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Research Findings: Children are increasingly using touchscreen technologies at home, which has become a recurring feature within their classroom too. Research has investigated the potential effect of using computer-based tests to assess pupils' performance rather than traditional paper tests. An agreement has still not been formed about the impact of the mode of assessment on pupils' mathematical test scores. A mixed methods design was employed to explore the impact of the testing on young children's mathematical test scores. Thirty-seven children 4-7-years old were recruited from a primary school in England with their parents. A mathematical test on paper and an iPad was administered to each participant which was accompanied by an interview. Data regarding the use of touchscreens at home were explored with an on-line parental questionnaire. The results showed that gender and test type impact mathematical test scores, with females performing the best on the iPad test. The findings also suggested that as tablet usage increased at home, iPad mathematical test scores decreased. The interviews revealed that children rely on different strategies when resolving mathematical problems. Practice or Policy: Digital testing may enable a better investigation of mathematical skills in the first years of schooling and of differences between males and females' responses to solving mathematical questions, which then could be used to tailor the curriculum. [ABSTRACT FROM AUTHOR]

A major reform of the Mathematics curriculum was published in England in 2016, implemented in 2017 and examined in 2019. In Bulgaria, the analogous reform was published in 2018, will be implemented in 2020 and examined in 2022. This paper takes the framework developed by Budgell and Kunchev (2019) and seeks to interpret the new curricula in terms of the Students, the State and the Curriculum with an introduction to Assessment. In terms of the Curriculum, the paper examines, at the highest level, General and Specific Objectives; followed by Overarching Themes; then the Topics covered and finally the Detailed Content Statements for each topic. The paper concludes that the real differences between the teaching of Mathematics in England and Bulgaria lie not in the Mathematics itself but in the overall curriculum and assessment frameworks within which Mathematics is taught. [ABSTRACT FROM AUTHOR]

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]

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]

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 England, students who were awarded A levels in the summer of 2021 experienced disruption in their education during Years 12 and 13 (i.e., throughout the whole of their A level studies) due to the COVID-19 pandemic. National examinations were cancelled in 2021 (as in 2020) and students were given Teacher-Assessed Grades (TAGs). In determining these grades, teachers were instructed to judge students' achievements in relation to the material that had been covered during Years 12 and 13 rather than against the complete A level syllabus. This small-scale study investigated potential impacts of the unusual experience of Year 13 A level mathematics students on factors including topics covered, confidence in mathematics, post-A level intentions and readiness for higher education, with a view to considering challenges around the transition to higher education. Data were gathered using student and teacher questionnaires. In total, 174 students and 27 teachers from 19 schools/colleges across the country (including one college in Wales) completed the questionnaires. This paper gives a high-level overview of the main messages emerging from the questionnaire responses. It is intended to undertake a more in-depth analysis of the data at a later date and report the findings from the more detailed analysis in subsequent papers. [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]

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]

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 design of good notation is a cause that was dear to Charles Babbage's heart throughout his career. He was convinced of the "immense power of signs" (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage's writings, for the first time in a systematic way. Babbage's desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

In this paper we investigate the translation of research into professional development (PD) materials for teachers of primary mathematics, by England's National Centre for Excellence in the Teaching of Mathematics, and related changes in teacher practices of teachers using the materials. We use interview data gathered from three teachers, via six teacher interviews, conducted over a two‐year period. The small sample allows us to explore the richness of their stories, while not being able to generalise to all teachers. Our results show that both implicit and explicit messages from research can become visible in new classroom practices. For instance, the teachers in our study all came to view the concept of number quite differently to how they had in the past, and in a way that was in keeping with research that informed the PD materials. A new view of number was implicit in the PD materials and in the teachers' descriptions of their practice. Other changes in teaching practices were explicitly spoken about by the teachers and were explicitly written about in the PD materials. Our work points to the efficacy of a team of practitioners working, with guidance, to create practical resources which embody research results. We propose viewing teachers as active partners in the process of translating research into practice. [ABSTRACT FROM AUTHOR]

This paper studies the formation of math and verbal skills during compulsory education and their impact on educational attainment. Using longitudinal data that follow students in England from elementary school to university, we find that the production functions of math and verbal skills are inherently different, where cross effects are present only in the production of math skills. Results on long-term educational outcomes indicate that verbal skills play a substantially greater role in explaining university enrollment than math skills. This finding, combined with the large female advantage in verbal skills, has key implications for gender gaps in college enrollment. [ABSTRACT FROM AUTHOR]

The mathematical topics which are of use to geography students are outlined, as are the methods used for teaching mathematical techniques in geography courses at Leeds over the last few years. The concluding section relates practice to goals, and the problems of providing the student with a framework into which he can fit all the pieces of knowledge he has acquired. Possible future developments are reviewed briefly in the light of the development of new mathematical techniques on the one hand, and criticisms of the existing state of the art on the other. The subject matter of the paper is limited to mathematical education, and there is only indirect and brief concern with statistics. [ABSTRACT FROM AUTHOR]

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]

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]

This paper offers a re-interpretation of the development of practical mathematics in Elizabethan England, placing artisanal know-how and the materials of the discipline at the heart of analysis, and bringing attention to Tudor economic policy by way of historical context. A major new source for the early instrument trade is presented: a manuscript volume of Chancery Court documents c.1565-c.1603, containing details of a patent granting a monopoly on making and selling mathematical instruments, circa 1575, to an unnamed individual, identified here as the instrument maker Humphrey Cole. Drawing on economic and legal history, the paper argues that practical mathematics needs to be understood as one 'project' among many, at a time when monopoly patents were used to advance industry, lower unemployment, secure the realm and reward invention. Drawing on the history and sociology of technology, it argues that the management and control of materials - mathematical instruments themselves, and the local socio-legal context within which they could be made - needs to be understood as prior to and separate from the rhetoric of mathematical authors, which is of interest in its own right but which may not have a direct relationship to mathematical practice.

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]

Taking lower-secondary schooling within the English educational system as an example, this paper illustrates the contribution of two bodies of international scholarship to the scoping of research-based pedagogical development aimed at improving student attitude and achievement in science and mathematics. After sketching the English context of systemic reform, the paper uses findings from the Trends in International Mathematics and Science Study (TIMSS) series to illuminate changes in performance, analysed within a framework of cross-system and between-subject comparison. Contrary to the optimistic picture from national assessment, the TIMSS findings suggest that systemic reform has produced fundamental gains only in student achievement in mathematics, and serious declines in student attitude towards both mathematics and science. Prompted by more favourable patterns elsewhere, the paper then triangulates the findings of recent meta-analytic research syntheses to identify promising lines of pedagogical development. Despite important differences in the conceptual frameworks and analytic methods of these syntheses, reasonably robust conclusions can be drawn about the effectiveness of four teaching components: domain-specific inquiry for student achievement in both subjects, student attitude in science, and learning processes in mathematics; cooperative group work for learning and attitude in science; contextual orientation for achievement in science; and active teaching for achievement in mathematics. Equally, discrepancies between findings or insufficiencies of evidence highlight a number of impacts particularly deserving deeper analysis or further investigation: cooperative group work on achievement outcomes, differing forms of learning assessment on both attitude and achievement outcomes, contextual orientation on outcomes in mathematics, and active teaching on outcomes in science. [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]

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]

Bernard Scott was born in London on 27 August 1915. At the time of his birth his name was Schultz. He was the only son of a Jewish family of fur and skin merchants who lived in North London; he had two sisters.Bernard attended the City of London School from 1925 to 1934. From school records it appears that he evinced an early taste for argument and debate. There is also testimony of his enthusiasm for sport, especially rugby. His talents for mathematics and for chess became evident at an early stage. While mathematics became his profession, it was the game of chess that aroused in him an abiding passion and made him a first-class player throughout his life.Bernard won an Open Scholarship in Mathematics to Magdalene College, Cambridge. He graduated with First Class Honours and a Distinction in Part III of the Mathematical Tripos in 1937. While pursuing his mathematical studies with evident success, he continued to cultivate his talent as a chess player. B. H. Neumann, who was a research student at Cambridge at that time, relates that he and Bernard Schultz (as he then was) went to London to take part in a weekend tournament and returned with all the prize money between them (about £7). [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]

Queuing theory can and has been used to inform bed pool capacity decision making, though rarely by managers themselves. The insights it brings are also not widely and properly understood by healthcare managers. These two shortcomings lead to the persistent fallacy of there being a globally applicable optimum average occupancy target, for example 85%, which can in turn lead to over- or under-provision of resources. Through this paper, we aim both to make queuing models more accessible and to provide visual demonstrations of the general insights managers should absorb from queuing theory. Occupancy is a consequence of the patient arrival rate and 'treatment' rate (the number of beds and length of stay). There is a trade-off between the average occupancy and access to beds (measured by, for example, the risk of access block due to all beds being full or the average waiting time for a bed). Managerially, the decision-making input should be the level of access to beds required, and so bed occupancy should be an output. Queuing models are useful to quickly draw the shape of these access-occupancy trade-off curves. Moreover, they can explicitly show the effect that variation (lack of regularity) in the times between arrivals and in the lengths of stay of individual patients has on the shape of the trade-off curves. In particular, with the same level of access, bed pools subject to lower variation can operate at higher average occupancy. Further, to improve access to a bed pool, reducing variation should be considered. [ABSTRACT FROM AUTHOR]

The Nursing and Midwifery Council (NMC, 2003) removed standard entry criteria for nursing programmes and asked Higher Education Institutions (HEIs) to consider the literacy and numeracy skills of prospective students. This triggered admissions staff within a Faculty of Health to consider ways of attracting people with the right skills but not the qualifications to prove it. It is important to encourage a wide range of people into nursing to meet the demands of strategic plans and policy, as well as to ensure the nursing profession reflects the diverse client groups it serves. Removing standard entry criteria and the widening participation agenda gave an ideal opportunity to try something new. A course entitled 'Portfolio of Evidence for Entry to Level 1 Study' was developed within the Faculty of Health at Staffordshire University to enable potential nursing students without standard entry qualifications to demonstrate their skills in numeracy and literacy. This paper reports on the background to this course and its success for three student cohorts (over an 18 month period) who have completed their first year of pre-registration nursing. The methodology employed is descriptive, qualitative analysis, comparing portfolio and standard entry students' assignment results., (Copyright 2009 Elsevier Ltd. All rights reserved.)

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 Nursing and Midwifery Council (2002a) reports that one of the most common examples of professional misconduct relates to the failure to administer medicines safely. In educating child-branch nurses, we have a duty to enhance students' calculation skills so that they are safe and can provide the best possible care to children. This paper presents a framework for numeracy within a child-branch curriculum, describing a practical approach to developing students' skills in the mathematical calculations they are likely to encounter in clinical practice. A pass mark of 70 per cent in relevant numeracy tests is considered too low for child branch students. Early identification of mathematical ability and provision of relevant tutorial support will ensure that the majority of students achieve the required standard.

At a time when many countries wish to improve their capacity in terms of scientifically and technologically educated young people, mathematics has an increasingly important role to play in support of this agenda. International studies tend to lead to headlines about performance and achievement, but widening participation in mathematics requires more than this. Fundamentally, we need students to develop positive dispositions towards mathematics and continued study of the subject. The articles brought together in this special issue explore underlying issues reporting on the work of a research project that focused on two different programmes of mathematical study in the first year of post-compulsory study in England. The wide-ranging work that is reported provides timely insights, through both quantitative and qualitative lenses, as students in transition negotiate their identities as young people in general, and in relation to mathematics in particular. [ABSTRACT FROM AUTHOR]

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway- Use of Mathematics-sits in parallel with long-established, traditional advanced level qualifications, what we call 'traditional Mathematics' herein. Traditional Mathematics is typically required for entry to mathematically demanding undergraduate programmes. The structure, pedagogy and assessment of Use of Mathematics is designed to better prepare students in the application of mathematics, and its development has surfaced some of the tensions between academic/pure and vocational/applied mathematics. Here, we explore what Use of Mathematics offers, but we also consider some of the objections to its introduction in order to explore aspects of the knowledge politics of mathematics education. Our evaluation of this curriculum innovation raises important issues for the mathematics education community as countries seek to increase the numbers of people that are well prepared to apply mathematics in science and technology-based higher education courses and work places. [ABSTRACT FROM AUTHOR]

Over the past 30 years, there has been a great deal of work directed at, first, understanding students' difficulties in algebra and, second, examining ways of tackling these difficulties. There is a vast research literature detailing successful ways of teaching algebra in experimental and laboratory settings. Yet, there is no clear evidence that this work has had a significant effect in terms of improving either attainment or engagement in algebra in ordinary, or non-experimental, classroom settings. Indeed, in England, current attainment in algebra appears to be no better than that of 30 years ago. In this paper, we analyse the algebra topics from two textbooks currently in widespread use in England, focusing on Grade 7 (ages 12-13). We examine the extent to which these textbooks draw on the research literature to support the teaching of algebra. Finally, we discuss the implications of this study. [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]

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]

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]

Spontaneous imaginary companion (SIC) creation in childhood is a typical imaginative play behaviour associated with advanced sociocognitive skills; however, the direction of causality has not been established. To investigate this experimentally, researchers must determine whether children can create, on request, qualitatively equivalent imaginary companions (ICs) to those created spontaneously. We examined whether children could create ICs, and how these compared to SICs. Nine elementary school children were encouraged to create ICs in a 3‐month intervention. Accounts of elicited ICs were compared with an age‐matched sample of interviewees with SICs. Seven children maintained ICs for 6 months post intervention. Template analysis of IC interviews found four themes: Realistic Play, Multifaceted IC Mind, Utility of the IC, and Elicited IC Across Time. Analysis suggests elicited and SICs were similar in nature and utility, although intervention ICs tended to have animal rather than human appearances. Findings support the argument that children can be encouraged to create ICs similar to SICs. [ABSTRACT FROM AUTHOR]

This article contains a short update on the work of the sigma Accessibility Special Interest Group. We announce the release of resources to assist mathematics tutors and coordinators with the support of mature students and those with dyslexia, dyscalculia and dyspraxia. We provide a brief background to the development of these resources and describe their pilot in two institutions, one in England and the other in Ireland. We close with a description of the next stages of work for the special interest group and a call for additional people to get involved. [ABSTRACT FROM AUTHOR]

Since policy changes in 2014 about who studies mathematics post-16 in England, the mathematics teaching workforce in further education (FE) colleges has grown and diversified. The question of how best to develop the professional practice of this changing workforce is, however, unresolved. Teachers in a recent national study report the benefits of non-formal learning but the diverse organisational structures of colleges impact on the size and focus of teacher communities and thereby the nature of professional learning. Where mathematics teachers are enabled to meet regularly or work in close proximity, teacher learning communities emerge but their development is constrained by a lack of consensus on the professional identities and competencies of mathematics teachers in FE colleges. Despite these obstacles, we argue that there is considerable potential to enhance professional learning for mathematics teachers in FE through a communities of practice approach and that such a strategy for professional development is a key component of a self-improving further education system. [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]

The Programme for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) are respected cross-national studies of pupil achievement. They have been specifically designed to study how countries’ educational systems are performing against one another, and how this is changing over time. These are, however, politically sensitive issues, where different surveys can produce markedly different results. This is shown via a case study for England, where apparent decline in PISA test performance has caused policymakers much concern. Results suggest that England's drop in the PISA ranking is not replicated in TIMSS, and that this contrast may be due to data limitations in both surveys. Consequently, I argue that the current coalition government should not base educational policies on the assumption that the performance of England's secondary school pupils has declined over the past decade. [ABSTRACT FROM PUBLISHER]

The Attention Deficit Hyperactivity Disorder (ADHD) criteria from the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders were used to assess a large sample of children at the end of their first year at school in England. These data were explored using Rasch measurement and the measures for the items together with their frequencies are reported. The data were further analysed in three ways: a) The results were compared with a previous similar analysis of college students. b) A principal components analysis of the item residuals from the Rasch analysis was conducted. c) The measures were linked to reading and mathematics attainment assessed at three different time points. The exploration supported previous work and theoretical positions, and in doing so raised issues about the appropriateness of the use of the criteria across all ages. It also suggested that one of the currently recognised ADHD sub-types could be further sub-divided into verbal and physical hyperactivity. The links to academic achievement raised questions about the integrity of the currently recognised ADHD sub-types and the paper calls for further investigations. [ABSTRACT FROM AUTHOR]

Women are a minority in science, technology, engineering and mathematics academic careers. In particular, few women in Japan choose to study physics and mathematics. In this study, we investigated the factors contributing to the masculine image of physics and mathematics based on the framework of our expanded model. We conducted online questionnaire surveys in Japan and England, and found that physics and mathematics occupations, and mathematical stereotypes were both related to a masculine image. Only in Japan were social factors, such as a person's attitude to intellectual women, related to viewing mathematics as 'masculine'. However, the experience of being told or having heard that the choice of a particular course of studies would make someone less attractive to the opposite sex was evident only in England. This finding suggests that social factors affect the masculine image of physics and mathematics, and that this could vary depending on the country. [ABSTRACT FROM AUTHOR]

Establishes whether mathematics is a barrier to higher education for adult returnees on Access courses, a project funded by the Higher Education Funding Council at the University of Exeter in England. Influence of social inequalities on participation in educational activities; Review of Access philosophy.

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This article addresses whether the introduction of end‐of‐course, linear General Certificate of Secondary Education (GCSE) examinations changed the socio‐economic equity gap in England. The GCSE is a national examination offered in a wide range of subjects and taken by almost the entire 16‐year‐old age cohort. Between the years 2007 and 2014, it underwent a number of reforms to both the underlying curriculum and the examination structure. At the beginning of the period, examinations were primarily modular in structure where the course was decomposed into discrete units tested in a staged manner. By 2014, all GCSE examinations were linear and the whole course content was tested simultaneously when study was complete. These structural changes and the curriculum reforms mean that the impact of modular and linear testing on the performance of students has been the focus of recent interest. Some educational commentators suggested that modular examinations are more suitable for lower‐performing students, including those with lower socio‐economic status (SES). This research has been conducted to monitor the socio‐economic equity gap in the light of the structural changes. It focuses on GCSE mathematics and concludes that, although there is still a clear gap in attainment between disadvantaged students and their peers, this gap does not seem to be exacerbated by the examination structure. In other words, the linearisation of GCSE mathematics is unlikely to have increased inequity between students of high and low SES. [ABSTRACT FROM AUTHOR]

'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]