An interrelated approach to teaching mathematics in secondary schools

This thesis is primarily concerned with the production and evaluation of ideas and materials, based upon an interrelated approach to teaching, which is aimed at arousing curiosity and interest in pupils in secondary schools from the age of fourteen upwards. A case is presented for the consideration of such an approach and a brief account given of how early ideas were formulated. These ideas resulted in the establishment of positive guidelines and strategies upon which the research was to be based. Much emphasis is placed on the significance of effective and attractive written materials for pupils with one chapter being specifically aimed at outlining important aspects of general module preparation. The thesis presents in some detail evaluations of trials carried out with groups of students studying a variety of topics involving mathematical principles. It attempts to describe the successes and failures of various modules of study devised during the research programme and takes special account of comments made by pupils and staff who participated in trials. With the recommendation for a new approach to teaching, effective in-service training of teachers is an essential exercise. Various in-service training programmes organised for teachers and ideas produced during these sessions by enthusiastic, stimulated participants are reported. In addition, the thesis contains proposals for the establishment of a professional centre for mathematical education in schools and colleges within Leicestershire where ideas produced from research projects such as this can be extended, developed fully and subsequently disseminated in an effective manner. In conclusion, the achievements of the research programme are discussed and recommendations and suggestions made for wider use of the interrelated approach to teaching in secondary schools

Social determinants of content selection in the age of (mis)information

Despite the enthusiastic rhetoric about the so called \emph{collective intelligence}, conspiracy theories -- e.g. global warming induced by chemtrails or the link between vaccines and autism -- find on the Web a natural medium for their dissemination. Users preferentially consume information according to their system of beliefs and the strife within users of opposite narratives may result in heated debates. In this work we provide a genuine example of information consumption from a sample of 1.2 million of Facebook Italian users. We show by means of a thorough quantitative analysis that information supporting different worldviews -- i.e. scientific and conspiracist news -- are consumed in a comparable way by their respective users. Moreover, we measure the effect of the exposure to 4709 evidently false information (satirical version of conspiracy theses) and to 4502 debunking memes (information aiming at contrasting unsubstantiated rumors) of the most polarized users of conspiracy claims. We find that either contrasting or teasing consumers of conspiracy narratives increases their probability to interact again with unsubstantiated rumors.Comment: misinformation, collective narratives, crowd dynamics, information spreadin

The MSSM invisible Higgs in the light of dark matter and g-2

Giving up the assumption of the gaugino mass unification at the GUT scale, the latest LEP and Tevatron data still allow the lightest supersymmetric Higgs to have a large branching fraction into invisible neutralinos. Such a Higgs may be difficult to discover at the LHC and is practically unreachable at the Tevatron. We argue that, for some of these models to be compatible with the relic density, light sleptons with masses not far above the current limits are needed. There are however models that allow for larger sleptons masses without being in conflict with the relic density constraint. This is possible because these neutralinos can annihilate efficiently through a Z-pole. We also find that many of these models can nicely account, at the 2\sigma level, for the discrepancy in the latest g-2 measurement. However, requiring consistency with the g-2 at the 1\sigma level, excludes models that lead to the largest Higgs branching fraction into LSP's. In all cases one expects that even though the Higgs might escape detection, one would have a rich SUSY phenomenology even at the Tevatron, through the production of charginos and neutralinos.Comment: 16 pages and 5 figures. New references added, text and figures unchange

Cosmological parameters from CMB and other data: a Monte-Carlo approach

We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.Comment: Quintessence results now include perturbations. Changes to match version accepted by PRD. MCMC code and data are available at http://cosmologist.info/cosmomc/ along with a B&W printer-friendly version of the pape

Important marine areas for the conservation of northern rockhopper penguins within the Tristan da Cunha Exclusive Economic Zone

The designation of Marine Protected Areas has become an important approach to conserving marine ecosystems that relies on robust information on the spatial distribution of biodiversity. We used GPS tracking data to identify marine Important Bird and Biodiversity Areas (IBAs) for the endangered northern rockhopper penguin Eudyptes moseleyi within the Exclusive Economic Zone (EEZ) of Tristan da Cunha in the South Atlantic. Penguins were tracked throughout their breeding season from 3 of the 4 main islands in the Tristan da Cunha group. Foraging trips remained largely within the EEZ, with the exception of those from Gough Island during the incubation stage. We found substantial variability in trip duration and foraging range among breeding stages and islands, consistent use of areas among years and spatial segregation of the areas used by neighbouring islands. For colonies with no or insufficient tracking data, we defined marine IBAs based on the mean maximum foraging range and merged the areas identified to propose IBAs around the Tristan da Cunha archipelago and Gough Island. The 2 proposed marine IBAs encompass 2% of Tristan da Cunha’s EEZ, and are used by all northern rockhopper penguins breeding in the Tristan da Cunha group, representing ~90% of the global population. Currently, the main threat to northern rockhopper penguins within the Tristan da Cunha EEZ is marine pollution from shipping, and the risk of this would be reduced by declaring waters within 50 nautical miles of the coast as ‘Areas To Be Avoided

Stigma in health facilities: Why it matters and how we can change it

Stigma in health facilities undermines diagnosis, treatment, and successful health outcomes. Addressing stigma is fundamental to delivering quality healthcare and achieving optimal health. This correspondence article seeks to assess how developments over the past 5 years have contributed to the state of programmatic knowledge - both approaches and methods - regarding interventions to reduce stigma in health facilities, and explores the potential to concurrently address multiple health condition stigmas. It is supported by findings from a systematic review of published articles indexed in PubMed, Psychinfo and Web of Science, and in the United States Agency for International Development's Development Experience Clearinghouse, which was conducted in February 2018 and restricted to the past 5 years. Forty-two studies met inclusion criteria and provided insight on interventions to reduce HIV, mental illness, or substance abuse stigma. Multiple common approaches to address stigma in health facilities emerged, which were implemented in a variety of ways. The literature search identified key gaps including a dearth of stigma reduction interventions in health facilities that focus on tuberculosis, diabetes, leprosy, or cancer; target multiple cadres of staff or multiple ecological levels; leverage interactive technology; or address stigma experienced by health workers. Preliminary results from ongoing innovative responses to these gaps are also described. The current evidence base of stigma reduction in health facilities provides a solid foundation to develop and implement interventions. However, gaps exist and merit further work. Future investment in health facility stigma reduction should prioritize the involvement of clients living with the stigmatized condition or behavior and health workers living with stigmatized conditions and should address both individual and structural level stigma

Simplification and analysis of a model of social interaction in voting

A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the interplay of the different elements present in the system – social influence, heterogeneity and noise – and leads to a better understanding of its properties. The origin of a regime of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the original model