regional aspiration criteria. The problem’s loading requirements are tackled by employing a two-dimensional packing heuristic which repetitively attempts to develop feasible loading patterns. These attempts are effectively coordinated via an innovative, simple-structured memory mechanism. The overall solution framework makes use of several memory components for drastically reducing the computational effort required. The performance of our metaheuristic development has been successfully evaluated on benchmark instances considering two distinct versions of the loading constraints. More specifically, the algorithm managed to improve or match the majority of best known solution scores for both problem versions.     

Covariance Decompositions for Accurate Computation in Bayesian Scale-Usage Models

Analyses of multivariate ordinal probit models typically use data augmentation to link the observed (discrete) data to latent (continuous) data via a censoring mechanism defined by a collection of “cutpoints.” Most standard models, for which effective Markov chain Monte Carlo (MCMC) sampling algorithms have been developed, use a separate (and independent) set of cutpoints for each element of the multivariate response. Motivated by the analysis of ratings data, we describe a particular class of multivariate ordinal probit models where it is desirable to use a common set of cutpoints. While this approach is attractive from a data-analytic perspective, we show that the existing efficient MCMC algorithms can no longer be accurately applied. Moreover, we show that attempts to implement these algorithms by numerically approximating required multivariate normal integrals over high-dimensional rectangular regions can result in severely degraded estimates of the posterior distribution. We propose a new data augmentation that is based on a covariance decomposition and that admits a simple and accurate MCMC algorithm. Our data augmentation requires only that univariate normal integrals be evaluated, which can be done quickly and with high accuracy. We provide theoretical results that suggest optimal decompositions within this class of data augmentations, and, based on the theory, recommend default decompositions that we demonstrate work well in practice. This article has supplementary material online.     

Comparative study of microscopic charge dynamics in crystalline acceptor-substituted oligothiophenes

By performing microscopic charge transport simulations for a set of crystalline dicyanovinyl-substituted oligothiophenes, we find that the internal acceptor-donor-acceptor molecular architecture combined with thermal fluctuations of dihedral angles results in large variations of local electric fields, substantial energetic disorder, and pronounced Poole-Frenkel behavior, which is unexpected for crystalline compounds. We show that the presence of static molecular dipoles causes large energetic disorder, which is mostly reduced not by compensation of dipole moments in a unit cell but by molecular polarizabilities. In addition, the presence of a well-defined π-stacking direction with strong electronic couplings and short intermolecular distances turns out to be disadvantageous for efficient charge transport since it inhibits other transport directions and is prone to charge trapping.     

Giant magnetoelastic effect at the opening of a spin-gap in Ba3BiIr2O9

As compared to 3d (first-row) transition metals, the 4d and 5d transition metals have much more diffuse valence orbitals. Quantum cooperative phenomena that arise due to changes in the way these orbitals overlap and interact, such as magnetoelasticity, are correspondingly rare in 4d and 5d compounds. Here, we show that the 6H-perovskite Ba(3)BiIr(2)O(9), which contains 5d Ir(4+) (S = 1/2) dimerized into isolated face-sharing Ir(2)O(9) bioctahedra, exhibits a giant magnetoelastic effect, the largest of any known 5d compound, associated with the opening of a spin-gap at T* = 74 K. The resulting first-order transition is characterized by a remarkable 4% increase in Ir-Ir distance and 1% negative thermal volume expansion. The transition is driven by a dramatic change in the interactions among Ir 5d orbitals, and represents a crossover between two very different, competing, ground states: one that optimizes direct Ir-Ir bonding (at high temperature), and one that optimizes Ir-O-Ir magnetic superexchange (at low temperature).     

Validation of a microsimulation of the Port of Dover

Modelling and simulating the traffic of heavily used but secure environments such as seaports and airports are of increasing importance. Errors made when simulating these environments can have long standing economic, social and environmental implications. This article discusses issues and problems that may arise when designing a simulation strategy. Data for the Port is presented, methods for lightweight vehicle assessment that can be used to calibrate and validate simulations are also discussed along with a diagnosis of overcalibration issues. We show that decisions about where the intelligence lies in a system has important repercussions for the reliability of system statistics. Finally, conclusions are drawn about how microsimulations can be moved forward as a robust planning tool for the 21st century.     

On whether azimuthal isotropy and alongshelf translational invariance are present in low-frequency acoustic propagation along the New Jersey shelfbreak

To understand the issues associated with the presence (or lack) of azimuthal isotropy and horizontal (along isobath) invariance of low-frequency (center frequencies of 600 Hz and 900 Hz) acoustic propagation in a shelfbreak environment, a series of experiments were conducted under the Autonomous Wide-Aperture Cluster for Surveillance component of the Shallow Water 2006 experiment. Transmission loss data reported here were from two mobile acoustic sources executing (nearly) circular tracks transmitting to sonobuoy receivers in the circle centers, and from one 12.5 km alongshelf acoustic track. The circle radii were 7.5 km. Data are from September 8, 2006. Details of the acoustic and environmental measurements are presented. Simple analytic and computer models are used to assess the variability expected due to the ocean and seabed conditions encountered. A comparison of model results and data is made, which shows preliminary consistency between the data and the models, but also points towards further work that should be undertaken specifically in enlarging the range and frequency parameter space, and in looking at integrated transmission loss.