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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.

Mathematics Learning Support (MLS), which is available in the majority of Higher Education Institutions (HEIs) in Ireland and the UK, is traditionally available only to students of those institutions. In this paper, we describe a drop-in model of MLS at Maynooth University (MU) which has been available for secondary school students since 2009. This service is mainly staffed by volunteer undergraduate trainee teachers. Their feedback, the main focus of this paper, which has been collected over ten years, indicates that this experience has had a positive impact on their teaching practice. School students are also very positive about the support and MU enthusiastically endorses the service. We conclude that there are no obvious downsides to the provision of this type of support and we believe that more institutions should consider making it available. [ABSTRACT FROM AUTHOR]

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]

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.

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]

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]

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]

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]

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]

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)'.

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)'.

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]

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]

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]

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]

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]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

This article describes the approach used to assess the performance of a Fourier transform infrared (FTIR) and principal component regression (PCR) chemometric method when measuring respirable quartz, kaolinite, and coal in samples from a variety of mines from different countries; relative to target assigned values determined using X-ray diffraction (XRD). For comparison, FTIR results using the partial least squares regression (PLSR) method are also available. Bulk dusts from 10 Australian mines were scanned using XRD and grouped into three sets based on the levels of quartz, kaolinite, and feldspar within their crystalline mineral composition. Prediction samples were generated from 5 of these Australian mine dusts, Durrans coal dust, 2 mine dusts from the UK, and a single South African mine dust (71 samples in total) by collecting the aerosolized respirable dust onto 25-mm diameter polyvinylchloride filters using the Safety in Mines Personal Dust Sampler (SIMPEDS) operating at 2.2 l min−1. The predicted values from the FTIR chemometric methods were compared with assigned target values determined using a direct on-aerosol filter XRD analysis method described in Method for the Determination of Hazardous Substances (MDHS) 101. Limits of detection (LOD) and uncertainty values for each analyte were calculated from a linear regression between target and predicted values. The uncertainty was determined using the calibration uncertainty equation for an unweighted regression. FTIR results from PCR and PLSR are very similar. For the PCR method, the LOD for quartz, kaolinite, and coal were 5, 25, and 71 µg, respectively. For quartz, an LOD of 5 µg corresponds to an airborne quartz concentration of 10 µg m−3, assuming a 4-h sampling time and collection flow rate of 2.2 l min−1. The FTIR measurement met the expected performance criteria outlined in ISO 20581 when sampling quartz for more than 4 h using a flow rate of 2.2 l min−1 at a concentration of 0.1 mg m−3 (100 µg m−3), the current workplace exposure limit in Great Britain. This method met the same performance criteria when measuring exposures at the Australian Workplace Exposure Standard (WES) concentration of 0.05 mg m−3, although in this case a sampling period greater than 8 h was needed. [ABSTRACT FROM AUTHOR]

Fluctuation scaling relationships have been observed in a wide range of processes ranging from internet router traffic to measles cases. Taylor’s law is one such scaling relationship and has been widely applied in ecology to understand communities including trees, birds, human populations, and insects. We show that monthly crime reports in the UK show complex fluctuation scaling which can be approximated by Taylor’s law relationships corresponding to local policing neighborhoods and larger regional and countrywide scales. Regression models applied to local scale data from Derbyshire and Nottinghamshire found that different categories of crime exhibited different scaling exponents with no significant difference between the two regions. On this scale, violence reports were close to a Poisson distribution (α = 1.057±0.026) while burglary exhibited a greater exponent (α = 1.292±0.029) indicative of temporal clustering. These two regions exhibited significantly different pre-exponential factors for the categories of anti-social behavior and burglary indicating that local variations in crime reports can be assessed using fluctuation scaling methods. At regional and countrywide scales, all categories exhibited scaling behavior indicative of temporal clustering evidenced by Taylor’s law exponents from 1.43±0.12 (Drugs) to 2.094±0081 (Other Crimes). Investigating crime behavior via fluctuation scaling gives insight beyond that of raw numbers and is unique in reporting on all processes contributing to the observed variance and is either robust to or exhibits signs of many types of data manipulation. [ABSTRACT FROM AUTHOR]

In this paper, we trace how mathematical models are made 'evidence enough' and 'useful for policy'. Working with the interview accounts of mathematical modellers and other scientists engaged in the UK Covid-19 response, we focus on two weeks in March 2020 prior to the announcement of an unprecedented national lockdown. A key thread in our analysis is how pandemics are made 'big'. We follow the work of one particular device, that of modelled 'doubling-time'. By following how modelled doubling-time entangles in its assemblage of evidence-making, we draw attention to multiple actors, including beyond models and metrics, which affect how evidence is performed in relation to the scale of epidemic and its policy response. We draw attention to: policy; Government scientific advice infrastructure; time; uncertainty; and leaps of faith. The 'bigness' of the pandemic, and its evidencing, is situated in social and affective practices, in which uncertainty and dis-ease are inseparable from calculus. This materialises modelling in policy as an 'uncomfortable science'. We argue that situational fit in-the-moment is at least as important as empirical fit when attending to what models perform in policy. • Pandemics are performed as crises of uncertain yet catastrophic potential. • Mathematical models are forms of scalar narrative affording epidemics their scale. • Models and projections are made useful as evidence in their situated policy events. • Calculations are given agency as affects in the evidencing of pandemics. • Modelling pandemics is a site of 'uncomfortable science' and 'dis-ease'. [ABSTRACT FROM AUTHOR]

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

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In terms of the history of mathematics higher education, mathematics and statistics support (MSS) is a very recent development, existing as a formal feature for less than 50 years. However, in this short time, MSS has displayed its own characteristics. A particularly notable feature of MSS in the United Kingdom (and in other countries) has been the way in which practitioners have collaborated with each other, almost from the outset. This collaboration has led to the creation of a community (the sigma network) with a written constitution and formal membership. This two-part article traces the history of the development of the MSS community in the UK from its earliest incarnations to the present day. The first part of the article reviews the period from the early 1990s to 2005 during which time the key events were the rise and demise of the Mathematics Support Association and the creation of sigma, Centre of Excellence in University-wide Mathematics and Statistics Support. [ABSTRACT FROM AUTHOR]