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George Gabriel Stokes spent most of his life at the University of Cambridge, where he undertook his undergraduate degree and later became Lucasian Professor of Mathematics and Master of Pembroke College. However, he spent the first 13 years of his life in Skreen, County Sligo, Ireland, a rural area right by the coastline, overlooking the Atlantic Ocean. As this paper will discuss, the time he spent there was short but its influence on him and his research was long reaching, with his childhood activities of walking by and bathing in the sea being credited for first piquing Stokes' interest in ocean waves, which he would go on to write papers about. More generally, it marked the beginning of an interest in fluid dynamics and a curious nature regarding natural phenomena in his surroundings. Stokes held a special affinity for the ocean for the rest of his life, constantly drawing inspiration for it in his mathematical and physical studies and referencing it in his correspondences. This commentary was written to celebrate Stokes' 200th birthday as part of the theme issue of Philosophical Transactions A . This article is part of the theme issue 'Stokes at 200 (Part 1)'.

George Gabriel Stokes won the coveted title of Senior Wrangler in 1841, a year in which the examination papers for the Cambridge Mathematical Tripos were notoriously difficult. Coming top in the Mathematical Tripos was a notable achievement, but for Stokes it was a prize hard won after several years of preparation, and not only years spent at Cambridge. When Stokes arrived at Pembroke College, he had spent the previous two years at Bristol College, a school which prided itself on its success in preparing students for Oxford and Cambridge. This article follows Stokes' path to the senior wranglership, tracing his mathematical journey from his arrival in Bristol to the end of his final year of undergraduate study at Cambridge. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Abstract: The long‐standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10–11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking. [ABSTRACT FROM AUTHOR]

This article discusses two of the reasons for the decline of formal Euclidean geometry in recent syllabi: (1) Traditional approach; and (2) Inherent difficulties. Suggested are some reasons and examples as to why the decline should be reversed. (YP)

Abstract: Charles Babbage (1791–1871) was the embodiment of a polymath: elected a Royal Society fellow, holder of the Lucasian Chair of mathematics at Cambridge, founder of the London Statistical Society, author of many papers and full-length monographs and, most famously from a 21st century perspective, the architect of modern computing with his difference engines and designs for the analytical engine. The scale and complexity of these machines meant their realisation was dependent upon the latest industrial advances like parts standardization and machine tool technology. As a result Babbage committed large amounts of his time and money to the theoretical and empirical study of advanced production and engineering practice. This paper argues that Charles Babbage deserves to be recognised as a pioneer in the field of operations management. His path-breaking contributions were born of a singular intellect and degree of creativity combined with a commitment to empiricist scientific method and statistical measurement. Moreover, he was working as Britain transformed itself into the most highly industrialized country the world had ever seen. The paper draws in particular upon the various editions of his best-selling book, ‘On the Economy of Machines and Manufactures’, first published in 1832. It reviews the many core operations principles evident in Babbage''s analyses and highlights insights that remain relevant to today''s theoretical and practical concerns. The paper concludes with a discussion of how a combination of contextual and biographical factors left Charles Babbage a largely unsung pioneer in the field of operations management. [Copyright &y& Elsevier]

As part of a broader research objective concerned with identifying the range of employer defined skill profiles that characterize workplace performance, this paper examines skill contexts for Application of Number, one of six UK defined Key Skills similar to Australian defined Key Competencies. Following the construction of questionnaires, grounded in the Analytic Hierarchy Process, applications of the instrument in both the UK and in Australia produced a ratio scale of priorities within the Key Skills area. This enabled a specification of the relative balance between classical competencies, e.g. facility with pen and paper calculations and emerging competencies demanded by the effective use of ICT. Relevance to workplace learning, including the transition from school to employment, and related aspects of mathematics education are discussed. Among the research outcomes is that spreadsheets are assuming a pre-eminent position and that this is an overriding priority for each defined activity and at each job level. [ABSTRACT FROM AUTHOR]

This paper focuses on the aspirations of 13- and 15-year-olds to continue with mathematics after the age of 16 and the association with perceptions of their mathematics education during the academic year 2008/9. A quantitative analysis was undertaken on the views of 12,176 UK students, obtained through surveys, with qualitative case studies on two of these students lending support to the quantitative findings. This paper also places a focus on a sub-set of 1,476 London students. The analysis indicates that girls and boys with high mathematics aspirations had similar responses towards their mathematics teachers and lessons, and had comparable extrinsic mathematics motivation. However, girls, regardless of mathematics aspirations, were less likely than boys to be encouraged by their families and others within their social circles to study mathematics post-16. Many of the London findings are similar to those we found across the UK, although girls within London schools with high mathematics aspirations perceived their mathematics education to be more equitable. Low aspiring girls across the UK and in London still reported less support and encouragement, and described their mathematics education less favourably than did boys. [ABSTRACT FROM AUTHOR]

Background Estimates of energy requirements are needed in weight management and are usually determined using prediction equations. The objective of these two systematic reviews was to identify which equations based on simple anthropometric and demographic variables provide the most accurate and precise estimates of (1) resting energy expenditure (REE) and (2) total energy expenditure ( TEE) in healthy obese adults. Methods Systematic searches for relevant studies in healthy adults with body mass index ( BMI) ≥25 kg m−2 and published in English were undertaken using Cinahl, Cochrane Library, OpenGrey, PubMed and Web of Science (completed March 2014). Search terms included metabolism, calorimetry, obesity and prediction equations. Data extraction, study appraisal and synthesis followed guidelines from PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses). Results From 243 REE papers and 254 TEE papers identified, 21 and four studies, respectively, met the inclusion criteria. (1) The most accurate REE predictions varied with BMI subgroup: WHO (weight and height) ≥25 and ≥30 kg m−2; Mifflin 30-39.9 kg m−2; Henry ≥40 kg m−2. The most precise REE predictions were obtained using Mifflin in BMI 30-39.9 and ≥40 kg m−2, where approximately 75% of predictions were within 10% of measured REE. (2) No accurate or precise predictions of TEE were identified. Conclusions No single prediction equation provides accurate and precise REE estimates in all obese adults. Mifflin equations are recommended in this population, although errors exceed 10% in 25% of those assessed. There is no evidence to support the use of prediction equations in estimating TEE in obesity. [ABSTRACT FROM AUTHOR]

This article presents the results of a small-scale, comparative study on the perceived impact that having students enter Mathematics competitions has on Mathematics teachers in Puerto Rico, Switzerland and the UK and on their classroom practice. The study surveyed a small number of Mathematics teachers in the three countries who teach in both public and private schools and in both rural and urban regions. The perceived advantages and disadvantages to students from taking part in competitions and to teachers who have students taking part in competitions are discussed and the findings compared across the three countries. The effect that Mathematics competitions have on the identification and development of the mathematical talent of students is considered together with the contribution of these activities to the academic environment of the classroom. For the teachers who did have students taking Mathematics competitions, the limitations of entry and the different methods in which teachers prepare or assist students to prepare for the competitions are compared between countries. Since the study is small in scale, no firm conclusions are drawn but suggestions are made as to where future, larger scale, studies might be carried out to see if the classroom experiences of all could be positively influenced by exposure to Mathematics competitions. [ABSTRACT FROM AUTHOR]

The European Emission Trading System (EU ETS) is commonly regarded as the key pillar of the European climate policy and as the main unifying tool to create a unique carbon price all over Europe. The UK has always played a crucial role in the EU ETS, being one of the most active national registry and a crucial hub for the exchange of allowances in the market. Brexit, therefore, could deeply modify the number and directions of such exchanges as well as the centrality of the other countries in this system. To investigate these issues, the present paper exploits network analysis tools to compare the structure of the EU ETS market in its first two phases with and without the UK, investigating a few different scenarios that might emerge from a possible reallocation of the transactions that have involved UK partners. We find that without the UK the EU ETS network would become in general much more homogeneous, though results may change focusing on the type of accounts involved in the transactions. [ABSTRACT FROM AUTHOR]

Abstract: Tablets have much to offer children with learning difficulties, but evidence of their effectiveness to teach academic skills is limited and cannot be easily separated from the quality of the software. This paper analyses data from 3 iterative cycles of designing an app for children with Down syndrome to support their awareness of quantity through an inclusive game. Research with neurotypical children suggests that representation of quantity (or magnitude) is an area with considerable potential in supporting the foundations for children's mathematical learning. It has received little attention as an aspect for intervention for children with Down syndrome. Data collected in this study illustrate the need to carefully align the game mechanic to the target skills, strengthen levels of access, and introduce gradations of attentional demand. They also signal the interrelationship between children's cognitive and affective responses to the game, making it essential to find the optimal level of challenge. Children's strategies in response to mistakes indicate the importance of creating an agile responsive system. The data also suggest that developers routinely extend the number of features that are optional, enabling a greater level of personalization and a more inclusive game. [ABSTRACT FROM AUTHOR]

The choice of mobile applications (apps) for learning has been heavily relied on customer and teacher reviews, designers' descriptions, and alignment with existing learning and human-computer interaction theories. There is limited empirical evidence to advise on the educational value of mobile apps as these are used by children. Understanding the impact of mobile apps on young children's learning is timely given the lack of evidence-based recommendations that could guide parents and teachers in selecting apps for their children. In this paper, we present the results of a series of Randomised Control Trials (RCTs) with 376 children aged 5 to 6 years old who interacted with two maths apps in three schools in the UK. Pre/post-test comparisons revealed learning gains in both the control and intervention groups, suggesting that the selected applications are equally good to standard maths practice. Implications for the selection and use of mobile apps are discussed. [ABSTRACT FROM AUTHOR]

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13-14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks. [ABSTRACT FROM AUTHOR]

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the system as well as suitable tasks and pedagogies that provide a substrate of activity and experience for the teaching and learning of algebraic generalizations. Using as reference illustrative cases of 12 to 13-year-old students' interaction with the microworld, we demonstrate the strong interplay between epistemology and the design of the microworld and draw conclusions regarding its potential to support the development of algebraic ways of thinking. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present evidence to support the idea that the art of successful influence lies in matching the strategies and style used to the context. The paper describes research into the relationship between the frequency with which people use six influence strategies, and how they combine them to form various influence styles, and a wide variety of contextual variables found by previous research to be linked to influence behaviour. It is relevant to everyone at work, including leaders, managers and professionals involved in training, development, coaching and mentoring activities.Design/methodology/approach – The model of influence behaviour identifies six sets of influence strategies used by people at work and three dimensions of influence style, based on research into how people tend to combine these strategies in practice. The research methodology involves looking at the degree of correlation and its statistical significance between the frequency with which people use these influence strategies and styles at work and 33 contextual variables. Data were collected from 161 men and women, at all levels, in a wide variety of public sector organisations in the UK, over a seven-year period.Findings – The author found support for the idea that influencing behaviour varied in different contexts. Statistically significant relationships were identified between the frequency of use of influence strategies and styles and the 33 contextual variables. Clusters of contextual variables were also shown to be related to influencing behaviour. It was argued that these findings can be used to guide action.Practical implications – The findings have implications for the development of leaders and managers. The model of interpersonal influence allows individuals to identify their particular situation and draw conclusions, rooted in theory and derived from research, about how to enhance their effectiveness in influencing others at work.Originality/value – The originality and value of this paper lies in the way in which it extends and develops previous theory and research, including that by the author and collaborators published in previous editions of Industrial and Commercial Training, thereby validating the model and the research instruments used to operationalise it. The findings confirm that influencing behaviour does vary in different contexts and provides evidence that clearly indicates the particular contextual variables linked to the frequency of use of specific influence strategies and styles. [ABSTRACT FROM AUTHOR]

The article provides updates concerning the field of mathematics as of March 2007. The British National Cataloguing Unit for the Archives of Contemporary Scientists has received a grant for a project on the archives of British physicists and mathematicians. A team of mathematicians and computer scientists in the U.S. has developed a pedagogical technique for teaching material in discrete mathematics. A quantity of primary and secondary materials for the history of mathematics is available online.

In a deliberately provocative first part to this paper, I argue that nineteenth-century British mathematicians had an unduly high opinion of themselves and a striking lack of appreciation for contemporary continental developments. I argue that this failure was rooted in the institutions that supported mathematics, and was only remedied towards the end of the century. In the more sober second half of the paper I ask if historians of mathematics have subscribed to this overestimate, and explore some related questions, among them what are historians doing when they write history: telling it as it was, or righting or defending the record? Historians of mathematics also need to consider British priorities for research in the nineteenth century, and a comparison with other minor players (such as Japan, Portugal, or Poland) might be illuminating. [ABSTRACT FROM AUTHOR]

Although the Victorian era was characterized by the dominance of Great Britain both militarily and economically, the achievements of the British in mathematics were considerably less spectacular. Nevertheless, significant contributions were made by British mathematicians, several of whose names are still well known today. This paper highlights the principal mathematical developments in Britain during this time, closing with some observations on the weaknesses and limitations of Victorian British mathematics. [ABSTRACT FROM AUTHOR]

Innovation in learning and teaching is an everyday requirement in contemporary higher education (HE), especially in challenging subjects such as mathematics. Teaching mathematics to students with limited experience of formal mathematical instruction is a good example of a demanding pedagogical undertaking where innovatory practice can help HE teachers rise to the challenge. This paper presents an innovative game-based learning approach to the teaching of basic mathematics in HE through the example of a first-year mathematics module of the BSc Computer Science course offered by the Aberystwyth University (UK). Excellent examination results and positive student feedback concerning the learning experience point to the value-addedness of this approach in HE and it is, therefore, offered here as an example of good teaching practice to be disseminated more widely in the sector. [ABSTRACT FROM AUTHOR]

Science, technology, engineering, and mathematics (STEM) skills are very valuable for economic growth. However, the number of young people pursuing STEM learning trajectories in the United Kingdom was lower than the predicted demand during the last decade. Several STEM enrichment and enhancement activities were thus funded by the government, private, and charitable organisations to improve understanding of and raise pupil interest in these subjects. One possible way of measuring the impact of these activities in supporting pupil understanding of maths was to track the proportion of young people obtaining a ‘good’ grade in standardised national tests such as the GCSEs. Attainment is of course only one possible outcome of education but certainly a very important one because students are more likely to continue studying subjects in which they score higher. This makes maths attainment even more important as it is a pre-requisite for admission to STEM degree courses. This longitudinal study makes use of the National Pupil Database to assess the impact of these schemes on maths attainment of participating schools. Following up 300 intervention schools for five years the study shows the intervention group did not do any better than the comparator. The paper suggests further directions for research and offers recommendations for practice. [ABSTRACT FROM PUBLISHER]

In this paper we explore a relational understanding of landscape qualities. We asked three independent groups of human observers to assess the expressive qualities of a range of landscapes in the UK and in Spain, either by means of personal visits or from a projected digital image. We employed a Free Choice Profiling (FCP) methodology, in which observers generated their own descriptive terminologies and then used these to quantify perceived landscape qualities on visual analogue scales. Data were analysed using Generalised Procrustes Analysis, a multivariate statistical technique that does not rely on fixed variables to identify underlying dimensions of assessment. The three observer groups each showed significant agreement, and generated two main consensus dimensions that suggested landscape ‘health’ and ‘development in time’ as common perceived themes of landscape expressivity. We critically discuss these outcomes in context of the landscape assessment literature, and suggest ways forward for further development and research. [ABSTRACT FROM AUTHOR]

Past research has shown that growth mindset and motivational beliefs have an important role in math and science career interest in adolescence. Drawing on situated expectancy-value theory (SEVT), this study extends these findings by investigating the role of parental motivational beliefs (e.g., expectancy beliefs, utility values) and parent growth mindset in math on adolescent career interest in math-intensive fields (e.g., mathematics, computer science, statistics, and engineering; MCSE) through adolescent motivational beliefs in math. Structural equation modeling was used to test the hypothesized model using data from 290 adolescents (201 girls, 69.3%; Mage = 15.20), who participate in informal STEM (science, technology, engineering, mathematics) youth programs, and their parents (162 parents, 87.7% female) in the United Kingdom and the United States. As hypothesized, adolescent expectancy beliefs, utility values, and growth mindset in math had a significant direct effect on MCSE career interest. Further, there was a significant indirect effect of parental expectancy beliefs in math on MCSE career interest through adolescents' expectancy beliefs. Similarly, there was a significant indirect effect from parental utility values in math to MCSE career interest through adolescents' utility values. The findings suggest that parents' math motivational beliefs play a critical role in adolescent math motivational beliefs and their career interest in math-intensive fields. [ABSTRACT FROM AUTHOR]

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Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the workplace lacking the required mathematical knowledge and skills. The situation in England, Wales and Northern Ireland reflects more general international concerns about decreasing educational standards. However, evidence to support this concern has been of limited scope, rarely subjected to peer-review and of questionable validity. Our study overcame the limitations of previous research into standards over time by applying a comparative judgement technique that enabled the direct comparison of mathematical performance across different examinations. Furthermore, unlike previous research, all examination questions were re-typeset and candidate responses rewritten to reduce bias arising from surface cues. Using this technique, mathematics experts judged A-level scripts from the 1960s, 1990s and the 2010s. We report that the experts believed current A-level mathematics standards to have declined since the 1960s, although there was no evidence that they believed standards have declined since the 1990s. We contrast our findings with those from previous comparison studies and consider implications for future research into standards over time. [ABSTRACT FROM AUTHOR]

This paper explores the views of a group of students who took an oral performance assessment in a first-year mathematics module. Such assessments are unusual for most subjects in the UK, but particularly within the generally homogenous assessment diet of undergraduate mathematics. The evidence presented here resonates with some, but not all, of the existing literature on oral assessment and suggests that, despite concerns about anxiety and fairness, students see oral assessments as encouraging a focus on understanding, being relatively authentic and reactive to their needs. We argue that, suitably implemented, oral assessment may be a viable assessment method for straddling the ‘assessment for’ and ‘assessment of’ learning divide in higher education. [ABSTRACT FROM PUBLISHER]

This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7–8, 10–11, and 13–14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability. [ABSTRACT FROM AUTHOR]

Genome sequencing is available as a clinical test in the UK through the Genomic Medicine Service (GMS). The GMS analytical strategy predominantly filters genome data on preselected gene panels. Whilst this reduces variants requiring assessment by reporting laboratories, pathogenic variants outside applied panels may be missed, and variants in genes without established disease–gene relationships are largely ignored. This study compares the analysis of a research exome to a GMS clinical genome for the same patients. For the research exome, we applied a panel-agnostic approach filtering for variants with High Pathogenic Potential (HiPPo) using ClinVar, allele frequency, and in silico prediction tools. We then restricted HiPPo variants to Gene Curation Coalition (GenCC) disease genes. These results were compared with the GMS genome panel-based approach. Twenty-four participants from eight families underwent parallel research exome and GMS genome sequencing. Exome HiPPo analysis identified a similar number of variants as the GMS panel-based approach. GMS genome analysis returned two pathogenic variants and one de novo variant. Exome HiPPo analysis returned the same variants plus an additional pathogenic variant and three further de novo variants in novel genes, where case series are underway. When HiPPo was restricted to GenCC disease genes, statistically fewer variants required assessment to identify more pathogenic variants than reported by the GMS, giving a diagnostic rate per variant assessed of 20% for HiPPo versus 3% for the GMS. With UK plans to sequence 5 million genomes, strategies are needed to optimise genome analysis beyond gene panels whilst minimising the burden of variants requiring clinical assessment. [ABSTRACT FROM AUTHOR]

This paper reports the outcomes of a ‘lesson study’ project conducted in a mathematics department with four serving teachers in a secondary school in England. Using Dudley’s lesson study framework and drawing on Hargreaves and Fullan’s notion of professional capital, the feasibility and value of collaborative lesson study as a vehicle for the development of teacher learning were explored. Planning and evaluation meetings as well as end-of-project interviews were analysed to investigate how teachers planned research lessons together and how these were evaluated. Despite time constraints, teachers who engaged in lesson study reported that the process improved understanding of their students; that collaboration helped them to develop less-teacher-centred approaches and created a stronger sense of teacher community. The project demonstrated that lesson study has potential as an alternative or complementary model of teachers’ learning, but it also throws up substantive organisational challenges if its use is to expand. [ABSTRACT FROM PUBLISHER]

Although the incidence of variant Creutzfeldt-Jakob disease (vCJD) has declined to 1 since 2012 in the UK, uncertainty remains regarding possible future cases and the size of the subclinical population that may cause secondary transmission of the disease through blood transfusion. Estimating the number of individuals who were exposed to the bovine spongiform encephalopathy (BSE) infectious agent and may be susceptible to vCJD will help to clarify related public health concerns and plan strategies. In this paper, we explore this estimate by describing the probability of potential exposure due to dietary intake throughout the BSE epidemic period from 1980 to 1996 as a stochastic Poisson process. We estimate the age- and gender-specific exposure intensities in food categories of beef and beef-containing dishes, burgers and kebabs, pies, and sausages, separating the two periods of 1980–1989 and 1990–1996 due to the specified bovine offal legislation of 1989. The estimated total number of (living) exposed individuals during each period is 5,089,027 (95% confidence interval [CI] 4,514,963–6,410,317), which was obtained by multiplying the population size of different birth cohorts by the probability of exposure via dietary intake and the probability of survival until the end of 2013. The estimated number is approximately doubled, assuming a contamination rate of . Among those individuals estimated, 31,855 (95% CI 26,849–42,541) are susceptible to infection. We also examined the threshold hypothesis by fitting an extreme-value distribution to the estimated infectious dose of the exposed individuals and obtained a threshold estimate of 13.7 bID50 (95% CI 6.6–26.2 bID50) (Weibull). The results provide useful information on potential carriers of prion disease who may pose a threat of infection via blood transfusion and thus provide insight into the likelihood of new incidents of vCJD occurring in the future. [ABSTRACT FROM AUTHOR]

Mathematics education is rarely out of the policy spotlight in England. Over the last 10 years, considerable attention has been given to improving 14–19 mathematics curriculum pathways. In this paper we consider some of the challenges of enacting curriculum change by drawing upon evidence from our evaluation of the Mathematics Pathways Project (MPP). From 2004 to 2010 this project, which was directed by England's Qualifications and Curriculum Authority, aimed to improve the engagement, attainment and participation rates of 14- to 19-year-old learners of mathematics. Our particular focus is upon the temporal problems of piloting new curriculum and assessment and we draw on Lemke's discussion of timescales, heterochrony and the adiabatic principle to consider the interlocking and interference of various change processes. [ABSTRACT FROM PUBLISHER]

Outdoor education has received greater attention in the United Kingdom with the launch of the Learning Outside the Classroom Manifesto. However, teachers' lack of confidence and competence appear to be key factors underpinning the extent of outdoor learning provision in schools. This paper reports on a partnership project in which student teachers worked alongside classroom teachers to create outdoor activities in primary mathematics. Findings suggest that such a partnership provides a supporting framework for both teachers and student teachers to develop confidence, competence and enthusiasm for the provision of future outdoor learning experiences. [ABSTRACT FROM AUTHOR]

Aim. This paper is a report of a study of the relationship between nurses' clinical experience and calibration of their self-confidence and judgement accuracy for critical event risk assessment judgements. Background. Miscalibration (i.e. under-confidence or over-confidence of confidence levels) has an important impact on the quality of nursing care. Despite this, little is known about how nurses' subjective confidence is calibrated with the accuracy of their judgments. Methods. A sample of 103 nursing students and 34 experienced nurses were exposed to 25 risk assessment vignettes. For each vignette they made dichotomous judgements of whether the patient in each scenario was at risk of a critical event, and assigned confidence ratings (0-100) to their judgement calls. The clinical vignettes and judgement criteria were generated from real patient cases. The methodology of confidence calibration was used to calculate calibration measures and generate calibration curves. Data were collected between March 2007 and January 2008. Findings. Experienced nurses were statistically significantly more confident than students but no more accurate. Whilst students tended towards under-confidence, experienced nurses were over-confident. Experienced nurses were no more calibrated than students. Experienced nurses were no better at discriminating between correct and incorrect judgements than students. These patterns were exacerbated when nurses and students were extremely over-confident or extremely under-confident. Conclusion. Nurses were systematically biased towards over/under-confidence in their critical event risk assessment judgements. In particular, experienced nurses were no better calibrated than their student counterparts; with student under-confidence countered by experienced nurses' greater susceptibility to over-confidence. [ABSTRACT FROM AUTHOR]

In this paper, I examine the properties of the handicapping system in the UK. Using a generalized ordered logistic regression model of hole by hole scores of individuals, simulation was employed to calculate the probability of winning for an individual in stroke play and match play head to heads and also in tournament competitions with multiple entrants. The results suggest that the current handicapping system does not produce equal probabilities of players with different handicaps winning. Specifically, lower handicappers have a higher probability of winning in both stroke play and match play games. Having investigated the possibility of employing scaling factors in order to level these probabilities, I pose the question of the extent to which equal probabilities is in fact a desirable property of a handicapping system. [ABSTRACT FROM AUTHOR]

• This paper explores whether ability grouping in UK primary schools at age 7 affects how much pupils like Maths, English and school generally by age 11. • How much pupils like particular school subjects and school generally is an important outcome to consider because there is no a priori reason why those in higher and lower ability groups should diverge over time with respect to the degree to which they enjoy their studies (as distinct from their perception of how well they are doing academically relative to other pupils). • Our key finding is that pupils placed in the lower ability groups were less likely than their peers in the high ability group to come to enjoy, continue to enjoy, or increase their enjoyment of Maths between the ages of 7 and 11, both before and after controlling for maths ability at age 7, sex and social class background. Similar patterns were evident in relation to liking of English and school generally before controlling for these factors, but were largely statistically insignificant after the inclusion of control variables. • This finding is robust to different modelling strategies including individual fixed effects. • Given that the extent to which pupils like their studies is known to influence their level of academic engagement and achievement, our findings lend support to the wealth of evidence indicating that ability grouping - at least as currently practiced in UK primary schools - is harmful for those judged to be of lower ability. Advocates of grouping pupils by measured ability for instructional purposes claim that ability-homogeneous classrooms increase the attainment of high-ability pupils without detriment to the attainment of pupils judged to be of lower ability. Opponents of ability grouping, in contrast, argue that high-ability pupils do at best only marginally better in ability-homogeneous classrooms than they would have done in mixed-ability settings, whereas low-ability pupils do significantly worse. One mechanism posited by the critics of ability grouping is that this practice causes psychological harm to those labelled low-ability, resulting in a self-fulfilling prophecy of low attainment. Most previous studies have measured this posited psychological impact of ability grouping in terms of pupils' "academic self-concept", a term which refers to pupils' perceptions of how good they are in relation to particular subjects or to academic study generally. This paper explores the related but distinct concept of "academic enjoyment", which refers to the extent to which pupils like the particular subjects they study, and like school generally, which has been shown to be positively correlated with academic engagement and achievement. While academic self-concept may change over time as pupils become aware of their level of academic performance, as indicated by test scores and/or their placement in particular ability groups, this need not be the case for change over time in pupils' enjoyment of their studies which could, in theory at least, remain stable or change in a uniform direction regardless of the ability group in which pupils are taught. In this paper we explore whether pupils' enjoyment of Maths, English, and school generally, changes in a differential manner between the ages of 7 and 11 depending on the ability group in which pupils were placed at age 7. We do so by drawing on data from the Millennium Cohort Study (MCS) which has followed a nationally representative sample of children in the UK born between 2000 and 2002. Compared to pupils in the high ability group, those in the low ability group were less likely to come to enjoy, continue to enjoy, or increase their enjoyment of Maths between the ages of 7 and 11, both before and after controlling for pupils' measured ability in Maths at age 7 and the key demographic variables of gender and social class background. Similar divergences with respect to enjoyment of English and school generally were evident before controlling for these additional factors, but were largely statistically insignificant after the inclusion of these controls. Overall our findings suggest that ability grouping in primary schools does more harm than good, at least in relation to pupils' enjoyment of Maths. [ABSTRACT FROM AUTHOR]

What difference do teacher educators really make? This paper explores the role of mathematics student-teachers' pre-training dispositions (habitus) in reproducing classroom practice, and the effect of different training contexts (habitat) upon what Bourdieu called "dispositional harmonisation". These Bourdieuan concepts are mobilised to examine aspects of pre-service teacher education, students' emerging teaching dispositions and the sociogeographical distribution of new mathematics teachers in the United Kingdom. This small-scale study suggests that it may be difficult for teacher-educators to influence the long-term practices of new teachers, by indicating how educational inequality is perpetuated through the positioning of new teachers in their "natural" teaching habitats. Finally, I examine the need for further research and the potential for disrupting these processes of social and pedagogical reproduction and consider the need to develop critical forms of mathematics teacher education. [ABSTRACT FROM AUTHOR]

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a 'probable preparedness' in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit. [ABSTRACT FROM AUTHOR]

There has been widespread concern over the lack of preparedness of students making the transition from school to university mathematics and the changing profile of entrants to mathematical subjects in higher education has been well documented. In this paper, using documentary analysis and data from an informal case study, we locate the antecedents of this changed profile in the general shift across all subjects to a more utilitarian higher education, alongside the more specific changes in A-level mathematics provision which have been largely market driven. Our conclusions suggest that, ironically, changes put in place to make mathematics more widely useful may result in it losing just those features that make it marketable. [ABSTRACT FROM AUTHOR]

Science, technology, engineering, and math (STEM) workers need both motivation and interpersonal skills in STEM disciplines. The aims of the study were to identify clusters of adolescents who vary in math and science motivation and interpersonal skills and to explore what factors are related to membership in a high math and science motivation and interpersonal skills cluster. Participants included 467 adolescents (312 female; M age = 15.12 to SD = 1.71 year) recruited from out-of-school STEM programs in the US and UK. Findings from latent class analyses revealed four clusters, including a "High Math and Science Motivation and Interpersonal Skills" group, as well as groups that exhibited lower levels of either motivation or interpersonal skills. STEM program belonging, and STEM identity are related to membership in the high motivation and skills cluster. Findings provide insight into factors that may encourage motivation and interpersonal skills in adolescents, preparing them for STEM workforce entry. [ABSTRACT FROM AUTHOR]

How does the design of technology-based service mathematics shape science students' understandings of mathematics? Reciprocally, how do the conceptions of undergraduate mathematics teachers concerning service mathematics shape their design decisions when building a technology-based course? The paper starts from the premise that simultaneous study of design and learning together may throw light on epistemological and psychological issues in learning mathematics. The corpus of data was derived from two university mathematics departments, each of which was attempting to design and implement a service course of undergraduate mathematics for science students. The findings reveal a complex relationship between design and learning, with implications for the design of instructional approaches. [ABSTRACT FROM AUTHOR]

This paper derives an optimal reflationary mix for the next decade and comments on the industrial implications of this policy. The discussion is based on simulations of the multi-sectoral dynamic model of the UK economy developed by members of the Cambridge Growth Project. The results suggest that the concentration on macroeconomic policy alone may be misguided and that instruments which attack the roots of Britain's industrial problems should receive more attention. The paper also demonstrates that the optimal control procedure is a reliable tool for steering an economy towards a desired target trajectory and that this is feasible for very large econometric models. [ABSTRACT FROM AUTHOR]

Is genuine individuality for staff throughout U.K. academia in general, and mathematics by association, becoming eroded? This opinion piece suggests that it is most certainly on the decline, arguing for the accommodation of a wide variety of character types to enhance a workplace now dominated by frenetic busyness and inextricably tangled up with an overbearing compliance threatening to run riot in H.E. [ABSTRACT FROM AUTHOR]

This study used semi-structured interviews with staff in 14 secondary schools in England to explore strategies for entering students to GCSE Mathematics, focusing on the use of early and multiple examination entry. The key findings suggest that teachers were keenly aware of performativity pressures and that this prompted the use of a number of strategic entry practices, including the frequent use of early entry to allow students multiple examination attempts. This approach aimed to maximise the number of students achieving a grade C, the threshold for school accountability measures and for accessing further education and employment opportunities. Widespread use of early and multiple entry is likely to cease in England following amendments to accountability measures announced in 2013, yet this study adds a further perspective to the well-established literature detailing the impact of accountability measures in schools, as well as depicting teachers’ views on the effects of early and multiple entry upon pupils’ education. [ABSTRACT FROM AUTHOR]

• Coordination of scientific research communities supported mathematical modelling of COVID-19. • Pre-existing research collaborations contributed to the success of coordination initiatives. • National infrastructure is key to support nationwide research networks. • Evidence synthesis important in supporting scientists providing advice to government. In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

Little research has examined the associations between perceived inclusivity within informal science learning sites, youth program belonging and perceptions of program career preparation. This study explored relations between these factors at three timepoints (T1 = start of program, T2 = 3 months and T3 = 12 months after start). Participants were a diverse sample of 209 adolescents participating in STEM youth programs within informal science learning sites situated in the United States and United Kingdom (70% females: Mage = 15.27, SDage = 1.60), with 53.1% British and 64.1% non-White. Path analysis revealed that only perceptions of inclusivity for own social identity group (i.e., gender, ethnicity) at T1 were associated with T2 STEM youth program belonging. There was a significant indirect effect of T1 perceptions of inclusivity for one's own social identity groups on T3 perceptions of program career preparation via T2 program belonging. This study highlights that, over time, perceptions of inclusivity around youth's own social identity groups (i.e., gender and ethnicity/culture) are related to a sense of youth program belonging, which in turn is later associated with perceptions of program career preparation. [ABSTRACT FROM AUTHOR]

We reflect on our experience in Japan and the UK in raising mathematics funding, from the public and private sectors, and establishing new mathematics institutes. We hope that some of this information and relevant examples will be of use for mathematicians in other countries. [ABSTRACT FROM AUTHOR]

This paper provides a critical discussion of the historical and theoretical meaningfulness of the distinction between ‘objective’ and ‘subjective’ probability, as it supposedly emerged around 1840, by examining whether and how it appeared in the work of the mid-nineteenth-century British revisionist probabilists. A detailed analysis of the contributions of Augustus De Morgan, John Stuart Mill, George Boole, Robert Leslie Ellis and John Venn to probability is put forward in order to show that in so far as the terms did not appear as contradictories it is not possible to understand or compare these contributions with reference to the modern binary of ‘objective’ and ‘subjective’. [ABSTRACT FROM AUTHOR]

We report on an action research study conducted by two mathematics teacher educators in the United Kingdom and Hong Kong. The project consisted of three phases, the first two taking place in our respective teacher education courses and a final phase in which prospective mathematics teachers from both locations engaged in dialogue through a speculative fiction task. Our aim was to explore how our prospective mathematics teachers can be supported in becoming mathematics teachers for sustainable futures by innovating our own mathematics teacher education curricula. This study suggests that generative methods which support teachers in speculating on paths to potential futures as teachers of mathematics, can provide access to how prospective teachers negotiate issues in relation to the climate crisis and ways in which they conceive of related changes in their practices. By identifying the aspects of mathematics teaching that are viewed by the prospective teachers as contingent, and through offering tasks that support an expansion of this view, teacher educators are better placed to support the development of teaching practices needed for sustainable futures. [ABSTRACT FROM AUTHOR]