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Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12–13 year olds, from 76 schools in England, who were allocated to between‐class attainment groups ('setting') in English and mathematics over the first 2 years of secondary schooling. After controlling for prior attainment, pupils in the top set performed significantly better than pupils in the middle and bottom sets in both English and mathematics. The findings indicate a widening gap in attainment, especially in the case of English. Findings, especially in the case of mathematics, provide more evidence of a relative benefit for pupils placed in top sets than a relative detriment for those in bottom sets. [ABSTRACT FROM AUTHOR]

Improving mathematical skills is a priority in England, and a series of policy levers and government change projects have focused on improving mathematical outcomes in further education (FE) in recent years. Yet little is known about the mathematics teacher workforce that supports these students on vocational and technical programmes. This paper addresses this knowledge gap by examining important features of the mathematics teacher workforce in colleges and the implications for recruitment, initial training and ongoing professional development. We report findings from a national survey targeted at all mathematics teachers in around one-sixth (N = 31) of England's general FE colleges. Teachers have transitioned into FE from three main areas: another career, curriculum area, or educational context. We discuss the varied assets and training needs of these three subgroups and argue that the mathematics teacher cohort in FE should be seen as distinct from that in either primary or secondary education. We highlight the bimodal distribution of mathematics qualifications amongst this workforce; those having level 2 mathematics qualifications being more likely to be teaching functional skills mathematics courses than GCSEs. The rapid expansion of the mathematics teacher workforce that followed the changes to the condition of funding in 2014 has come disproportionately from teachers who were previously working in schools. This, together with a trend of funnelling increasing numbers of FE students into academic mathematics rather than functional skills courses, raises important questions about the nature of mathematical education for learners on vocational and technical programmes, and the teachers thereof. [ABSTRACT FROM AUTHOR]

The problem of low attainment in mathematics has been an increasingly prominent feature of the policy discourse in England over the last 60 years; however, evidence from comparative studies indicates that little progress has been made in finding a solution. In this paper, we analyse the changing policy discourse of low attainment in mathematics through the main reports and speeches published in England, beginning with the Newsom Report, Half Our Future, in 1963, and continuing to the present day. We chart the evolving perspectives on the nature of ability, expectations, curriculum ideology and frame of reference through the changing language used in these documents, noting tensions and inconsistencies which arise through continuing lack of clarity about definitions and assumptions. [ABSTRACT FROM AUTHOR]

In a short fragment published for the first time with his lost notebook in 1988 (Ramanujan, The lost notebook and other unpublished papers (Narosa, New Delhi, 1988)), Ramanujan offered two beautiful identities, associated, respectively, with the classical circle and divisor problems. In fact, they are analogues, with an additional variable, but not generalizations, of classical identities associated with these two famous problems. After Ramanujan's death in 1920, the lost notebook and fragments of papers of Ramanujan were sent to Hardy. We do not have any official record of what was included in this mailing, but it is likely that the aforementioned fragment was included in this parcel. If so, then it is possible that Ramanujan wrote it at the end of his life in either 1919 or 1920. On the other hand, from a paper that Hardy published in 1915 (Hardy, Quart. J. Math. (Oxford) 46 (1915) 263–283) on the circle problem, we are aware that by early in his stay in England, Ramanujan had a strong interest in these problems, and so the fragment may emanate from this period. Two of the present authors and Kim published a proof of the identity connected with the circle problem in 2013 (Berndt, Kim and Zaharescu, Adv. Math. 236 (2013) 24–59). In this paper, a proof of the second identity is given for the first time. [ABSTRACT FROM AUTHOR]

The core of Beverton and Holt's seminal work of the 1950s had been anticipated by Baranov 30 years earlier, but his contributions, published in Russian, remained poorly known to Anglophone scientists until after 1945. By that time, Russell and Graham had presented parallel ideas, though without Baranov's mathematics. Limited subsequent acknowledgement of the Russian's contributions has left an impression that each of his advances was achieved independently in England, hence that they contributed little to the Beverton–Holt model. I here construct a timeline of events linking and separating the Russian and English studies. From it, I argue that both Russell's presentation of the underlying concepts and Graham's decision to pursue a mathematical realization of his "Modern Theory" may have been influenced by translations of Baranov's papers. Moreover, when Holt developed the "simple" Beverton–Holt model during 1946–1947, he certainly drew on Baranov's exponential model of mortality, though perhaps only via Ricker. [ABSTRACT FROM AUTHOR]

Abstract Girls' uptake of physical science, technology, engineering and mathematics (PSTEM) degrees continues to be poor. Identifying and targeting interventions for girl groups that are likely to go into STEM degrees may be a possible solution. This paper, using a self-determination theory and self-socialisation framework, determines whether one girl group's, "geek girls", video gaming behaviour is associated with their choice of undergraduate degree by using two secondary datasets: a cross-sectional study of the Net Generation (n = 814) and the Longitudinal Study of Young People in England (LSYPE) dataset (n = 7342). Chi-square analysis shows that girls who were currently studying a PSTEM degree were more likely to be gamers and engage in multiplayer gamers. Further, using logistic regressions, girls who were heavy gamers (>9 h/wk) at 13–14 years were found to be more likely to pursue a PSTEM degree but this was influenced by their socio-economic status. Similar associations with boys and PSTEM degrees were not found or were weak. Therefore, girls were self-socialising or self-determining their identity groups through gaming. This research can provide the basis for whether encouraging gaming in adolescent girls can help them onto PSTEM pathways. Highlights • Girls who are heavy gamers are more likely to study a physical STEM degree. • Playing multiplayer games is associated with studying a physical STEM degree. • The studying of physical STEM degrees is dependent on level of social deprivation. • Girls are 58 times less likely to do a physical STEM degree than no degree at all. • Levels of participation in video gaming can change for girls over a year. [ABSTRACT FROM AUTHOR]

The political importance of mathematics in post-16 education is clear. Far less clear is how mathematics does and should relate to vocational education. Successive mathematics curricula (e.g. core skills, key skills) have been developed in England with vocational learners in mind. Meanwhile, general mathematics qualifications remain largely disconnected from vocational learning. Following a brief historical survey of mathematics within vocational education, the paper presents findings from a nested case study of student groups in three large Further Education colleges in England. The primary unit of analysis herein is student groups learning Functional Mathematics in two vocational areas: construction and hairdressing. We show how approaches to organising teaching, developing connected curricula and classroom pedagogy tend toisolateorintegratemathematics from/with the vocational experience.Integratedapproaches are shown to impact positively on student engagement and attitudes to learning mathematics. The paper concludes by discussing the potential impact of academic qualifications displacing vocationally relevant mathematics. [ABSTRACT FROM PUBLISHER]

The accuracy of the results of the national tests in English, mathematics and science taken by 11-year olds in England has been a matter of much debate since their introduction in 1994, with estimates of the proportion of students incorrectly classified varying from 10 to 30%. Using live data from the 2009 and 2010 administration of the national tests, this paper uses a number of models, drawing on both classical and modern test theories, to explore the relationship between test reliability, and the extent of misclassification when a student’s test score is reported in terms of one of a small number of discrete levels of achievement. The results indicate that across the two cohorts (2009 and 2010) and six models, the averages of classification accuracy of the tests were about 85%, 90% and 87% in English, mathematics and science, respectively. Moreover, the different models yielded very similar results; the standard deviations of the values of classification accuracy generated were 1.9% for English, 1.0% for mathematics and 1.3% for science. [ABSTRACT FROM PUBLISHER]

A large-scale multiple surveillance system for infectious disease outbreaks has been in operation in England and Wales since the early 1990s. Changes to the statistical algorithm at the heart of the system were proposed and the purpose of this paper is to compare two new algorithms with the original algorithm. Test data to evaluate performance are created from weekly counts of the number of cases of each of more than 2000 diseases over a twenty-year period. The time series of each disease is separated into one series giving the baseline (background) disease incidence and a second series giving disease outbreaks. One series is shifted forward by twelve months and the two are then recombined, giving a realistic series in which it is known where outbreaks have been added. The metrics used to evaluate performance include a scoring rule that appropriately balances sensitivity against specificity and is sensitive to variation in probabilities near 1. In the context of disease surveillance, a scoring rule can be adapted to reflect the size of outbreaks and this was done. Results indicate that the two new algorithms are comparable to each other and better than the algorithm they were designed to replace. [ABSTRACT FROM AUTHOR]

Smoking has been identified as the second greatest risk factor for global death and disability and has impacts on the oral cavity from aesthetic changes to fatal diseases such as oral cancer. The paper presents a secondary analysis of the National Adult Dental Health Survey (2009). The analysis used descriptive statistics, bivariate analyses and logistic regression models to report the self-reported oral health status and dental attendance of smokers and non-smokers in England. Of the 9,657 participants, 21% reported they were currently smoking. When compared with smokers; non-smokers were more likely to report ‘good oral health’ (75% versus 57% respectively, p<0.05). Smokers were twice as likely to attend the dentist symptomatically (OR = 2.27, CI = 2.02–2.55) compared with non-smoker regardless the deprivation status. Smokers were more likely to attend symptomatically in the most deprived quintiles (OR = 1.99, CI = 1.57–2.52) and perceive they had poorer oral health (OR = 1.77, CI = 1.42–2.20). The present research is consistent with earlier sub-national research and should be considered when planning early diagnosis and management strategies for smoking-related conditions, considering the potential impact dental teams might have on smoking rates. [ABSTRACT FROM AUTHOR]

The 2007 Trends in International Mathematics and Science Survey highlighted how attitudes to mathematics had declined sharply for students in many of the high attaining countries in the survey, England being no exception. There is a notable drop in positive attitudes to mathematics between 9 and 14, as well as a remarkable decline for 14 year olds over time. This paper explores survey data collected from over 3000 11-year-olds in 16 schools during 2008 with the goal of exploring possible factors that might be contributing to this attitudinal decline. The association between student-centred teaching and enjoyment of learning mathematics is reported as part of a multi-scale analysis that shows the extent to which student experiences differ between schools and between classes within schools. [ABSTRACT FROM AUTHOR]

The Thames Water ring main extension is a 4·5 km long tunnel from Stoke Newington, in the London borough of Hackney, to New River Head in Finsbury, in the London borough of Islington. The 2·85 m i.d. tunnel was excavated by an earth pressure balance tunnel-boring machine (TBM) at depths between 40 and 60 m below the surface. Surface settlements along the route were measured by precise levelling, and were found to be small. It was therefore even more important to measure these settlements as accurately as possible, in order to provide informed estimates of subsurface movements induced in third-party underground structures much closer to the tunnel horizon. Because of the relatively large magnitude of the background movements measured, when compared with the small tunnel-induced settlements, it was necessary to adopt a rigorous statistical method to fit a Gaussian curve to the data. This exploited the analogy of the 'error function' to define the Gaussian curve parameters and . In all, 13 tunnels were underpassed successfully by the TBM, all within the 'conservative expected value' predictions, and without incident. The predictions and structural monitoring schemes undertaken for the High Speed 1 tunnels near Corsica Street and the Northern line tunnels near Angel station are described in the paper. It was found that the surface and subsurface trough width parameter did not vary with depth as predicted: therefore a new relationship is proposed. [ABSTRACT FROM AUTHOR]

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular cultural texts, we argue that popular discourses overwhelmingly construct mathematicians as white, heterosexual, middle-class men, yet also construct them as 'other' through systems of binary oppositions between those doing and those not doing mathematics. Turning to the analysis of a corpus of 27 focus groups with school and university students in England and Wales, we explore how such images are deployed by learners. We argue that while learners' views of mathematicians parallel in key ways popular discourses, they are not passively absorbing these as they are simultaneously aware of the cliched nature of popular cultural images. [ABSTRACT FROM AUTHOR]

Is there such a thing as Irish mathematics, as opposed to mathematics which happens to have been done in Ireland or by thoseborn in Ireland? Certainly, Ireland in the nineteenth century was in one of its mathematically richest phases, with such men as William Rowan Hamilton, James MacCullagh, George Salmon, and George Fitzgerald to inspire generations of students and researchers, as well as exporting to England such talented mathematicians as Kelvin, Stokes and Larmor. This paper seeks to explore, through examining the mathematics taught and researched, whether the category of ‘Irish mathematics’ is one that makes sense for this period. [ABSTRACT FROM AUTHOR]

The National Numeracy Strategy was introduced in England in 1998 to reform mathematics teaching in all primary schools. The strategy has been widely implemented and this paper investigates some of the changes that are evident after the first five years. Reporting a comparison between studies in 1998 and 2003 of pupils’ calculating strategies for division, this study shows a small improvement overall but lack of the uniformity that may be expected from a national Strategy. Structured written recording, progressively developed from more intuitive understanding, was not evident in much of the pupils’ work. In some schools there was success with the new ‘chunking’ written method, identified in the Framework as ‘informal’, while in less successful schools, pupils continued to use various informal and inefficient strategies. While in 1998 success of boys and girls was not significantly different, in 2003 the boys were more successful. The boys made more use of informal working and mental strategies, while the girls relied on more structured written methods and in the schools where girls did better they used mostly the chunking algorithm. [ABSTRACT FROM AUTHOR]

This paper describes a study exploring young people's perceptions of the mathematics involved in five everyday activities. It is based on individual interviews with pupils in Years 7 and 10 in four English secondary schools. Results suggest that young people are more aware of the mathematics embedded in everyday activities than previously thought. There was no evidence to support existing theories that young people have particular difficulties identifying mathematics within practical activities or those traditionally performed by women. However, participants did seem to restrict the label mathematics to activities involving a problem with a single or limited solution, and to activities which require a formal rather than experimental or intuitive approach. Some participants also seemed to relate their discussion of mathematics only to the aspect of each activity which takes most time and attention. [ABSTRACT FROM AUTHOR]

The article presents a summary of a paper on a class of Riemann-Hilbert problems with almost periodic polynomial coefficients presented by speaker Cristina Camara at the Thirty-First Summer Symposium in Real Analysis held at the University of Oxford, England from August 13 to 15, 2007. The presentation focuses on the interaction between some simple classical results from real analysis and problems arising in other areas of mathematics. Also studied is the existence and actual determination of almost-periodic solutions of a class of such problems.