Mathematically gifted and talented learners: Theory and practice

This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development

Multipolarity of quasicontinuum γ-rays from collective high-spin states in 152Dy

Measured internal conversion coefficients for quasicontinuum transitions in 152Dy in the spin range of 30–50 establish their predominantly stretched E2 character. Those transitions are attributed to triaxial bands near the yrast line as calculated in terms of the cranking approximation using the Woods-Saxon potential

Classification of Westminster Parliamentary constituencies using e-petition data

In a representative democracy it is important that politicians have knowledge of the desires, aspirations and concerns of their constituents. Opportunities to gauge these opinions are however limited and, in the era of novel data, thoughts turn to what alternative, secondary, data sources may be available to keep politicians informed about local concerns. One such source of data are signatories to electronic petitions (e-petitions). Such e-petitions have risen greatly in popularity over the past decade and allow members of the public to initiate and sign an e-petition online, with popular e-petitions resulting in media attention, a response from the government or ultimately a debate in parliament. These data are thus novel in their availability and have not yet been widely used for research purposes. In this article we will use the e-petition data to show how semantic classes of Westminster Parliamentary constituencies, fitted as Gaussian finite mixture models via EM algorithm, can be used to typify constituencies. We identify four classes: Domestic Liberals; International Liberals; Nostalgic Brits and Rural Concerns, and illustrate how they map onto electoral results. The findings and the utility of this approach to incorporate new e-petitions and adapt to changes in electoral geography are discussed

Stable isotope analysis provides new information on winter habitat use of declining avian migrants that is relevant to their conservation

Winter habitat use and the magnitude of migratory connectivity are important parameters when assessing drivers of the marked declines in avian migrants. Such information is unavailable for most species. We use a stable isotope approach to assess these factors for three declining African-Eurasian migrants whose winter ecology is poorly known: wood warbler Phylloscopus sibilatrix, house martin Delichon urbicum and common swift Apus apus. Spatially segregated breeding wood warbler populations (sampled across a 800 km transect), house martins and common swifts (sampled across a 3,500 km transect) exhibited statistically identical intra-specific carbon and nitrogen isotope ratios in winter grown feathers. Such patterns are compatible with a high degree of migratory connectivity, but could arise if species use isotopically similar resources at different locations. Wood warbler carbon isotope ratios are more depleted than typical for African-Eurasian migrants and are compatible with use of moist lowland forest. The very limited variance in these ratios indicates specialisation on isotopically restricted resources, which may drive the similarity in wood warbler populations' stable isotope ratios and increase susceptibility to environmental change within its wintering grounds. House martins were previously considered to primarily use moist montane forest during the winter, but this seems unlikely given the enriched nature of their carbon isotope ratios. House martins use a narrower isotopic range of resources than the common swift, indicative of increased specialisation or a relatively limited wintering range; both factors could increase house martins' vulnerability to environmental change. The marked variance in isotope ratios within each common swift population contributes to the lack of population specific signatures and indicates that the species is less vulnerable to environmental change in sub-Saharan Africa than our other focal species. Our findings demonstrate how stable isotope research can contribute to understanding avian migrants' winter ecology and conservation status

Occupational cancer in Britain: Exposure assessment methodology

To estimate the current occupational cancer burden due to past exposures in Britain, estimates of the number of exposed workers at different levels are required, as well as risk estimates of cancer due to the exposures. This paper describes the methods and results for estimating the historical exposures. All occupational carcinogens or exposure circumstances classified by the International Agency for Research on Cancer as definite or probable human carcinogens and potentially to be found in British workplaces over the past 20–40 years were included in this study. Estimates of the number of people exposed by industrial sector were based predominantly on two sources of data, the CARcinogen EXposure (CAREX) database and the UK Labour Force Survey. Where possible, multiple and overlapping exposures were taken into account. Dose–response risk estimates were generally not available in the epidemiological literature for the cancer–exposure pairs in this study, and none of the sources available for obtaining the numbers exposed provided data by different levels of exposure. Industrial sectors were therefore assigned using expert judgement to ‘higher'- and ‘lower'-exposure groups based on the similarity of exposure to the population in the key epidemiological studies from which risk estimates had been selected. Estimates of historical exposure prevalence were obtained for 41 carcinogens or occupational circumstances. These include exposures to chemicals and metals, combustion products, other mixtures or groups of chemicals, mineral and biological dusts, physical agents and work patterns, as well as occupations and industries that have been associated with increased risk of cancer, but for which the causative agents are unknown. There were more than half a million workers exposed to each of six carcinogens (radon, solar radiation, crystalline silica, mineral oils, non-arsenical insecticides and 2,3,7,8-tetrachlorodibenzo-p-dioxin); other agents to which a large number of workers are exposed included benzene, diesel engine exhaust and environmental tobacco smoke. The study has highlighted several industrial sectors with large proportions of workers potentially exposed to multiple carcinogens. The relevant available data have been used to generate estimates of the prevalence of past exposure to occupational carcinogens to enable the occupational cancer burden in Britain to be estimated. These data are considered adequate for the present purpose, but new data on the prevalence and intensity of current occupational exposure to carcinogens should be collected to ensure that future policy decisions be based on reliable evidence

Comparison of the haptic and visual deviations in a parallelity task

Deviations in both haptic and visual spatial experiments are thought to be caused by a biasing influence of an egocentric reference frame. The strength of this influence is strongly participant-dependent. By using a parallelity test, it is studied whether this strength is modality-independent. In both haptic and visual conditions, large, systematic and participant-dependent deviations were found. However, although the correlation between the haptic and visual deviations was significant, the explained variance due to a common factor was only 20%. Therefore, the degree to which a participant is “egocentric” depends on modality and possibly even more generally, on experimental condition

Short-term efficacy of physical interventions in osteoarthritic knee pain. A systematic review and meta-analysis of randomised placebo-controlled trials.

BACKGROUND: Treatment efficacy of physical agents in osteoarthritis of the knee (OAK) pain has been largely unknown, and this systematic review was aimed at assessing their short-term efficacies for pain relief. METHODS: Systematic review with meta-analysis of efficacy within 1-4 weeks and at follow up at 1-12 weeks after the end of treatment. RESULTS: 36 randomised placebo-controlled trials (RCTs) were identified with 2434 patients where 1391 patients received active treatment. 33 trials satisfied three or more out of five methodological criteria (Jadad scale). The patient sample had a mean age of 65.1 years and mean baseline pain of 62.9 mm on a 100 mm visual analogue scale (VAS). Within 4 weeks of the commencement of treatment manual acupuncture, static magnets and ultrasound therapies did not offer statistically significant short-term pain relief over placebo. Pulsed electromagnetic fields offered a small reduction in pain of 6.9 mm [95% CI: 2.2 to 11.6] (n = 487). Transcutaneous electrical nerve stimulation (TENS, including interferential currents), electro-acupuncture (EA) and low level laser therapy (LLLT) offered clinically relevant pain relieving effects of 18.8 mm [95% CI: 9.6 to 28.1] (n = 414), 21.9 mm [95% CI: 17.3 to 26.5] (n = 73) and 17.7 mm [95% CI: 8.1 to 27.3] (n = 343) on VAS respectively versus placebo control. In a subgroup analysis of trials with assumed optimal doses, short-term efficacy increased to 22.2 mm [95% CI: 18.1 to 26.3] for TENS, and 24.2 mm [95% CI: 17.3 to 31.3] for LLLT on VAS. Follow-up data up to 12 weeks were sparse, but positive effects seemed to persist for at least 4 weeks after the course of LLLT, EA and TENS treatment was stopped. CONCLUSION: TENS, EA and LLLT administered with optimal doses in an intensive 2-4 week treatment regimen, seem to offer clinically relevant short-term pain relief for OAK

Lactic acid production from lime-treated wheat straw by Bacillus coagulans: neutralization of acid by fed-batch addition of alkaline substrate

Conventional processes for lignocellulose-to-organic acid conversion requires pretreatment, enzymatic hydrolysis, and microbial fermentation. In this study, lime-treated wheat straw was hydrolyzed and fermented simultaneously to lactic acid by an enzyme preparation and Bacillus coagulans DSM 2314. Decrease in pH because of lactic acid formation was partially adjusted by automatic addition of the alkaline substrate. After 55 h of incubation, the polymeric glucan, xylan, and arabinan present in the lime-treated straw were hydrolyzed for 55%, 75%, and 80%, respectively. Lactic acid (40.7 g/l) indicated a fermentation efficiency of 81% and a chiral l(+)-lactic acid purity of 97.2%. In total, 711 g lactic acid was produced out of 2,706 g lime-treated straw, representing 43% of the overall theoretical maximum yield. Approximately half of the lactic acid produced was neutralized by fed-batch feeding of lime-treated straw, whereas the remaining half was neutralized during the batch phase with a Ca(OH)2 suspension. Of the lime added during the pretreatment of straw, 61% was used for the neutralization of lactic acid. This is the first demonstration of a process having a combined alkaline pretreatment of lignocellulosic biomass and pH control in fermentation resulting in a significant saving of lime consumption and avoiding the necessity to recycle lime