Exploiting unexpected situations in the mathematics classroom

The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement

Data mining: a tool for detecting cyclical disturbances in supply networks.

Disturbances in supply chains may be either exogenous or endogenous. The ability automatically to detect, diagnose, and distinguish between the causes of disturbances is of prime importance to decision makers in order to avoid uncertainty. The spectral principal component analysis (SPCA) technique has been utilized to distinguish between real and rogue disturbances in a steel supply network. The data set used was collected from four different business units in the network and consists of 43 variables; each is described by 72 data points. The present paper will utilize the same data set to test an alternative approach to SPCA in detecting the disturbances. The new approach employs statistical data pre-processing, clustering, and classification learning techniques to analyse the supply network data. In particular, the incremental k-means clustering and the RULES-6 classification rule-learning algorithms, developed by the present authors’ team, have been applied to identify important patterns in the data set. Results show that the proposed approach has the capability automatically to detect and characterize network-wide cyclical disturbances and generate hypotheses about their root cause

Directors of public health as ‘a protected species’: qualitative study of the changing role of public health professionals in England following the 2013 reforms

Background: The Health and Social Care Act 2012 gave councils in England responsibility for improving the health of their populations. Public health teams were transferred from the NHS, accompanied by a ring-fenced public health grant. This study examines the changing role of these teams within local government. Methods: In-depth case study research was conducted within 10 heterogeneous councils. Initial interviews (n=90) were carried out between October 2015 and March 2016, with follow-up interviews (n=21) 12 months later. Interviewees included elected members, directors of public health (DsPH) and other local authority officers, plus representatives from NHS commissioners, the voluntary sector and Healthwatch. Results: Councils welcomed the contribution of public health professionals, but this was balanced against competing demands for financial resources and democratic leverage. DsPH – seen by some as a ‘protected species’ – were relying increasingly on negotiating and networking skills to fulfil their role. Both the development of the existing specialist public health workforce and recruitment to, and development of, the future workforce were uncertain. This poses both threats and opportunities. Conclusions: Currently the need for staff to retain specialist skills and maintain UKPH registration is respected. However, action is needed to address how future public health professionals operating within local government will be recruited and developed

STEREO and ACE observations of CIR particles

In the present solar minimum, corotating interaction regions (CIRs) produce frequent particle enhancements at 1 AU as observed at STEREO and ACE. As the two STEREO spacecraft move apart, differences in CIR time profiles observed at each spacecraft are becoming large. The timing differences are often roughly similar to the corotation time lag between the two spacecraft, however many of the features seen at Ahead and Behind require more than just a time shift. Perhaps transient disturbances in the solar wind affect connection to or transport from the shock, or temporal changes occur in the CIR shock itself. Additional timing differences of >1 day result from the different heliographic latitudes of the two STEREO spacecraf

Anomalous Microwave Emission from the HII region RCW175

We present evidence for anomalous microwave emission in the RCW175 \hii region. Motivated by 33 GHz 13\arcmin resolution data from the Very Small Array (VSA), we observed RCW175 at 31 GHz with the Cosmic Background Imager (CBI) at a resolution of 4\arcmin. The region consists of two distinct components, G29.0-0.6 and G29.1-0.7, which are detected at high signal-to-noise ratio. The integrated flux density is $5.97\pm0.30$ Jy at 31 GHz, in good agreement with the VSA. The 31 GHz flux density is $3.28\pm0.38$ Jy ($8.6\sigma$) above the expected value from optically thin free-free emission based on lower frequency radio data and thermal dust constrained by IRAS and WMAP data. Conventional emission mechanisms such as optically thick emission from ultracompact \hii regions cannot easily account for this excess. We interpret the excess as evidence for electric dipole emission from small spinning dust grains, which does provide an adequate fit to the data.Comment: 5 pages, 2 figures, submmited to ApJ Letter

Systematic review of economic evaluations and cost analyses of guideline implementation strategies

Objectives To appraise the quality of economic studies undertaken as part of evaluations of guideline implementation strategies; determine their resources use; and recommend methods to improve future studies. Methods Systematic review of economic studies undertaken alongside robust study designs of clinical guideline implementation strategies published (1966-1998). Studies assessed against the BMJ economic evaluations guidelines for each stage of the guideline process (guideline development, implementation and treatment). Results 235 studies were identified, 63 reported some information on cost. Only 3 studies provided evidence that their guideline was effective and efficient. 38 reported the treatment costs only, 12 implementation and treatment costs, 11 implementation costs alone, and two guideline development, implementation and treatment costs. No study gave reasonably complete information on costs. Conclusions Very few satisfactory economic evaluations of guideline implementation strategies have been performed. Current evaluations have numerous methodological defects and rarely consider all relevant costs and benefits. Future evaluations should focus on evaluating the implementation of evidence based guidelines. Keywords: Cost-effectiveness analysis, physician (or health care professional) behaviour, practice guidelines, quality improvement, systematic review.Peer reviewedAuthor versio

Constraints on Free-Free Emission from Anomalous Microwave Emission Sources in the Perseus Molecular Cloud

We present observations performed with the Green Bank Telescope at 1.4 and 5 GHz of three strips coincident with the anomalous microwave emission features previously identified in the Perseus molecular cloud at 33 GHz with the Very Small Array. With these observations we determine the level of the low frequency (~1-5 GHz) emission. We do not detect any significant extended emission in these regions and we compute conservative 3σ upper limits on the fraction of free-free emission at 33 GHz of 27%, 12%, and 18% for the three strips, indicating that the level of the emission at 1.4 and 5 GHz cannot account for the emission observed at 33 GHz. Additionally, we find that the low frequency emission is not spatially correlated with the emission observed at 33 GHz. These results indicate that the emission observed in the Perseus molecular cloud at 33 GHz, is indeed in excess over the low frequency emission, hence confirming its anomalous nature

The occupation of a box as a toy model for the seismic cycle of a fault

We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.Comment: Final version of the published paper, with an erratum and an unpublished appendix with some proof

Vacuum ultraviolet and infrared spectra of condensed methyl acetate on cold astrochemical dust analogs

Following the recent report of the first identification of methyl acetate (CH3COOCH3) in the interstellar medium (ISM) we have carried out Vacuum UltraViolet (VUV) and InfraRed (IR) spectroscopy studies on methyl acetate from 10 K until sublimation in an ultrahigh vacuum (UHV) chamber simulating astrochemical conditions. We present the first VUV and IR spectra of methyl acetate relevant to ISM conditions. Spectral signatures clearly showed molecular reorientation to have started in the ice by annealing the amorphous ice formed at 10 K. An irreversible phase change from amorphous to crystalline methyl acetate ice was found to be between 110 K and 120 K