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A "crisis account" of shortages of well-qualified scientists, engineers, mathematicians and technologists has shaped education policy in the UK and the USA for decades. The apparent poor quality of school science education along with insufficient numbers of well-qualified teachers have been linked to skills shortages by government and other agencies since at least the time of the Second World War. There is, however, an alternative account that challenges the received view of a skills deficit and questions the evidence for sustained and long-term shortages across the sector. This paper provides an historical account of some of the main events that have characterised debates over the supply and demand of science and engineering professionals in the UK and the USA and the implications that this has had for science education policy. Starting from the end of the Second World War, the paper looks at the key challenges to the evidence that underpins the shortage debate and considers the consequences that more than seven decades of crisis accounts have had on the recruitment and retention of highly skilled scientists and engineers. The paper shows that while the shortage debate has a long history, it is one that is characterised by poor quality data as well as methodological and conceptual challenges. It argues that there is no consensus view about the existence of a skills deficit and that while there may have been short-lived shortfalls in specialist areas, there is little evidence in support of widespread and far reaching shortages as the rhetoric often claims.

Lesson Study is rapidly becoming one of the most adopted models of teacher professional development worldwide. In this paper, we examine the teachers' discussions that are an integral part of the Lesson Study research cycle. In particular, we investigate the "dialogic mechanisms" that enable teachers' pedagogical intentions to be developed within the context of discussions that stem from observations of students as they address mathematical problems. In so doing we hypothesize about the nature of the "dialogic space" that is created and how this allows teachers to move from the collaborative analysis of student outcomes to an enhanced understanding of pedagogical intentions in mathematics. Data for this paper derive from a large research project taking place in Camden, London. This project aims to implement Lesson Study in the context of the introduction of a New National Curriculum for Mathematics in England. It involves a large cohort of mathematics teachers across primary and secondary schools. Quantitative analysis of video-recorded Lesson Study discussions is reviewed and one illustrative case study is included to contextualise the quantitative data. Findings suggest that a focus on student outcomes enables teachers to collaborate effectively on developing pedagogical intentions to directly address student need. Further, it seems that particular features of dialogue are evident where teachers move to an agreed perspective on pedagogic change; and evidence of 'supportive moves' in interactions suggest that a form of dialogic space is necessary if all teachers in a Lesson Study group are to learn from shared understandings about future teaching and learning needs.

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills, such as debate, argument and disagreement. The students were told in advance to use the online material to prepare, which had a short handout on matrix determinants posted, as the lesson would be interactive and would rely on them having studied this. At the beginning of the lesson, the two mathematicians worked together to model the skill of professional disagreement, one arguing for the cofactor expansion method and the other for the row reduction method. After voting for their preferred method, the students worked in small groups on examples to defend their choice. Each group elected a spokesperson and a political style debate followed as the students argued the pros and cons of each technique. Although one lecture does not establish whether the flipped lecture model is preferable for student instruction, the paper presents a case study for pursuing this approach and for further research on incorporating this style of teaching in Science, Technology, Engineering and Mathematics subjects.

Due to the empirical nature of the discipline, psychology students, during the course of their degree, are required to become proficient with a range of quantitative methods. Unfortunately many of these students experience high levels of maths anxiety, which can have a damaging effect on this aspect of their educational development. The first study in this paper used focus groups to identify, from psychology undergraduate and postgraduate students, potential interventions that could be used to reduce anxiety in an undergraduate sample. The second study implemented those interventions that were deemed valid and practical on a sample of 246 psychology first and second year undergraduates. The effectiveness of these interventions was mixed, but does suggest further avenues that tertiary educational institutions could take to reduce maths anxiety in their student body, in particular enhancing the use of real-life examples in quantitative methods teaching.

In this paper I report findings from a four year study of beginning elementary school teachers which investigated development in their mathematical knowledge for teaching (MKT). The study took a developmental research approach, in that the teachers and the researcher collaborated to develop the mathematics teaching of the teachers, while also trying to understand how such development occurred and might be facilitated. The Knowledge Quartet (KQ) framework was used as a tool to support focused reflection on the mathematical content of teaching, with the aim of promoting development in mathematical content knowledge. Although I focused primarily on whether and how focused reflection using the KQ would promote development, it was impossible to separate this from other influences, and in this paper I discuss the ways in which reflection was found to interrelate with other areas of influence. I suggest that by helping the teachers to focus on the content of their mathematics teaching, within the context of their experience in classrooms and of working with others, the KQ framework supported development in the MKT of teachers in the study.

Purpose: The purpose of this paper is to evaluate the effectiveness of using several commercial tools in science, technology, engineering and maths (STEM) subjects for enterprise education at Newcastle University, UK. Design/methodology/approach: The paper provides an overview of existing toolkit use in higher education, before reviewing where and how tools are used across science and engineering disciplines. Feedback was collated from Newcastle educators and students to determine whether the projected enterprise learning outcomes were achieved. STEM learning outcomes were also mapped to the NCEE entrepreneurship learning outcomes framework. Findings: The paper investigated the use of three key enterprise toolkits across the Faculty of Science, Agriculture and Engineering and the Faculty of Medical Sciences, where the focus is on innovation and product/service development, rather than on the desire to "be an entrepreneur." This reflection on practice evaluates the benefits and student perceptions of workshop tools for enterprise, decision making and teamwork. It makes comparison between the perceived employability needs of these students, and addresses the intended and actual outcomes of these tools. Research limitations/implications: Evaluating toolkit use within a single university is constrained by common internal workings, however as exemplars of good practice this is of value to other UK higher education institutions. Practical implications: Consideration is given to entrepreneurial support and development, and whether using existing tools should be used for summative or for formative assessment. It also questions whether tools are fit for purpose. Originality/value: This paper reveals patterns of tool use and their effectiveness across science and engineering. (Contains 1 figure and 3 tables.)

This paper describes how a cluster of nine secondary science teachers and lecturers from five schools and colleges in the United Kingdom designed and undertook small-scale action research projects as an approach to their own continuing professional development. The participating teachers identified a range of topics for investigation such as: student voice to inform curriculum planning; the use of STEM (Science Technology Engineering Mathematics) to raise student engagement and motivation in mathematics and literacy; and assessment and learning in practical work. The participants brought their research into practice either as individuals, pairs or within a team. Central to each project was the use of reflection as a primary approach to enable the teachers to self-evaluate their professional practice and gain a greater understanding of the wider contexts of teaching and learning. The key aim of establishing a cluster was to foster collaborative reflective practice and encourage a teacher-led process. Reflective practice was developed through the use of several approaches including: reflective discussions, audio reflections, a paper-based learning and evaluation tool, and an online hub. Teachers were particularly encouraged to use the latter three tools in an attempt to stimulate and structure their reflections critically about what was taking place in a given situation during their designed interventions, to identify suitable options, and to make tacit the knowledge gained about their approaches to classroom-based research. (Contains 1 figure and 1 table.)

This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and explores the ways in which young people deploy the discourses produced in these texts. We argue that there are particular (and sometimes contradictory) meanings and discourses about mathematics that circulate in popular culture, that young people use these as resources in identity making as (non-)mathematicians, negotiating their meaning in ways that are not always predictable, and that their influence on young people is diffuse and nevertheless important. The paper discusses the discourses that prevail in some of the popular cultural images of mathematics and mathematicians that came up in our research. We show how mathematics is represented as a secret language, while mathematicians are often mad, mostly male and almost invariably white. We then explore how young people negotiate these discourses, positioning themselves in relation to mathematics. Here we draw attention to the fact that both those who continue with mathematics after it ceases to be compulsory and those who do not, deploy similar images of mathematics and mathematicians. What is different is how they respond to and negotiate these images. (Contains 7 notes.)

This paper outlines the difficulties with the current system of tiering in GCSE Mathematics exams, indicating both the problem of equality across tiers of the same grade and a particular problem in Mathematics, which with three tiers has a foundation tier on which it is not possible to gain a C grade.The authors outline a different system in which all candidates take basic papers on which all grades from G to C can be awarded and then an extension paper is available for the higher grades. This system has been tried out with a sample of pupils from a number of schools and a non-operational award was made. The authors describe the results of this and discuss potential difficulties with this system. Comparisons between the systems are made, showing that the established system of tiering is inherently unstable, while the proposed system, though not perfect, has much to commend it. [ABSTRACT FROM AUTHOR]

This paper gives a short overview of the UK government's STEM agenda and then considers one aspect in depth--the STEM Advisory Forum. It explains how the Forum operates to draw together views from across the STEM community through online discussions and face-to-face events. Four examples are given of topics that have been dealt with by the Forum. Firstly the topic of engineering, enrichment and engagement is covered through samples of various events and discussions. A major issue covered is the number of young people taking A Level mathematics. The background to the issue is explained and how views expressed on the Forum might have had some influence upon the Government's advanced level target and may yet impact on admissions behaviour in universities. A third short example of impact on the number of university places for STEM subjects is given and the piece finishes with an example of impact at local level in schools. (Contains 4 figures.)

The success of policies to attract adults back to the learning of mathematics, at various levels, is often linked to questions of motivation. However, motivations depend on relevant beliefs, attitudes and emotions about mathematics--which themselves reflect, together with experiences with maths in school and in the home, wider cultural discourses on mathematics. The work presented here is part of a larger study examining the complex relations between popular cultural products such as advertisements and films, the way that knowledge is portrayed by them, and possible consequences for people's affective responses. The initial phase of the project (Evans, 2003, 2004) analysed small "opportunistic" samples of advertisements and films. The advertisements portrayed mathematics as generally negative, whereas the films were more ambivalent. In the next phase, we produced larger samples of both advertisements and films. In this paper, we report on our search through a systematic sample of issues of UK daily newspapers for "mathematical" advertisements. A notable finding was the very small number of advertisements containing images of mathematics. Those few advertisements we found were most frequently for cars, or for services to businesses. Using a discourse theoretical perspective and a hybrid methodology, we categorise advertisements according to features such as their "appeal" to potential consumers--and we also produce semiotic readings of a sub-sample of advertisements, as to their "message", in particular their images of mathematics, and of people doing, using, or teaching mathematics. Here we find these images to be much more varied and subtle than in the initial phase. We end by discussing some of the consequences of our analysis for perceptions, teaching and use of mathematics in today's market economy societies.

This paper presents a study in a UK university that investigated how first-year (freshman) Information Systems undergraduates perceive learning through courseware containing real-world erroneous examples derived from their peers and what obstacles had to be overcome to implement effective e-Learning support for using and creating such courseware. The study finds that students find the courseware very effective in dealing with their personal misconceptions while also providing other secondary pedagogic benefits for both students and lecturers.

The paper investigates semiotics as an integrative, foundational framework for operational research (OR). To this end, the semiotics of the pragmatist C.S. Peirce is explained and its application in OR research, and consulting practice is explored. It is the fourth in a series of papers each seeking to ground OR in a different logic: philosophic/mathematical logic, pragmatic logic, economic logic and now semiotic logic. For Peirce, semiotics is a logic, and as such it is argued in the paper that it can embrace philosophical/mathematical, pragmatic and economic logics. The comprehensive nature of semiotics is such that it brings to a close the research programme aimed at establishing foundations for OR. However, the closure of one programme opens up another—the application of semiotics in OR practice and academic research. Possible avenues for further research include learning from, and collaboration with, neighbouring disciplines such as information systems and computer science. [ABSTRACT FROM AUTHOR]

Between 1809 and 1820, Thomas Knight (1775–1853) published quite a few papers on mathematics and its applications. These show him to have been surprisingly well-versed in French analytical mathematics at a time when French works were little read by his British contemporaries. InBSHM Bulletin2, Gloria Edwards and I published a paper (Craik and Edwards 2004) entitled ‘In search of Thomas Knight’, designated below as ‘[1]’, that examined Knight’s life and work. This follow-up paper gives further biographical information that links him with Edinburgh; it describes some more of his publications that were previously overlooked (for notice of the latter, I am grateful to a correspondent who wishes to remain anonymous); and it records some remarks about his work by his contemporaries. [ABSTRACT FROM PUBLISHER]

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In this article we address the issue of how students over this period have been expected to engage with the specialised discourse of school mathematics. We explain our analytic methods and present some outcomes of the analysis. We identify changes in engagement with algebraic manipulation, proving, relating mathematics to non-mathematical contexts and making connections between specialised mathematical objects. These changes are discussed in the light of public and policy domain debates about "standards" of examinations.

This paper describes the results of a small empirical study (n = 130), in which undergraduate students in the Business Faculty of a UK university were asked to express views and expectations relating to the study of a mathematics. Factor analysis is used to identify latent variables emerging from clusters of the measured variables and these are interpreted within the context of a simple model of student engagement. The potential impact of the latent variables on student self-efficacy (a student's belief in their ability to achieve successful outcomes) is discussed, and suggestions are made as to how this type of information can be utilized by lecturers to help promote better student engagement and provide effective support in mathematics.

In this paper, we present, analyse and critique an episode from a secondary school lesson involving an introduction to the definition of the scalar product. Although the teacher attempted to be explicit about the difference between a definition and a theorem, emphasizing that a definition was just an arbitrary assumption, a student rejected the teacher's definition in favour of his own alternative. With reference to this particular case, we seek to explore some ways in which teachers can introduce mathematical definitions to students so as to support, rather than attempt to circumvent, their mathematical sense making. In this regard, we believe that it is important to develop learning opportunities for students which help them to gain some appreciation of important structural and historical reasons that underpin the definitional choices made.

Many children who would not be identified as having special educational needs are low-attaining in mathematics, which often has a severe impact on their progress at school and their successes in later life. This paper describes Catch Up Numeracy, a non-intensive targeted intervention for children who are low-attaining in mathematics, which is delivered by classroom assistants in only thirty minutes per week. Data for 440 children, including controls, show that children receiving Catch Up Numeracy intervention attained average gains more than twice that expected of typically attaining children, and more than twice that attained by children receiving non-targeted mathematics support. The evidence suggests that Catch Up Numeracy is effective for children who are low-attaining in mathematics. More generally, it supports the view that many children's arithmetical difficulties are highly susceptible to intervention, and that the intervention does not need to be intensive or delivered by highly-trained teachers to be effective.

Following the publication of the higher education white paper increasing entry tariff and widening participation have become even more important issues for universities. This report examines the relationship between entry tariff and undergraduate achievement in Biosciences at the University of Exeter. We show that, whilst there is a significant correlation between A-level tariff and both level 1 and final degree marks, the magnitude of the correlation decreases with increasing A-level tariff. It was also found that, contrary to anecdotal evidence, there is no link between A-level maths or chemistry and degree success in biosciences. However gender was found to have a marked effect on degree success independent of A-level tariff. Female students consistently obtained marks more than one third of a degree classification higher than male students with equivalent entry qualifications. These results are compared to investigations in other disciplines, notably medicine, and in the context of the drive to increase entry tariff to allow unrestricted recruitment of the top students. (Contains 2 figures, 1 footnote, and 6 tables.)

Much research and many papers on mathematics pedagogy have discussed assessment and, in particular, the need to provide a varied diet of methods by which students are assessed for the award of their degree. In this article, we explore the mix of assessment methods provided across a range of UK university mathematics departments. We examine the relationship between the mix of assessment methods and type of institution and between the type of assessment and the mathematical topic. We found that closed book exam is still the most common assessment method in undergraduate mathematics, with some new assessment methods, such as projects and presentations, now used in most UK institutions.

We report on a project currently in progress that aims to identify through research the range of factors (individual, school and out-of-school, including home) and their interactions that influence post-16 (i.e. post-compulsory) participation in mathematics and physics in the UK and to assess their relative importance among different student populations. In this project, we are beginning to elucidate the views of students and examine the sources of these views by exploring the contexts in which both school and university students experience barriers or opportunities and form their identities with regard to participation in mathematics and physics. Our focus in this paper is on our methodology, the reasons for it and how and why our approach to data collection developed during the project. We situate our work within a mixed-methods approach, using multilevel modelling and discourse analysis to analyse and interpret our findings that derive from our own questionnaires, interviews and ethnography and from existing large-scale datasets. We argue that greater acknowledgement in the education literatures that investigate student participation in mathematics and science needs to be made than is usual of the range of factors, including unconscious forces that may affect participation.

This paper investigates whether the inter-generational benefits of parental adult education exist over and above the achievement of parental educational qualifications during schooling and whether returns to parental adult learning are greatest for children of parents with low levels of education. Using data from the UK Avon Longitudinal Study of Parents and Children, ALSPAC, results show that mothers' participation in adult education is not associated with improvements in their children's academic attainment in English and mathematics at age 14 once the previous parental academic qualifications are included. This lack of relationship was found for the overall sample, and for subgroups defined by the type of adult education (accredited, unaccredited or informal learning), the intensity of learning (duration and engagement) and by mothers' prior educational qualifications. Although our results suggest that maternal adult learning is not a key factor for improvement in children's test scores at age 14, further research is needed to investigate the role of parental adult learning at other stages of children's cognitive development. (Contains 7 notes, 1 figure and 5 tables.)

One of the themes of the recent sociology of higher education has been the globalisation of knowledge and the professional transfer of scientists and researchers. In this paper we show how these transfers of people and knowledge are disproportionately characteristic of: (a) some institutions; and (b) some cost centres. We argue that universities form part of an international labour market for high skilled workers in prestige institutions. However, globalisation also has a second face in relation to labour markets in higher education. This refers to the deployment of overseas junior staff in areas unsupplied by the British system. (Contains 4 tables, 3 figures, and 5 notes.)

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. (Contains 13 notes.)

It has long been established that marking accuracy in public examinations varies considerably among subjects and markers. This is unsurprising, given the diverse cognitive strategies that the marking process can entail, but what makes some questions harder to mark accurately than others? Are there distinct but subtle features of questions and their mark schemes that can affect accuracy? Such features could potentially contribute to a broad rationale for designating questions to markers according to personal expertise. The aim of this study was to identify question features that can distinguish those questions that are marked highly accurately from those that are marked less accurately. The study comprised an exploration of maths and physics questions from past GCSE examinations, which were marked in an experimental setting by groups of markers and yielded differing marking accuracies. The questions also varied in their difficulty for GCSE candidates, and in the cognitive strategies needed to mark them. Kelly's Repertory Grid technique and semi-structured interview schedules were used in meetings with highly experienced principal examiners, who had led the experimental marking of the questions. The data generated comprised ratings for each question on a number of question features (constructs). The ratings were analysed together with the marking accuracy data, enabling an investigation of possible relationships between each question feature and (i) marking accuracy, (ii) question difficulty for the candidate, and (iii) apparent cognitive marking strategy usage. For both subjects, marking accuracy was found to be related to various subject-specific question features, some of which were also related to question difficulty (for the candidate) and/or apparent marking strategy complexity. For both maths and physics, several other subject-specific question features were found to be unrelated to accuracy. Overall, the findings have potential implications for the management of markers and for question design. (Contains 53 tables and 2 notes.)

In this theoretical paper the informal assessment practices of two experienced teachers are used as cases for generating questions about future developments in formative assessment practice. Both teachers maintain a consistent formative assessment focus on the development of their students as enquirers, and one of them supplements this with explicit self-assessment activities. However, there are subject-specific gaps in the ways in which they assess and describe their students and these are not addressed in widely promulgated advice about formative assessment. Questions are raised about how teachers might be supported to develop their assessment of subject-specific behaviour. (Contains 3 notes.)

Mathematics is commonly seen as a discipline with no place for linguistic ambiguity. In this paper, the treatment of ambiguity in two data extracts is critically examined. Analysis draws on two contrasting models of the nature of mathematics and mathematical language. The formal model sees meaning as fixed and relating to language relatively unproblematically. The discursive model sees meaning as situated in and by interaction, and so as shifting and changing as interaction unfolds. Analysis of the extract from the National Numeracy Strategy suggests that it is based on the formal model. This analysis is contrasted with analysis of classroom interaction which reveals how, from a discursive perspective, ambiguity can be seen as a resource for doing mathematics and for learning the language of mathematics.

Background: Children with persistent speech disorder (PSD) are at higher risk of difficulties with literacy, with some evidence suggesting an association with poorer educational attainment. However, studies to date have either used small clinical samples, which exclude children who have not been referred to clinical services, or relied on parent–teacher report of children's speech development. There is a need for an inclusive study to investigate the impact of PSD on educational outcomes using a population‐based sample and robust measures of speech development. Aim: Using a large prospective UK population‐based study—the Avon Longitudinal Study of Parents and Children (ALSPAC)—this study investigated: (1) how children identified with PSD at age 8 years perform on educational attainment tests at ages 10–11 and 13–14 years in comparison with children without PSD; and (2) whether children identified with PSD at age 8 years are more likely to receive a label of special educational needs (SEN) in secondary school. Methods & Procedures: We examined the data for 263 children with PSD and 6399 controls who had speech assessed at age 8 years in a research clinic. Educational attainment was measured using data from English school standard attainment tests. Data on SEN categorization were obtained between 11 and 13 years of age. Children with PSD and controls were compared using regression analyses adjusted for biological sex, maternal age, verbal, performance and full‐scale IQ. Outcomes & Results: Children with PSD at age 8 years were more likely to achieve lower attainment scores at ages 10–11 years in English and mathematics and across all three subjects of English, mathematics and science at ages 13–14 years after controlling for biological sex and maternal education; score below target levels for English at both time points after controlling for verbal IQ, and at ages 13–14 years after controlling for performance IQ; and receive a label of SEN (typically for the category of cognition and learning needs or communication and interaction needs) in secondary school. Conclusions & Implications: PSD identified at age 8 years is associated with poor educational attainment at ages 10–11 and 13–14 years in the core subjects of English, mathematics and science. Children with PSD at age 8 years are more likely to be identified with SEN at ages 11–13 years, particularly cognition and learning needs, and communication and interaction needs. We need to be aware of the potential for the long‐term impact of PSD on educational attainment in providing appropriate and effective support throughout school. What this paper addsWhat is already known on the subjectSpeech‐sound disorder is associated with reading and spelling difficulties, with some evidence to suggest that PSD is associated with a higher risk of literacy difficulties. Limited evidence also suggests that speech‐sound disorder may be associated with poorer educational attainment. However, studies to date have used small clinical samples or parent–teacher report of speech development and there is a need to determine whether the association is observed in larger and more inclusive population‐based samples.What this paper adds to existing knowledgeThis prospective, longitudinal study of a large community‐based sample of English children has shown that PSD is associated with poorer educational attainment at the end of primary school and at ages 13–14 years. Children with PSD are also more likely to be identified as having SEN in secondary school, especially communication and interaction needs but also including cognition and learning needs.What are the potential or actual clinical implications of this work?Understanding the long‐term implications of PSD on educational attainment highlights the importance of ongoing monitoring and support to enable children to reach their potential throughout primary and secondary school. The identification of children with a history of PSD during transition to secondary school will enable effective support to be put in place. The intervention for children with PSD should involve close collaboration between speech and language therapists and education professionals. [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)

The underrepresentation of women in Science, Technology, Engineering and Maths (STEM) occupations is a world‐wide phenomenon. The UK is simultaneously encountering a shortage of STEM skills. While gender imbalances in STEM study in higher education and A‐level study are widely documented, gender imbalances are apparent in vocational post‐16 education, though the existence and causes of these imbalances have received little attention. This paper uses administrative data to explore the extent of gender imbalances in STEM qualifications attempted and achieved in vocational post‐16 education routes. Gender differentials in the uptake of vocational STEM qualifications are much starker than they are in A‐levels and the roles of ability, socio‐economic status and school characteristics in explaining gender differentials differ with the education route taken, though their power in explaining these gaps is limited. [ABSTRACT FROM AUTHOR]

At the Open University in the UK, students taking undergraduate degree qualifications in areas such as Data Science and Economics are now the largest cohort of students on a second-year undergraduate statistics module, originally written for specialist mathematics and statistics students. This paper outlines an ongoing project to identify how more targeted support could be provided to students who are studying non-mathematics and statistics qualifications. This has involved engaging all the tutors who provided support in the project to create a new way of adapting their teaching styles and tutorial content. By grouping students who had similar qualification goals together and linking these groups to individual tutors, the new way of working created an atmosphere where students feel able to share their own misunderstandings and see how statistics is useful within their chosen qualifications. [ABSTRACT FROM AUTHOR]

As an established part of the infrastructure of many higher education institutions in the UK and across the world, Mathematics and Statistics Support (MSS), was forced to move to an online setting as a result of restrictions put in place due to the COVID-19 pandemic. With institutions offering limited online support prior to the pandemic, MSS practitioners were mostly unprepared to deliver online provisions. Survey data from May 2020 gives a first look at the immediate response of practitioners to online MSS. Interview data from January/February 2021 explores opinions after a period of reflection, and survey data from June 2021, over a year on from the initial sample, provides a direct comparison in opinion of online support a year later. This paper explores these three datasets, investigating the practitioner perspective and offers an overall reflection of how MSS practitioners' opinions of online support measures have changed from their "crisis-reaction" at the beginning of the pandemic to a more considered response as COVID-19 prevention measures are beginning to ease a year later. [ABSTRACT FROM AUTHOR]

This paper will consider the range of British participation in mathematics internationally during the nineteenth century through an analysis of British mathematical contributions to scientific journals outside of Britain. Viewing scientific papers contained in journals as significant indicators of research, we consider scientists who authored or read and responded in print to papers in a given area within a given group of journals to constitute a publication community. The extent of publication by British mathematicians in these journals can help characterize the role of foreign publication in nineteenth-century British mathematics. Moreover, the isolation of educational, societal, and personal circumstances which motivated British mathematicians to present their work to foreign journals highlights limited but concentrated groups of mathematicians committed to developing and strengthening international mathematical ties with Britain. [ABSTRACT FROM AUTHOR]

The Capsule Reviews are intended to provide a short succinct review of each paper in the issue in order to bring it to a wider readership. The Capsule Reviews were compiled by Fairouz Kamareddine. Professor Kamareddine is an Associate Editor of The Computer Journal and is based in the Department of Mathematical and Computer Sciences at Heriot-Watt University, Edinburgh, UK. [ABSTRACT FROM AUTHOR]

Background: Centile curves and standard scores are common in epidemiological research. However, standardised norms and centile growth curves for language disorder that reflect the entire UK local school population do not exist. Methods: Scores on six language indices assessing receptive and expressive functioning of children were obtained from the SCALES population survey. Monolingual English speaking participants were aged between five and nine years. Children who attended special schools at study intake, or who were learning English as an additional language were excluded. We constructed language norms using the LMS method of standardisation which allows for skewed measurements. We made use of probability weights that were produced from a two-step logistic model. Distributions of estimated standard scores from an intensively assessed sub-population and from the full population were contrasted to demonstrate the role of weights. Results: Non-overlapping centile curves and standardised scores at each age were obtained for the six language indices. The use of weights was essential at retrieving the target distribution of the scores. An online calculator that estimates standardised scores for the measures was constructed and made freely available. Conclusions: The findings highlight the usefulness and flexibility of the LMS method at dealing with the standardisation of linguistic and educational measures that are sufficiently continuous. The paper adds to the existing literature by providing population norms for a number of language tests that were calculated from the same group of individuals. [ABSTRACT FROM AUTHOR]

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]

Results of a British study indicate that, among potential applicants (N=177), a small demand exists for a proposed science education degree program. Findings suggest that recruitment of science and math teachers may be hampered because the satisfactions provided by teaching are unlike those sought by science and math specialists. (IAH)

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)'.

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]

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]

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]

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]

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]