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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 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.

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.

This paper examines the characteristics of gifted mathematicians, highlighting the differences and essences in the lives of several eminent mathematicians and applying the findings to characteristics of mathematically gifted children and appropriate instructional provisions in the United Kingdom. (DB)

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)

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)