The Aetiology of Maths Anxiety: Identifying the Influential Factors of Year 4 Pupils’ Attitudes to Mathematics attending Schools in North West England

This study took place during relatively recent times where it was culturally acceptable to say that we are not strong in mathematics in wider society, and some of us establish that lacking ability as part of our identity. Whilst adults in the UK are known to lack numerical skills and have poor attitudes to mathematics, children in primary schools are needed to fulfil the demand of future STEM graduates that the UK is not expected to meet, posing serious future economic risk. Primary schools situate within an increasingly intensified culture of assessment, impacting the practice of teachers and the pupils’ understanding of mathematics as a result. This quantitative study identifies factors of attitudes to mathematics in Year 4 pupils in primary schools located in North West England. The study worked with 10 primary schools, 19 teachers, and 508 pupils, using self-completion questionnaires to measure pupils’ attitudes, aspects of identity, self-confidence, motivation and perceived value of mathematics. Pupils’ teachers who agreed to take part also answered an attitudinal questionnaire measuring their attitudes to mathematics and confidence in teaching. The research also measured the deprivation levels of the schools, along with other standard mathematical performance measures. The current research consists of an innovative newly designed measure, ‘Attitudes 2 Mathematics’. Specifically, this PhD provides evidence to suggest that pupils’ attitudes to mathematics are not only dependent on their own identity and self-confidence, but also by the attitudes of their teachers and the school attended. The findings of this study contribute to the knowledge of: measurements of attitudes to mathematics through new creative means of eliciting responses in questionnaires, such as using Emojis and drawings that can be quantified, and a model that measures and assesses the impacts of multiple factors on pupils’ developing those attitudes

Using Emojis and drawings in surveys to measure children’s attitudes to mathematics

This article considers the implementation of Emojis as responses within survey research, measuring attitudes towards mathematics in children aged eight and nine years old. Participants answered two multi-item scales. The first required them to provide an Emoji to provide their responses to statements, whilst the second additionally required them to draw the Emoji they wished to use. The rationale was to allow children to feel more familiar with the common means of communication used in a ‘digital era’ in order to aid reliability and validity of thge measures. Evidence suggests that future research be carried out to measure and assess children’s attitudes with techniques from the current study to help them understand the nature of what is being researched. This article concludes that children as young as eight years old can be deemed reliable respondents for survey methods and that more research should be carried out to capture children’s attitudes to concepts

Using draw a person tasks to measure children’s assigned Gender Ability Beliefs

The UK-based article develops a quantitative method for measuring 8–9-year-old children’s Gender Ability Beliefs through drawings, assessing the reliability and validity of the measure and its association with respondents’ self-reported gender. The measure, originally used in the US by Beilock et al. (2010), required respondents to draw two pictures: one of someone good at mathematics and another good at reading. They also had to show whether each drawing was of a male or female by ticking a provided box. Findings indicate children are more likely to draw someone of the same assigned gender as their own for both skillsets. Male respondents were found to be more likely to indicate more traditional views in males being good at mathematics and females good at reading. The article concludes that drawings can be used as quantitative self-completion methods with child respondents, whilst presenting evidence to consider how we do so with concepts like gender that require validity and can be used internationally

Towards an Accurate Determination of Parameters for Very Massive Stars: the Eclipsing Binary LMC-SC1-105

This paper presents a photometric and spectroscopic study of the bright blue eclipsing binary LMC-SC1-105, selected from the OGLE catalog as a candidate host of very massive stars (>=30Mo). The system is found to be a double-lined spectroscopic binary, which indeed contains massive stars. The masses and radii of the components are M1= 30.9+/-1.0 Mo, M2= 13.0+/-0.7 Mo, and R1= 15.1+/-0.2 Ro, R2= 11.9+/-0.2 Ro, respectively. The less massive star is found to be filling its Roche lobe, indicating the system has undergone mass-transfer. The spectra of LMC-SC1-105 display the Struve-Sahade effect, with the HeI lines of the secondary appearing stronger when it is receding and causing the spectral types to change with phase (O8+O8 to O7+O8.5). This effect could be related to the mass-transfer in this system. To date, accurate (<=10%) fundamental parameters have only been measured for 15 stars with masses greater than 30 Mo, with the reported measurements contributing valuable data on the fundamental parameters of very massive stars at low metallicity. The results of this work demonstrate that the strategy of targeting the brightest blue stars in eclipsing binaries is an effective way of studying very massive stars.Comment: 32 pages, 13 figures, 5 tables; accepted for publication in The Astrophysical Journa

On the cross-section of Dark Matter using substructure infall into galaxy clusters

We develop a statistical method to measure the interaction cross-section of Dark Matter, exploiting the continuous minor merger events in which small substructures fall into galaxy clusters. We find that by taking the ratio of the distances between the galaxies and Dark Matter, and galaxies and gas in accreting sub-halos, we form a quantity that can be statistically averaged over a large sample of systems whilst removing any inherent line-of-sight projections. In order to interpret this ratio as a cross-section of Dark Matter we derive an analytical description of sub-halo infall which encompasses; the force of the main cluster potential, the drag on a gas sub-halo, a model for Dark Matter self-interactions and the resulting sub-halo drag, the force on the gas and galaxies due to the Dark Matter sub-halo potential, and finally the buoyancy on the gas and Dark Matter. We create mock observations from cosmological simulations of structure formation and find that collisionless Dark Matter becomes physically separated from X-ray gas by up to 20h^-1 kpc. Adding realistic levels of noise, we are able to predict achievable constraints from observational data. Current archival data should be able to detect a difference in the dynamical behaviour of Dark Matter and standard model particles at 6 sigma, and measure the total interaction cross-section sigma/m with 68% confidence limits of +/- 1cm2g^-1. We note that this method is not restricted by the limited number of major merging events and is easily extended to large samples of clusters from future surveys which could potentially push statistical errors to 0.1cm^2g^-1.Comment: 14 pages, 11 figure

Retrieving the three-dimensional matter power spectrum and galaxy biasing parameters from lensing tomography

With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining galaxy-galaxy lensing and galaxy clustering, this can be extended to probe the 3D galaxy-matter and galaxy-galaxy power spectrum or, alternatively, galaxy biasing parameters. To achieve this aim, this paper introduces and discusses minimum variance estimators and a more general Bayesian approach to statistically invert a set of noisy tomography 2-point correlation functions, measured within a confined opening angle. Both methods are constructed such that they probe deviations of the power spectrum from a fiducial power spectrum, thereby enabling both a direct comparison of theory and data, and in principle the identification of the physical scale and redshift of deviations. By devising a new Monte Carlo technique, we quantify the measurement noise in the correlators for a fiducial survey, and test the performance of the inversion techniques. We conclude that a shear tomography analysis of near future weak lensing surveys promises fruitful insights into the effect of baryons on the nonlinear matter power spectrum at z<~0.3 around k~2 h/Mpc, and into galaxy biasing (z<~0.5). However, a proper treatment of anticipated systematics -- not included in the mock analysis but discussed here -- is likely to reduce the signal-to-noise in the analysis so that a robust assessment of the 3D matter power spectrum probably asks for a survey area of at least 1000 sdeg. [Abridged]Comment: 17 pages, 11 figures, accepted for publication by A&A; latest update is subject to language correction

A proposal for detecting second order topological quantum phase

Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.Comment: 7 pages, 4 figure

Social Enterprise in the United Kingdom: Models and Trajectories

This paper begins by describing (in part A) the UK concept of social enterprise and how it is operationalised (section A.1); this is followed by an overview of the challenges of estimating the population of social enterprise in the UK, despite or because of different government-sponsored surveys (section A.2); this first part concludes with a review of the evolution of policy discourse for social enterprise (section A.3). The second part of the paper goes on to describe (sections B.1 to B.4) the different models that have evolved from different origins in the UK (with the main emphasis being on experience in England); in order to contextualise an understanding of these models, it describes three fields (section B.5)—work integration, community development, and public services; these illustrate the fluidity of models in the UK, where typically different models may be found within each field. Finally, Part C describes at a general level the relevant institutional frameworks and trajectories of the main social enterprise models

High Resolution K-band Spectroscopy of MWC 480 and V1331 Cyg

We present high resolution (R=25,000-35,000) K-band spectroscopy of two young stars, MWC 480 and V1331 Cyg. Earlier spectrally dispersed (R=230) interferometric observations of MWC 480 indicated the presence of an excess continuum emission interior to the dust sublimation radius, with a spectral shape that was interpreted as evidence for hot water emission from the inner disk of MWC 480. Our spectrum of V1331 Cyg reveals strong emission from CO and hot water vapor, likely arising in a circumstellar disk. In comparison, our spectrum of MWC 480 appears mostly featureless. We discuss possible ways in which strong water emission from MWC 480 might go undetected in our data. If strong water emission is in fact absent from the inner disk, as our data suggest, the continuum excess interior to the dust sublimation radius that is detected in the interferometric data must have another origin. We discuss possible physical origins for the continuum excess.Comment: 29 pages, 5 figures, to appear in Ap