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

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]

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

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 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]

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 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 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]

In this paper, I examine the properties of the handicapping system in the UK. Using a generalized ordered logistic regression model of hole by hole scores of individuals, simulation was employed to calculate the probability of winning for an individual in stroke play and match play head to heads and also in tournament competitions with multiple entrants. The results suggest that the current handicapping system does not produce equal probabilities of players with different handicaps winning. Specifically, lower handicappers have a higher probability of winning in both stroke play and match play games. Having investigated the possibility of employing scaling factors in order to level these probabilities, I pose the question of the extent to which equal probabilities is in fact a desirable property of a handicapping system. [ABSTRACT FROM AUTHOR]

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 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]

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]

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]