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This article explores the effect on assessment of ‘translating’ paper and pencil test items into their computer equivalents. Computer versions of a set of mathematics questions derived from the paper-based end of key stage 2 and 3 assessments in England were administered to age appropriate pupil samples, and the outcomes compared. Although in most cases the change to the different medium seems to make little difference, for some items the affordances of the computer profoundly affect how the question is attempted, and therefore what is being assessed when the item is used in a test. These differences are considered in terms of validity and legitimacy, that is whether the means used to answer a question in a particular medium are appropriate to the assessment intention. The conclusion is not only that translating paper and pencil items into the computer format sometimes undermines their validity as assessments, it is also that some paper and pencil items are less valid as assessments than their computer equivalents would be. [ABSTRACT FROM AUTHOR]

Despite extensive research on attainment grouping, the impact of attainment grouping on pupil attainment remains poorly understood and contested. This paper presents evidence from a study conducted with 2944 12–13 year olds, from 76 schools in England, who were allocated to between‐class attainment groups ('setting') in English and mathematics over the first 2 years of secondary schooling. After controlling for prior attainment, pupils in the top set performed significantly better than pupils in the middle and bottom sets in both English and mathematics. The findings indicate a widening gap in attainment, especially in the case of English. Findings, especially in the case of mathematics, provide more evidence of a relative benefit for pupils placed in top sets than a relative detriment for those in bottom sets. [ABSTRACT FROM AUTHOR]

Improving mathematical skills is a priority in England, and a series of policy levers and government change projects have focused on improving mathematical outcomes in further education (FE) in recent years. Yet little is known about the mathematics teacher workforce that supports these students on vocational and technical programmes. This paper addresses this knowledge gap by examining important features of the mathematics teacher workforce in colleges and the implications for recruitment, initial training and ongoing professional development. We report findings from a national survey targeted at all mathematics teachers in around one-sixth (N = 31) of England's general FE colleges. Teachers have transitioned into FE from three main areas: another career, curriculum area, or educational context. We discuss the varied assets and training needs of these three subgroups and argue that the mathematics teacher cohort in FE should be seen as distinct from that in either primary or secondary education. We highlight the bimodal distribution of mathematics qualifications amongst this workforce; those having level 2 mathematics qualifications being more likely to be teaching functional skills mathematics courses than GCSEs. The rapid expansion of the mathematics teacher workforce that followed the changes to the condition of funding in 2014 has come disproportionately from teachers who were previously working in schools. This, together with a trend of funnelling increasing numbers of FE students into academic mathematics rather than functional skills courses, raises important questions about the nature of mathematical education for learners on vocational and technical programmes, and the teachers thereof. [ABSTRACT FROM AUTHOR]

The problem of low attainment in mathematics has been an increasingly prominent feature of the policy discourse in England over the last 60 years; however, evidence from comparative studies indicates that little progress has been made in finding a solution. In this paper, we analyse the changing policy discourse of low attainment in mathematics through the main reports and speeches published in England, beginning with the Newsom Report, Half Our Future, in 1963, and continuing to the present day. We chart the evolving perspectives on the nature of ability, expectations, curriculum ideology and frame of reference through the changing language used in these documents, noting tensions and inconsistencies which arise through continuing lack of clarity about definitions and assumptions. [ABSTRACT FROM AUTHOR]

Much comparative research into education-related beliefs has exploited questionnaires developed in one culture for use in another. This has been particularly the case in mathematics education, the focus of this paper. In so doing, researchers have tended to assume that translation alone is sufficient to warrant a reliable and valid instrument for cross-cultural research, prompting concerns that a number of necessary equivalences are unlikely to have been addressed. In this paper, we consider the nature of these equivalences before examining the literature of a different field, healthcare research, to synthesise an approach to instrument adaptation that is pragmatic but rigorous. Finally, we demonstrate how this pragmatic approach, incorporating extensive cognitive interviews, enabled us to adapt and refine a mathematics-related beliefs questionnaire, developed in Flanders, for use with students aged 14–15 in England and Spain. Analyses indicate that the instrument so developed is multidimensional, reliable and cross-culturally valid. Some implications are discussed. [ABSTRACT FROM PUBLISHER]

In England and Wales government pressures to raise attainment has led many schools to implement structured “ability” grouping in the form of setting. The introduction of selective grouping has been justified with the assumption that the differentiation of students by “ability” advances students’ motivation, social skills, independence and academic success in national tests and examinations because students are “better engaged in their own learning”. This paper critically engages with this assumption. Drawing upon qualitative research conducted in primary and secondary mathematics, science and English setted classrooms in England the aim of this literature review is to consider how teachers’ pedagogic practices with low, middle and high “ability” sets facilitates and/or constrains students’ learning and potential achievement. We also explore why, despite strenuous criticism and moves towards egalitarianism in schools, the segregation of students on the basis of “ability” continues to be a common feature in schools in England and Wales. This literature review draws attention to a number of substantive issues including (but not restricted to) fixed and permanent grouping; the potential misplacement of students to sets and a culture of stereotyping where learners within a set are taught as a single homogenous unit. We conclude the paper by suggesting foci for future research in the hope of eliciting renewed critical interest in and investigation of setting by “ability” in a broader range of subjects of the curriculum. [ABSTRACT FROM PUBLISHER]

There is considerable interest within mathematics teacher education in mapping the career development of teachers. Although there is an agreement that professional learning is embedded in workplace practice, there has been little attention to the effect of variations within the teaching profile. This paper focuses on pre-university mathematics and its contribution to teacher development in the early career stage. Our longitudinal multiple-case study mapped induction for A-level teaching in England, and identified opportunities and demands that led to professional learning. We found a common understanding of such teaching as a privilege. Teachers experienced rapidly reducing formal support, with little mentoring directed at reflective development of A-level teaching, and claimed this limited their growth as teachers. However, A-level teaching offered professional learning opportunities complementary to those offered by teaching of earlier mathematics; teachers came to better appreciate connections within mathematics, and the need for development of rigour and deep conceptual foundations, as well as deepening their own mathematical knowledge. [ABSTRACT FROM AUTHOR]

There has, for some years, been a growing concern about participation in university-entrance level mathematics in England and across the developed world. Extensive statistical analyses present the decline but offer little to help us understand the causes. In this paper we explore a concern which cannot be explored through national data-sets, namely the retention of mathematics students on Advanced level (A-level) mathematics courses. Drawing on survey data from 15 secondary schools in the Midlands of England, we examine subject differences in decisions to study, withdraw from, and continue in a range of A-level subjects. Not only is the rate of attrition from mathematics higher than most other subjects, but there are substantial differences between schools. In order to explore this high rate of attrition further we consider one school (Queensbury Park) in which a large proportion of students decided not to continue with their study of mathematics from Year 12 to Year 13. Drawing on performance data and focus group interviews we explore some of the reasons for the students’ decisions. [ABSTRACT FROM PUBLISHER]

This paper explores the factors that contribute to the development of positive stress and distress in teachers within secondary schools in England. It draws on narrative interviews undertaken with 12 mathematics and science teachers in six schools and focuses on three of these teachers to explore issues in more depth. The findings demonstrate that the use by teachers of appropriate coping mechanisms, e.g. actively seeking out preferable alternatives, and access to professional and personal support, with the right frame of mind, namely, seeing stressors as capable of being overcome, can produce desirable consequences for the teachers through their use of stress in a positive, healthy manner and lessen the likelihood of negative long-term effects associated with distress. [ABSTRACT FROM AUTHOR]

We draw on two studies of mathematics departments in 11-18 comprehensive maintained schools in England to compare and contrast the insights provided by differing theoretical perspectives. In one study, activity theory was used to describe common features of the work of three departments. In the other, a mathematics department was viewed and analysed as a complex system. In both cases, it was the learning of the departments as systems rather than of individuals that was of interest. The affordances and limitations of the analytical perspectives are discussed. Taken as a whole, this paper opens up the workings of school mathematics departments in a country which has a strong department culture. [ABSTRACT FROM AUTHOR]

This paper examines how A-level students construct relationships between work and happiness in their accounts of choosing mathematics and further mathematics A-level. I develop a theoretical framework that positions work and happiness as opposed, managed and working on the self and use this to examine students' dual engagement with individual practices of the self and institutional practices of school mathematics. Interviews with students acknowledge four imperatives that they use as discursive resources to position themselves as successful/unsuccessful students: you have to work, you have to not work, you have to be happy, you have to work at being happy. Tensions in these positions lead students to rework their identities or drop further mathematics. I then identify the practices of mathematics teaching that students use to explain un/happiness in work, and show how dependable mathematics and working together are constructed as 'happy objects' for students, who develop strategies for claiming control over these shapers of happiness. [ABSTRACT FROM AUTHOR]

In recent years the mathematics education research community has undergone a social turn towards a greater interest in the values and broader educational purposes of mathematics education, including issues of social justice and citizenship education. Building on these developing interests, this paper presents a conceptual framework that links the teaching of school mathematics with moral education. Then, in a case study involving two countries, England and Canada, this framework is used to explore the affordances and constraints faced by mathematics teachers in those countries if they want to intentionally practice moral education in the classroom. [Copyright &y& Elsevier]

Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular. [ABSTRACT FROM AUTHOR]

For a number of years, Loughborough's Mathematics Education Centre, recently awarded national Centre for Excellence in Teaching and Learning status, has worked with others to provide innovative learning resources to enhance the teaching and learning of mathematics. This paper describes some of the uses we are making of technology to help and support our engineering undergraduates learning of mathematics; most are taught mathematics using the HELM (Helping Engineers Learn Mathematics) resources, which we briefly describe. HELM was a major curriculum development project involving a consortium of five UK universities led by Loughborough that uses interactive technology for teaching and assessment. Its success is evidenced by their considerable uptake at other institutions. Elearning is part of our overall learning and teaching strategy and a key component of our work is to develop the use of emerging modern technology in the delivery of mathematics at all levels, whilst pursuing the relevant pedagogic research. Consequently we describe some recent developments in our teaching with engineers; these include the use of Tablet PCs and electronic voting systems. We make significant use of our university's VLE to deliver the material, and ongoing developments include the use of podcasts and Moodle quizzes for formative assessment, which we outline. Finally, we comment on some of the issues involved. [ABSTRACT FROM AUTHOR]

In this paper, we consider our use of activity theory to examine empirical data from a study of reform in England - the implementation of the mathematics strand of the Key Stage 3 Strategy in two schools. Our concerns are largely methodological - we consider the aspects of reform that more traditional activity theory methods and foci were able to theorise - questions related to "what" had changed, and then consider those aspects that were left aside - participants' experiences of reform and the influences of broader dominant discourses relating to mathematics classroom practices. We then go onto show how concepts related to the notion of "boundaries" - boundary objects and boundary crossing can be used within an activity theoretical frame to theorise the gaps. We conclude by detailing the ways in which this expansion of foci adds to our understandings of policy implementation. [ABSTRACT FROM AUTHOR]

Abstract: Researchers have been aware for some time of the differences between extensive and intensive quantities but the significance of these differences has not been recognized in mathematics curricula. In England children are provided with many opportunities in their first few years in school to manipulate, measure and reason about extensive quantities but have virtually no opportunity to do the same with intensive quantities. This paper contrasts extensive and intensive quantities and describes the obstacles to primary school children''s understanding of intensive quantities: the need to consider two variables simultaneously and the difficulty of understanding inverse relations between variables. Study 1 shows that children have considerable difficulty in using inverse relations reasoning. Study 2 shows that this form of reasoning is more difficult in the context of intensive than extensive quantities problems. Implications for education are considered and examples of experiences with intensive quantities that could provided in school are presented. [Copyright &y& Elsevier]

The inspection by OFSTED's Initial Teacher Education and Training (ITET) team of courses of initial teacher education is high stakes. An unsatisfactory report can lead to course closure. Even a satisfactory report can lead to reductions in quota resulting in a spiral of decline in course viability. The high stakes nature of the inspection means that there has to be complete confidence in the level of validity and reliability of the inspection process. This paper presents an analysis of the complete cohort of published inspection reports of providers of secondary mathematics initial teacher education Post-graduate Certificate of Education (PGCE) courses carried out by the OFSTED ITET team in the period 1996-1998. The analysis demonstrates that there is considerable variation in the reports in terms of word length, how particular criteria seem to be applied and how judgements are expressed. With the complexity of the framework for inspection it is impossible, given the current model of inspection report, to properly distinguish between consistency of application and the loading given to any particular criterion. Attention to the transparency of the inspection process and to matters of validity and reliability is crucial if there is to be confidence in the inspection system. [ABSTRACT FROM AUTHOR]

The challenges facing those charged with teaching mathematics to engineers are enormous. Faced with large groups of students possessing a considerable range of abilities, prior experiences, and motivations, it is incumbent upon the developers and deliverers of mathematics programmes to engineers to ensure that such programmes are as inclusive as possible and take into account the particular and often individual needs of the student. Often a mathematics lecturer is caught between the demands of an engineering department expecting students to know and apply advanced techniques, and the needs of groups of students who lack confidence, have serious gaps in their knowledge and sometimes lack ability in mathematics. This paper describes an innovative approach to these challenges which involves a mix of traditional and modern technologies and which has been used with some effect at Loughborough University, for the teaching of mathematics to first year undergraduate engineering students. [ABSTRACT FROM AUTHOR]

Published data analysing entry and progression of mature students has generally been aggregated over all subject areas, or broken down into broad areas such as Arts or Sciences. In this paper we discuss mature students in the single subject area of mathematics, in a single institution, the University of Southampton. UCCA figures for mathematics have enabled us to make some comparisons with 'traditional' universities. We discuss some features of the age distribution, entry qualifications, degree class distribution, non-completion rates and gender distribution. [ABSTRACT FROM AUTHOR]

In 1989, the progressive introduction of a National Curriculum of subjects to all maintained schools in England and Wales brought compulsory science education into the primary sectors of these two countries for the first time. Such was its considered importance, science was placed alongside English and mathematics in what became known simply as 'the core'. As a result of its elevated profile and an immense amount of hard work and effort by teachers and other professionals responding to requirements, science education provision appeared to benefit enormously. Successive revisions of the national primary science curriculum have brought about many changes, however, each impacting on the primary profession individually in different ways and as a whole. Findings from a recently completed 'preparation to teach' survey across several geographically distinct regions of England are presented here which contribute to our ongoing understanding of the overall status of science teaching within primary schools. Twenty years on from when the national primary science curriculum was first introduced and independently evaluated, attention is drawn to the continued progress being made at the 'chalk-face' and to those factors widely perceived as continuing to inhibit delivery. [ABSTRACT FROM AUTHOR]