A-level Mathematics Module Choice and Subsequent Performance in First Year of an Engineering Degree

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules. The flexibility in choice of applied modules has led to concerns that many students would proceed to study engineering at university with little background in mechanics. A survey of aerospace and mechanical engineering students in our university revealed that a combination of mechanics and statistics (the basic module in both) was by far the most popular choice of optional modules in A-level Mathematics, meaning that only about one-quarter of the class had studied mechanics beyond the basic module within school mathematics. Investigation of student performance in two core, first-year engineering courses, which build on a mechanics foundation, indicated that any benefits for students who studied the extra mechanics at school were small. These results give concern about the depth of understanding in mechanics gained during A-level Mathematics.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

Interpreting A-level Mathematics grades – as easy as A, B, C?

Many concerns have been expressed that students’ basic mathematical skills have deteriorated during the 1990s and there has been disquiet that current A-level grading does not distinguish adequately between the more able students. This study reports the author’s experiences of teaching maths to large classes of first-year engineering students and aims to enhance understanding of levels of mathematical competence in more recent years. Over the last four years, the classes have consisted of a very large proportion of highly qualified students – about 91% of them had at least grade B in A-level Mathematics. With a small group of students having followed a non-traditional route to university (no A-level maths) and another group having benefitted through taking A-level Further Mathematics at school, the classes have contained a very wide range of mathematical backgrounds. Despite the introductory maths course at university involving mainly repetition of A-level material, students’ marks were spread over a very wide range – for example, A-level Mathematics grade B students have scored across the range 16 – 97%. Analytical integration is the topic which produced the largest variation in performance across the class but, in contrast, the A-level students generally performed well in differentiation. Initial analysis suggests some stability in recent years in the mathematical proficiency of students with a particular A-level Mathematics grade. Allowing choice of applied maths modules as part of the A-level maths qualification increases the variety of students’ mathematical backgrounds and their selection from mechanics, statistics or decision maths is not clear from the final qualification.

Developing mathematics support for first-year engineering students with non-traditional mathematics backgrounds

A maths support system for first-year engineering students with non-traditional entry qualifications has involved students working through practice questions structured to correspond with the maths module which runs in parallel. The setting was informal and there was significant one-to-one assistance. The non-traditional students (who are known to be less well prepared mathematically) were explicitly contacted in the first week of their university studies regarding the maths support and they generally seemed keen to participate. However, attendance at support classes was relatively low, on average, but varied greatly between students. Students appreciated the personal help and having time to ask questions. It seemed that having a small group of friends within the class promoted attendance – perhaps the mutual support or comfort that they all had similar mathematical difficulties was a factor. The classes helped develop confidence. Attendance was hindered by the class being timetabled too soon after the relevant lecture and students were reluctant to come with no work done beforehand. Although students at risk due to their mathematical unpreparedness can easily be identified at an early stage of their university career, encouraging them to partake of the maths support is an ongoing, major problem.

Applied physics: Trawling for complements

A method has been invented for determining nanoscale variations in the distribution of electric charge on surfaces. It has so far been used to examine specific inorganic materials, but could find widespread applications in imaging.

Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

Mathematics and reading difficulty subtypes: Minor phonological influences on mathematics for 5-7 year olds

Linguistic influences in mathematics have previously been explored throughsubtyping methodology and by taking advantage of the componential nature ofmathematics and variations in language requirements that exist across tasks. Thepresent longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5-7 years. Initially, 256 children were screened for mathematics and reading difficulties using standardised measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the MD (n=26), MDRD (n=32), reading difficulty (RD, n=22) and typically achieving (TA, n=35) subtypes. These children were tested at four time points, separated by six monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypescould have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.

Multi-bubble sonoluminescence: Laboratory curiosity, or real world application?

Sonoluminescence (SL) involves the conversion of mechanical [ultra]sound energy into light. Whilst the phenomenon is invariably inefficient, typically converting just 10^-4 of the incident acoustic energy into photons, it is nonetheless extraordinary, as the resultant energy density of the emergent photons exceeds that of the ultrasonic driving field by a factor of some 10 ¹². Sonoluminescence has specific [as yet untapped] advantages in that it can be effected at remote locations in an essentially wireless format. The only [usual] requirement is energy transduction via the violent oscillation of microscopic bubbles within the propagating medium. The dependence of sonoluminescent output on the generating sound field's parameters, such as pulse duration, duty cycle, and position within the field, have been observed and measured previously, and several relevant aspects are discussed presently. We also extrapolate the logic from a recently published analysis relating to the ensuing dynamics of bubble 'clouds' that have been stimulated by ultrasound. Here, the intention was to develop a relevant [yet computationally simplistic] model that captured the essential physical qualities expected from real sonoluminescent microbubble clouds. We focused on the inferred temporal characteristics of SL light output from a population of such bubbles, subjected to intermediate [0.5-2MPa] ultrasonic pressures. Finally, whilst direct applications for sonoluminescent light output are thought unlikely in the main, we proceed to frame the state-of-the- art against several presently existing technologies that could form adjunct approaches with distinct potential for enhancing present sonoluminescent light output that may prove useful in real world [biomedical] applications.

An alternative methodology in Schottky diode physics

The fabrication and electrical characterization of Schottky junction diodes have been extensively researched for three-quarters of a century since the original work of Schottky in 1938. This study breaks from the highly standardized regime of such research and provides an alternative methodology that prompts novel, more efficient applications of the adroit Schottky junction in areas such as chemical and thermal sensing. The core departure from standard Schottky diode configuration is that the metal electrode is of comparable or higher resistance than the underlying semiconductor. Further, complete electrical characterization is accomplished through recording four-probe resistance-temperature (R-D-T) characteristics of the device, where electrical sourcing and sensing is done only via the metal electrode and not directly through the semiconductor. Importantly, this results in probing a nominally unbiased junction while eliminating the need for an Ohmic contact to the semiconductor. The characteristic R-D-T plot shows two distinct regions of high (metal) and low (semiconductor) resistances at low and high temperatures, respectively, connected by a crossover region of width, DT, within which there is a large negative temperature coefficient of resistance. The R-D-T characteristic is highly sensitive to the Schottky barrier height; consequently, at a fixed temperature, R-D responds appreciably to small changes in barrier height such as that induced by absorption of a chemical species (e.g., H-2) at the interface. A theoretical model is developed to simulate the R-D-T data and applied to Pd/p-Si and Pt/p-Si Schottky diodes with a range of metal electrode resistance. The analysis gives near-perfect fits to the experimental R-D-T characteristics, yielding the junction properties as fit parameters. The modelling not only helps elucidate the underlying physics but also helps to comprehend the parameter space essential for the discussed applications. Although the primary regime of application is limited to a relatively narrow range (DT) for a given type of diode, the alternative methodology is of universal applicability to all metal-semiconductor combinations forming Schottky contacts. (C) 2015 AIP Publishing LLC.

The TARANIS laser : A multi-terawatt system for laser plasma physics

The Terawatt Apparatus for Relativistic And Non-linear Interdisciplinary Science (TARANIS), installed in the Centre for Plasma Physics at the Queen's University Belfast, supports a wide ranging science program, including laser-driven particle acceleration, X-ray lasers and high energy density physics experiments. We present (1) an overview of the laser facility, (2) results of preliminary investigations on proton acceleration, laser action at 13.9 nm and Kα sources and (3) speculation on future experiments using these extreme sources.

Mathematics Learning Support in Ireland in 2015

The provision of mathematics learning support in higher-level institutions on the island of Ireland has developed rapidly in recent times with the number of institutions providing some form of support doubling in the past seven years. The Irish Mathematics Learning Support Network aims to inform all mathematics support practitioners in Ireland on relevant issues. Consequently it was decided that a detailed picture of current provision was necessary. A comprehensive online survey was conducted to amass the necessary data. The ultimate aim of the survey is to benefit all mathematics support practitioners in Ireland, in particular those in third-level institutions who require further support to enhance the mathematical learning experience of their students. The survey reveals that the majority of Irish higher-level institutions provide mathematics learning support to some extent, with 65% doing so through a support centre. Learners of service mathematics are the primary users: first-year science, engineering and business undergraduates, with non-traditional students being a sizeable element. Despite the growing recognition for the need to offer mathematics learning support almost half of the centres are subject to annual review. Further, less than half the support offerings have a dedicated full-time manager, while 60% operate with a staff of five or fewer. The elevation of mathematics support as a viable and worthwhile career in order to attract and retain high quality staff is seen by many respondents as the crucial next phase of development.

The application of atomic physics within impurity diagnostics for fusion plasmas

With the focus of ITER on the transport and emission properties of tungsten, generating atomic data for complex species has received much interest. Focusing on impurity influx diagnostics, we discuss recent work on heavy species. Perturbative approaches do not work well for near neutral systems so non-perturbative data are required, presenting a particular challenge for these influx diagnostics. Recent results on Mo+ are given as an illustration of how the diagnostic applications can guide the theoretical calculations for such systems.