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This paper derives an optimal reflationary mix for the next decade and comments on the industrial implications of this policy. The discussion is based on simulations of the multi-sectoral dynamic model of the UK economy developed by members of the Cambridge Growth Project. The results suggest that the concentration on macroeconomic policy alone may be misguided and that instruments which attack the roots of Britain's industrial problems should receive more attention. The paper also demonstrates that the optimal control procedure is a reliable tool for steering an economy towards a desired target trajectory and that this is feasible for very large econometric models. [ABSTRACT FROM AUTHOR]

The object of this paper is examine possible reasons for the emergence of the Cambridge Mathematical Tripos, an institution which was to serve as a model for the introduction of competitive examinations throughout nineteenth-century Britain. After tracing the evolution of the Tripos, the links between this examination and the changing pattern of teaching within the Univesity are investigated and the possible influence of the threatened parliamentary visitation of 1749 on the formation of the Tripos is also discussed. The degree to which the early Tripos served meritocratic ideals is investigated through an analysis of the pattern of appointment to fellowships and college livings. Lastly, the reasons why mathematics loomed so large in Cambridge's early examination system are explored and the situation there contrasted with that at Oxford where logic, rather than mathematics, remained pre-eminent. [ABSTRACT FROM AUTHOR]

This article discusses two of the reasons for the decline of formal Euclidean geometry in recent syllabi: (1) Traditional approach; and (2) Inherent difficulties. Suggested are some reasons and examples as to why the decline should be reversed. (YP)

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)

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)

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

Explores the development and assessment of safety and security use of computer systems in Great Britain. Assessment of security in the finance sector; Evaluation of assessment practices; Use of mathematical proof in designing a program.

Focuses on a project in United Kingdom universities by the UK Higher Education Funding Council, aimed at sharing of innovative practices in the teaching and assessing of mathematics in higher education. Background information on the project; Outline of the project; Key concerns of those teaching undergraduate mathematics; Details on the experiences of mathematicians as teachers.

How does the design of technology-based service mathematics shape science students' understandings of mathematics? Reciprocally, how do the conceptions of undergraduate mathematics teachers concerning service mathematics shape their design decisions when building a technology-based course? The paper starts from the premise that simultaneous study of design and learning together may throw light on epistemological and psychological issues in learning mathematics. The corpus of data was derived from two university mathematics departments, each of which was attempting to design and implement a service course of undergraduate mathematics for science students. The findings reveal a complex relationship between design and learning, with implications for the design of instructional approaches. [ABSTRACT FROM AUTHOR]

Highlights the history of the British Association's Mathematical Tables Committee. How the subject of mathematical tables was raised in the committee; Decline in the activity of the committee; Downfall of the committee.

Dans cet article, nous démontrons l'utilité d'une approche micro-fondamentale dans la compréhension de phénomènes sociaux de plus grande ampleur. Grâce à l'analyse des questions de recours collectifs, qui se sont posées aux différents acteurs, au Canada et en Angleterre, nous établissons un lien informel entre la macrovariable de « structure de l'industrie » et les formes divergentes de réglementation corporatiste instaurées dans les années 1930 Après avoir expliqué les caractéristiques centrales de l'approche microfondamentale et souligné les aspects importants de la théorie des jeux et du concept de choix rationnel, nous examinons les témoignages élaborés, présentés dans le cadre de commissions et de comités du gouvernement Ces données comparatives et historiques fournissent les bases qui permettent de comprendre la manière dont les différentes structures de l'industrie ont causé des problèmes de réglementation uniques pour les gouvernements canadien et britannique [ABSTRACT FROM AUTHOR]

As part of a broader research objective concerned with identifying the range of employer defined skill profiles that characterize workplace performance, this paper examines skill contexts for Application of Number, one of six UK defined Key Skills similar to Australian defined Key Competencies. Following the construction of questionnaires, grounded in the Analytic Hierarchy Process, applications of the instrument in both the UK and in Australia produced a ratio scale of priorities within the Key Skills area. This enabled a specification of the relative balance between classical competencies, e.g. facility with pen and paper calculations and emerging competencies demanded by the effective use of ICT. Relevance to workplace learning, including the transition from school to employment, and related aspects of mathematics education are discussed. Among the research outcomes is that spreadsheets are assuming a pre-eminent position and that this is an overriding priority for each defined activity and at each job level. [ABSTRACT FROM AUTHOR]

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

There has been widespread concern over the lack of preparedness of students making the transition from school to university mathematics and the changing profile of entrants to mathematical subjects in higher education has been well documented. In this paper, using documentary analysis and data from an informal case study, we locate the antecedents of this changed profile in the general shift across all subjects to a more utilitarian higher education, alongside the more specific changes in A-level mathematics provision which have been largely market driven. Our conclusions suggest that, ironically, changes put in place to make mathematics more widely useful may result in it losing just those features that make it marketable. [ABSTRACT FROM AUTHOR]

In a recent survey Sutherland and Dewhurst itemized the extent to which various types of departments expected selected mathematical topics in the background of incoming undergraduates. Using the results of diagnostic tests it is possible to estimate the actual capability of students with given prior qualifications to provide a 'probable preparedness' in specific topics. This paper compares expectations with probable preparedness in a range of topics. It is found that while some departments have realistic expectations about the background of their incoming students, others seem over-optimistic about the mathematical knowledge of today's students. Sometimes, topics that the department actually requires must in fact be covered ab initio with the students that they recruit. [ABSTRACT FROM AUTHOR]

Recent curriculum reforms have led to a wider variety of methods of assessment in formal 'high stakes' assessment regimes in many countries. Morgan's study of mathematics coursework assessment in UK schools identified a number of positions adopted by teachers as they assessed student texts. Using Bernstein's theoretical framework, we revisit Morgan's study in order to construct a model for understanding teachers' assessment practices and positionings. The model consists of opposing forms, generated by modelling agencies, agents, practices and specialised forms of communication, to identify their principles of construction, displayed as changes in the strength of boundary. This helps to distinguish practices of assessment as different modalities of regulation, and to understand the tensions within and between discourses and practices. Thus, for example, by interpreting tensions between discourses of 'mathematical investigation' and of 'assessment' in terms of the contradictory demands made by different modes of pedagogic practice, we can reveal the social assumptions of the pedagogic discourse. [ABSTRACT FROM AUTHOR]

Editorial. Focuses on the educational system of Great Britain. Significance of inclusion of statistics in the mathematics curriculum of education; Methods suggested to evoke in interest of pupils in mathematics; Proposed changes in the education system of Great Britain.

The expansion of higher education in the UK in the 1980s and the subsequent increase in student numbers has created greater variation in cohorts of students entering university. Entry requirements are more relaxed and students with lower pre-university (A-level) qualifications or alternative qualifications (BTEC, GNVQ) are routinely accepted onto MPharm degree programmes within the UK. Mathematics is a key component in the pharmacy degree programme and an understanding of basic mathematics is essential. This wide variation in mathematical ability coupled with increasing class sizes has led to various strategies being introduced to ensure that all students attain the required level of mathematical ability to complete the degree programme. This study investigates the use of a diagnostic test to improve both the teaching and learning experience. The paper describes an investigation into what may be learnt about students' background knowledge and skills from initial assessment and information about their prior qualifications, and how this information may be used to devise effective teaching and learning strategies. [ABSTRACT FROM AUTHOR]

What difference do teacher educators really make? This paper explores the role of mathematics student-teachers' pre-training dispositions (habitus) in reproducing classroom practice, and the effect of different training contexts (habitat) upon what Bourdieu called "dispositional harmonisation". These Bourdieuan concepts are mobilised to examine aspects of pre-service teacher education, students' emerging teaching dispositions and the sociogeographical distribution of new mathematics teachers in the United Kingdom. This small-scale study suggests that it may be difficult for teacher-educators to influence the long-term practices of new teachers, by indicating how educational inequality is perpetuated through the positioning of new teachers in their "natural" teaching habitats. Finally, I examine the need for further research and the potential for disrupting these processes of social and pedagogical reproduction and consider the need to develop critical forms of mathematics teacher education. [ABSTRACT FROM AUTHOR]

The introduction of the National Numeracy Strategy (NNS) in England in September 1999 represented a very significant attempt to change the way mathematics was taught in primary schools. In Wales, where the NNS does not apply, an alternative strategy required Local Education Authorities (LEAs), in consultation with their schools, to develop locally based numeracy initiatives. This article presents and discusses results from a comparative study of the way in which headteachers viewed these contrasting attempts to raise standards of numeracy and their perception of the way in which the initiatives impacted upon pupils, teachers and teaching approaches. Whilst the data presented within the article may be of particular interest to policy makers and practitioners in England and Wales there would also appear to be some messages for those who may be concerned with similar large-scale reform efforts elsewhere. [ABSTRACT FROM AUTHOR]

This article cautions on OECD's recent educational survey or the PISA survey. The OECD's international survey of 15-year-olds' educational attainments carried out in Spring 2001 aroused surprise and even astonishment in Great Britain when its results were published because the new OECD survey put the pupils among the world's top performers in mathematics. Questions in the new PISA survey, were deliberately not directed to curricular techniques, but to the more difficult issues of the candidate's ability to choose appropriate techniques and apply them to authentic skills for life problems, making it much more difficult for teachers to know what to do in order to improve pupils' capabilities.

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 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.

Abstract: This paper traces the ebbs and flows of the history of geometry at Cambridge from the time of Cayley to 1940, and therefore the arrival of a branch of modern mathematics in Great Britain. Cayley had little immediate influence, but projective geometry blossomed and then declined during the reign of H.F. Baker, and was revived by Hodge at the end of the period. We also consider the implications these developments have for the concept of a school in the history of mathematics. [Copyright &y& Elsevier]

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.)

Although the Victorian era was characterized by the dominance of Great Britain both militarily and economically, the achievements of the British in mathematics were considerably less spectacular. Nevertheless, significant contributions were made by British mathematicians, several of whose names are still well known today. This paper highlights the principal mathematical developments in Britain during this time, closing with some observations on the weaknesses and limitations of Victorian British mathematics. [ABSTRACT FROM AUTHOR]

In a deliberately provocative first part to this paper, I argue that nineteenth-century British mathematicians had an unduly high opinion of themselves and a striking lack of appreciation for contemporary continental developments. I argue that this failure was rooted in the institutions that supported mathematics, and was only remedied towards the end of the century. In the more sober second half of the paper I ask if historians of mathematics have subscribed to this overestimate, and explore some related questions, among them what are historians doing when they write history: telling it as it was, or righting or defending the record? Historians of mathematics also need to consider British priorities for research in the nineteenth century, and a comparison with other minor players (such as Japan, Portugal, or Poland) might be illuminating. [ABSTRACT FROM AUTHOR]

This article expresses concern for the sloppy language that is often used by the media to describe numerical comparisons and suggests guidelines for how such comparisons should be described such that the meanings are unambiguous. [ABSTRACT FROM AUTHOR]

The article provides updates concerning the field of mathematics as of March 2007. The British National Cataloguing Unit for the Archives of Contemporary Scientists has received a grant for a project on the archives of British physicists and mathematicians. A team of mathematicians and computer scientists in the U.S. has developed a pedagogical technique for teaching material in discrete mathematics. A quantity of primary and secondary materials for the history of mathematics is available online.

Abstract: Charles Babbage (1791–1871) was the embodiment of a polymath: elected a Royal Society fellow, holder of the Lucasian Chair of mathematics at Cambridge, founder of the London Statistical Society, author of many papers and full-length monographs and, most famously from a 21st century perspective, the architect of modern computing with his difference engines and designs for the analytical engine. The scale and complexity of these machines meant their realisation was dependent upon the latest industrial advances like parts standardization and machine tool technology. As a result Babbage committed large amounts of his time and money to the theoretical and empirical study of advanced production and engineering practice. This paper argues that Charles Babbage deserves to be recognised as a pioneer in the field of operations management. His path-breaking contributions were born of a singular intellect and degree of creativity combined with a commitment to empiricist scientific method and statistical measurement. Moreover, he was working as Britain transformed itself into the most highly industrialized country the world had ever seen. The paper draws in particular upon the various editions of his best-selling book, ‘On the Economy of Machines and Manufactures’, first published in 1832. It reviews the many core operations principles evident in Babbage''s analyses and highlights insights that remain relevant to today''s theoretical and practical concerns. The paper concludes with a discussion of how a combination of contextual and biographical factors left Charles Babbage a largely unsung pioneer in the field of operations management. [Copyright &y& Elsevier]

This study examines the mental computation strategies used by pupils at the end of primary school. In 1998 a new strategy for teaching mathematics was introduced into British schools (the National Numeracy Strategy) that specifically focused on mental calculation. The first part of the study took place in 1999, one year after the implementation of the National Numeracy Strategy. These results were compared with those obtained in 2005, six years later. The study shows that the National Numeracy Strategy has improved pupils' performance both mentally and when given the option to use written working. But some discrepancies deserve further study; for example, the greater use of the 'rounding and adjusting; method for subtraction than for addition. [ABSTRACT FROM AUTHOR]

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.