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This paper seeks to identify significant trends in mathematics curricula and teaching approaches in two education systems: the United States (a highly decentralised education system) and England (a highly centralised education system), with focus on 16-to-19-year-olds. The paper adopts a two-fold perspective: an historical overview, and comparison of the areas of convergence and divergence across both education systems. The trajectory of mathematical development is expressed through timelines of core concepts and ideas which chronicle the sequence of events and philosophies that have shaped the development of mathematics teaching and learning. By tracing the trajectory of mathematics through history, the paper provides a greater awareness of how different factors influence how mathematics is taught across two disparate educational jurisdictions. The paper affords opportunities to reflect on and draw conclusions about what constitutes meaningful mathematics teaching and curriculum approaches for 21st century learner. [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]

Fifty years ago, a small one and a half page paper without a single reference was published in the leading journal Nature. The paper laid out the most general mathematical formulation of natural selection that would work for all kinds of selection processes and under any form of inheritance (not just biological evolution and Mendelian genes), although the paper discussed the issue in a genetical framework. Written by a maverick American expatriate in England, with no prior background of studying evolution or genetics, the paper had initially been turned down by the editor of Nature as too difficult to understand. Largely ignored by the evolutionary biology community till the 1990s, the Price Equation is now widely recognized as an extremely useful conceptualization, permitting the incorporation of non-genetic inheritance into evolutionary models, serving to clarify the relationship between kin-selection and group-selection, unifying varied approaches used in the past to model evolutionary change, and forming the foundation of multi-level selection theory. [ABSTRACT FROM AUTHOR]

The paper presents and explores the experience of maths students studying in a context shaped by a core concept maths curriculum. The three vignettes that illuminate experience are drawn from a larger research project that worked with five teachers and 630 learners aged 16–18 in Further Education classrooms in England. Analysis involved distinguishing different understandings of being good at maths, different views of a good maths curriculum and identifying enablers and barriers to being a 'successful' maths student. Dewey's ideas about focused experience and collateral learning were used to deepen this analysis. The paper reports a surprising finding. In some cases, students recognize the positive impact learning maths had on developing their wider human capabilities. Maths teachers in England, working in the context of 'new public management', may find reasons to take heart from the accounts of teaching and learning presented. For the international reader who is grappling with the challenge of reengaging maths students, the accounts of what matters to students could spur a reconsideration of priorities and practice. [ABSTRACT FROM AUTHOR]

We developed and trained a prototype AI-based object-recognition app, blockplay.ai, to recognise Cuisenaire rods placed on a tabletop, and speak the rods' lengths. We challenged 6-year-olds in a primary school in England to play a 'game': can you make the app say the two times table? Drawing methodologically on theories of embodiment, we analyse two videoclips, each of a child interacting with rods, the app and the task set by the researchers, as a dynamic, complex child-rods-app-task body-artefact system. Theoretically we draw on Davydovian concepts of learning as a concrete-to-abstract-to-new-concrete cycle, using abstract artefacts such as mathematical language to coordinate new perceptually-guided actions on concrete objects. In one videoclip the child's pattern of actions are consistent with a change, within a few minutes, from perceiving and acting on rods as counters, to perceiving and acting on rods as lengths; in the other videoclip, this does not happen. We analyse the changes in patterns of interactions as shifts to new stable attractors in a dynamic child-rods-app-task body-artefact system, driven by tensions generated by unexpected concrete-to-abstract relationships. We end by looking forward to the range of possible uses of object-recognition technology in the learning of mathematics, for example, provoking algebraic awareness. [ABSTRACT FROM AUTHOR]

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 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]

Recently, teacher recruitment and retention has been the focus of the government and a step taken to support recruitment was the abolishing of the skills tests. Initial teacher training providers became responsible for assessing trainees' mathematics rather than having it externally assessed. The purpose of this literature review is to synthesise the findings of recent studies conducted in the UK about the trainees' competence in mathematics and confidence in teaching it. Six electronic databases were searched, utilising a systematic approach, which identified only six relevant articles. This is significant as it demonstrates that, despite the evidence about the urgent need for intervention, there is limited research that explore how to address the issue of improving prospective primary school teachers' mathematics competence and confidence, especially in England. This systematic review contributes to the field by bringing attention to the important findings of these studies. Findings suggest that while some primary ITT trainees' competence and confidence about teaching mathematics is low, holding advanced level mathematics qualifications does not guarantee knowledge required to teach primary mathematics effectively. Some trainees have positive attitudes towards mathematics and, more importantly when this is not the case, both trainees' attitude towards learning and teaching mathematics can be improved. [ABSTRACT FROM AUTHOR]

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'Mastery' is central to current policy in mathematics education in England, influenced by East Asian success in transnational assessments. We scrutinise the prospects for mastery pedagogies to improve pupil attainment in English primary schools. The Mathematics Teacher Exchange (MTE)—an element of the mastery innovation—involves teachers visiting Shanghai and then hosting Shanghai teachers in their schools. Informed by programme evaluation, core component practices are analysed, which were implemented by schools belonging to the first cohort of MTE schools. These consist of: varied and interactive teaching; meaningful and coherent mathematical activity; and full curriculum access for all. These elements are supported, optimally, by collaborative, embedded, and mathematically focused professional development. Details of the implemented pedagogy and forms of professional development are reported. Differences from prevailing practice in primary mathematics in England are highlighted. Evidence is reviewed from quasi-experimental trials, reviews and meta-analyses, and rigorous observational studies of the efficacy of practices similar to the MTE mastery pedagogy components in order to assess the prospects for increases in pupil attainment. The analysis suggests that many of the specific practices, if considered individually, have the potential to improve attainment, though overall policy ambitions may not be realised. Based on the review, component practices are identified for which existing evidence justifies immediate implementation by schools and teachers. In addition, practices that would benefit from further testing and evaluation are highlighted. [ABSTRACT FROM AUTHOR]

England’s national Improving Access to Psychological Therapies (IAPT) programme advocates stepped care as its organizational delivery of psychological therapies to common mental health problems. There is limited evidence regarding the efficacy of stepped care as a service delivery model, heterogeneity of definition and differences in model implementation in both research and routine practice, hence outcome comparison in terms of effectiveness of model is difficult. Despite sound evidence of the efficacy of low intensity interventions there appears to be a perpetuation of the notion that severity and complexity should only be treated by a high intensity intervention through the continuation of a stratified care model. Yet no psychotherapy treatment is found to be more superior to another, and not enough is known about what works for whom to aid the matching of treatment decision. In the absence of understanding precise treatment factors optimal for recovery, it may be useful to better understand the impact of a service delivery model, and whether different models achieve different outcomes. This study aims to contribute to the discussion regarding the stepped care definition and delivery, and explores the impact on clinical outcomes where different types of stepped care have been implemented within the same service. An observational cohort study analysed retrospective data (n = 16,723) over a 4 year period, in a single IAPT service, where delivery changed from one type of stepped care model to another. We compared the outcomes of treatment completers with a stratified care model and a progression care model. We also explored the assumption that patients who score severe on psychological measures, and therefore are potentially complex, would achieve better outcomes in a stratified model. Outcomes in each model type were compared, alongside baseline factor variables. A significant association was observed between a recovery outcome and model type, with patients 1.5 times more likely to recover in the progression delivery model. The potential implications are that with a progression stepped care model of service delivery, more patients can be treated with a lower intensity intervention, even with initial severe presentations, ensuring that only those that need high intensity CBT or equivalent are stepped up. This could provide services with an effective clinical model that is efficient and potentially more cost effective. [ABSTRACT FROM AUTHOR]

Many disciplines of scholarship are interested in the Relative Age Effect (RAE), whereby age-banding confers advantages on older members of the cohort over younger ones. Most research does not test this relationship in a manner consistent with theory (which requires a decline in frequency across the cohort year), instead resorting to non-parametric, non-directional approaches. In this article, the authors address this disconnect, provide an overview of the benefits associated with Poisson regression modelling, and two managerially useful measures for quantifying RAE bias, namely the Indices of Discrimination and Wastage. In a tutorial-like exposition, applications and extensions of this approach are illustrated using data on professional soccer players competing in the top two tiers of the “Big Five” European football leagues in the search to identify paragon clubs, leagues, and countries from which others may learn to mitigate this form of age-discrimination in the talent identification process. As with OLS regression, Poisson regression may include more than one independent variable. In this way we test competing explanations of RAE; control for unwanted sources of covariation; model interaction effects (that different clubs and countries may not all be subject to RAE to the same degree); and test for non-monotonic versions of RAE suggested in the literature. [ABSTRACT FROM AUTHOR]

Aim: To gain a better understanding of the complex relationships of different measures of social position, educational level and income with alcohol consumption in England. Method: Between March 2014 and April 2018 data were collected on n = 57,807 alcohol drinkers in England taking part in the Alcohol Toolkit Study (ATS). Respondents completed the AUDIT-C measure of frequency of alcohol consumption, amount consumed on a typical day and binge drinking frequency. The first two questions were used to derive a secondary measure of quantity: average weekly unit consumption. Socio-economic factors measured were: social-grade (based on occupation), employment status, educational qualifications, home and car ownership and income. Models were constructed using ridge regression to assess the contribution of each predictor taking account of high collinearity. Models were adjusted for age, gender and ethnicity. Results: The strongest predictor of frequency of alcohol consumption was social-grade. Those in the two lowest occupational categories of social grade (e.g. semi-skilled and unskilled manual workers, and unemployed, pensioners, casual workers) has fewer drinking occasions than those in professional-managerial occupations (β = -0.29, 95%CI -0.34 to -0.25; β = -0.31, 95%CI -0.33 to -0.29). The strongest predictor of consumed volume and binge drinking frequency was lower educational attainment: those whose highest qualification was an A-level (i.e. college/high school qualification) drank substantially more on a typical day (β = 0.28, 95%CI 0.25 to 0.31) and had a higher weekly unit intake (β = 3.55, 95%CI 3.04 to 4.05) than those with a university qualification. They also reported a higher frequency of binge drinking (β = 0.11, 95%CI 0.09 to 0.14). Housing tenure was a strong predictor of all drinking outcomes, while employment status and car ownership were the weakest predictors of most outcomes. Conclusion: Social-grade and educational attainment appear to be the strongest socioeconomic predictors of alcohol consumption indices in England, followed closely by housing tenure. Employment status and car ownership have the lowest predictive power. [ABSTRACT FROM AUTHOR]

Background: It has been suggested that greater maternal adiposity during pregnancy affects lifelong risk of offspring fatness via intrauterine mechanisms. Our aim was to use Mendelian randomisation (MR) to investigate the causal effect of intrauterine exposure to greater maternal body mass index (BMI) on offspring BMI and fat mass from childhood to early adulthood.Methods and Findings: We used maternal genetic variants as instrumental variables (IVs) to test the causal effect of maternal BMI in pregnancy on offspring fatness (BMI and dual-energy X-ray absorptiometry [DXA] determined fat mass index [FMI]) in a MR approach. This was investigated, with repeat measurements, from ages 7 to 18 in the Avon Longitudinal Study of Parents and Children (ALSPAC; n = 2,521 to 3,720 for different ages). We then sought to replicate findings with results for BMI at age 6 in Generation R (n = 2,337 for replication sample; n = 6,057 for total pooled sample). In confounder-adjusted multivariable regression in ALSPAC, a 1 standard deviation (SD, equivalent of 3.7 kg/m2) increase in maternal BMI was associated with a 0.25 SD (95% CI 0.21-0.29) increase in offspring BMI at age 7, with similar results at later ages and when FMI was used as the outcome. A weighted genetic risk score was generated from 32 genetic variants robustly associated with BMI (minimum F-statistic = 45 in ALSPAC). The MR results using this genetic risk score as an IV in ALSPAC were close to the null at all ages (e.g., 0.04 SD (95% CI -0.21-0.30) at age 7 and 0.03 SD (95% CI -0.26-0.32) at age 18 per SD increase in maternal BMI), which was similar when a 97 variant generic risk score was used in ALSPAC. When findings from age 7 in ALSPAC were meta-analysed with those from age 6 in Generation R, the pooled confounder-adjusted multivariable regression association was 0.22 SD (95% CI 0.19-0.25) per SD increase in maternal BMI and the pooled MR effect (pooling the 97 variant score results from ALSPAC with the 32 variant score results from Generation R) was 0.05 SD (95%CI -0.11-0.21) per SD increase in maternal BMI (p-value for difference between the two results = 0.05). A number of sensitivity analyses exploring violation of the MR results supported our main findings. However, power was limited for some of the sensitivity tests and further studies with relevant data on maternal, offspring, and paternal genotype are required to obtain more precise (and unbiased) causal estimates.Conclusions: Our findings provide little evidence to support a strong causal intrauterine effect of incrementally greater maternal BMI resulting in greater offspring adiposity. [ABSTRACT FROM AUTHOR]

Background: We have assessed whether the linkage between routine primary and secondary care records provided an opportunity to develop an improved population based co-morbidity score with the combined information on co-morbidities from both health care settings. Methods: We extracted all people older than 20 years at the start of 2005 within the linkage between the Hospital Episodes Statistics, Clinical Practice Research Datalink, and Office for National Statistics death register in England. A random 50% sample was used to identify relevant diagnostic codes using a Bayesian hierarchy to share information between similar Read and ICD 10 code groupings. Internal validation of the score was performed in the remaining 50% and discrimination was assessed using Harrell’s C statistic. Comparisons were made over time, age, and consultation rate with the Charlson and Elixhauser indexes. Results: 657,264 people were followed up from the 1st January 2005. 98 groupings of codes were derived from the Bayesian hierarchy, and 37 had an adjusted weighting of greater than zero in the Cox proportional hazards model. 11 of these groupings had a different weighting dependent on whether they were coded from hospital or primary care. The C statistic reduced from 0.88 (95% confidence interval 0.88–0.88) in the first year of follow up, to 0.85 (0.85–0.85) including all 5 years. When we stratified the linked score by consultation rate the association with mortality remained consistent, but there was a significant interaction with age, with improved discrimination and fit in those under 50 years old (C = 0.85, 0.83–0.87) compared to the Charlson (C = 0.79, 0.77–0.82) or Elixhauser index (C = 0.81, 0.79–0.83). Conclusions: The use of linked population based primary and secondary care data developed a co-morbidity score that had improved discrimination, particularly in younger age groups, and had a greater effect when adjusting for co-morbidity than existing scores. [ABSTRACT FROM AUTHOR]

This essay is an account of the making of England and her Soldiers (1859) by Harriet Martineau and Florence Nightingale. The book is a literary account of the Crimean War, written by Martineau and based on Nightingale's statistical studies of mortality during the conflict. Nightingale was passionate about statistics and healthcare. Whilst working as a nurse in the Crimea, she witnessed thousands of soldiers die of infectious diseases that might have been prevented with proper sanitation. After the war, she launched a campaign to convince the British government to make permanent reforms to military healthcare, compiling a dataset on mortality in the Crimea. She worked with the government's Royal Commission investigating healthcare during the war, but also worked privately with Martineau to publicise her findings. Martineau and Nightingale grasped that the lay reader was more receptive to statistical information in a literary format than in dense statistical reports. As such, Nightingale's data was interwoven with Martineau's text. The pair illustrated their book with Nightingale's 'Rose Diagram', a statistical graphic which simply illustrated the rate of mortality. [ABSTRACT FROM AUTHOR]

Background: Coronary Heart Disease (CHD) remains a major cause of mortality in the United Kingdom. Yet predictions of future CHD mortality are potentially problematic due to population ageing and increase in obesity and diabetes. Here we explore future projections of CHD mortality in England & Wales under two contrasting future trend assumptions. Methods: In scenario A, we used the conventional counterfactual scenario that the last-observed CHD mortality rates from 2011 would persist unchanged to 2030. The future number of deaths was calculated by applying those rates to the 2012–2030 population estimates. In scenario B, we assumed that the recent falling trend in CHD mortality rates would continue. Using Lee-Carter and Bayesian Age Period Cohort (BAPC) models, we projected the linear trends up to 2030. We validate our methods using past data to predict mortality from 2002–2011. Then, we computed the error between observed and projected values. Results: In scenario A, assuming that 2011 mortality rates stayed constant by 2030, the number of CHD deaths would increase 62% or approximately 39,600 additional deaths. In scenario B, assuming recent declines continued, the BAPC model (the model with lowest error) suggests the number of deaths will decrease by 56%, representing approximately 36,200 fewer deaths by 2030. Conclusions: The decline in CHD mortality has been reasonably continuous since 1979, and there is little reason to believe it will soon halt. The commonly used assumption that mortality will remain constant from 2011 therefore appears slightly dubious. By contrast, using the BAPC model and assuming continuing mortality falls offers a more plausible prediction of future trends. Thus, despite population ageing, the number of CHD deaths might halve again between 2011 and 2030. This has implications for how the potential benefits of future cardiovascular strategies might best be calculated and presented. [ABSTRACT FROM AUTHOR]

Background: South Asians in England have an increased risk of childhood cancer but incidence by their individual ethnicities using self-assigned ethnicity is unknown. Our objective was to compare the incidence of childhood cancer in British Indians and Whites in Leicester, which has virtually complete, self-assigned, ethnicity data and the largest population of Indians in England. Methods: We obtained data on all cancer registrations from 1996 to 2008 for Leicester with ethnicity obtained by linkage to the Hospital Episodes Statistics database. Age-standardised incidence rates were calculated for childhood cancers in Indians and Whites as well as rate ratios, adjusted for age. Results: There were 33 cancers registered among Indian children and 39 among White children. The incidence rate for Indians was greater compared to Whites for all cancers combined (RR 1.82 (95% CI 1.14 to 2.89); p = 0.01), with some evidence of increased risk of leukaemia (RR 2.20 (0.95 to 5.07); p = 0.07), lymphoma (RR 3.96 (0.99 to 15.84); p = 0.04) and central nervous system tumours (RR 2.70 (1.00 to 7.26); p = 0.05). Rates were also higher in British Indian children compared to children in India. Conclusions: British Indian children in Leicester had an increased risk of developing cancer compared to White children, largely due to a higher incidence of central nervous system and haematological malignancies. [ABSTRACT FROM AUTHOR]

This research investigates the potential for a one-to-one coaching tool used by adults other than teachers to be able to deliver greater mathematics progress for primary school children without adding significantly to school costs. Plus 1 and Power of 2 (+1 and Po2) are workbooks designed to be used by adults other than teachers working on a one-to-one basis with children to develop numeracy skills. This quantitative study seeks to examine the impact of +1 and Po2 by considering performance data aggregated at the school level. The attainment of children at 1071 English schools which use the +1 and Po2 products was compared with that of peers in other schools using a quasi-experimental research design based on England's national performance measures. Statistical analysis suggests that schools using +1 and Po2 show higher levels of mathematics attainment than those who may have used other resources. Furthermore, there is an important finding that assessment attendance is higher, and disapplication from the curriculum lower, in schools using +1 and Po2. This indicates that use of this one-to-one intervention improves access to national tests for children and represents an opportunity for school leaders to maximise the cost effectiveness of existing non-teaching staff or volunteers. [ABSTRACT FROM AUTHOR]

This article reports the findings of a retrospective study of 'tracked' grouping in a mathematics department in a co-educational comprehensive school in Greater London. Tracking consisted here of just two tracks, a 'fast track' for the top 25-30% of a cohort, and a 'mixed track' for the remainder. The article outlines the reasons for introducing tracking and explores its effects through interviews with teachers and data on the progress of students from age 14 to age 16. The teachers reported that tracking impacted differently on different students, and this is borne out by the quantitative data. It was not possible to provide for 'setting' across all the mathematics classrooms in the focal cohort, and therefore one mixed-ability class was created. The use of analysis of covariance (ANCOVA) models shows that fast-track students were not significantly advantaged by their placement in these tracks, but the progress of students in the mixed-ability group showed a significant interaction between progress and prior attainment, with placement in the mixed-ability group conferring a significant advantage on lower attaining students, while the disadvantage to higher attaining students was much smaller. [ABSTRACT FROM AUTHOR]

This study analyses the pedagogical ideas underpinning teachers' accounts of the successful use of computer-based tools and resources to support the teaching and learning of mathematics. These accounts were elicited through group interviews with the mathematics departments in seven English secondary schools, conducted in the first half of 2000. The central themes are organised to form a pedagogical model, capable of informing use of such technologies in classroom teaching, and of generating theoretical conjectures for future research. The thematic components of the model are summarised and related to prior research into computer use in mainstream schooling. [ABSTRACT FROM AUTHOR]

Analyzes the responses of children to realistic mathematics problems in England. Details of the problems; Ability of the students to offer reasons in support of their answer; Absence of difference between girls and boys.