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.

Mechanochemical interconversion between discrete complexes and coordination networks - formal hydration/dehydration by LAG

Using a small planetary ball mill, liquid-assisted grinding (LAG) of metal salts or oxides (ZnO, CdO, CdCO3, Cu(OAc)(2)center dot H2O, Co(OAc)(2)center dot 4H(2)O, Mn(OAc)(2)center dot 4H(2)O, Ni(OAc)(2)center dot 4H(2)O, FeSO4 center dot 7H(2)O) with two equivalents of isonicotinic acid (HINA) and small amounts of water ( up to 5.6 molar equivalents) gave discrete aquo complexes trans-[M(INA)(2)(OH2)(4)] (M = Zn, Cd, Cu, Fe, Co, Ni, Mn) efficiently within 30 min. For M = Zn, Cd and Cu these complexes readily undergo reversible formal dehydration to the extended network structures [M(INA)(2)] (M = Zn, Cu) or [Cd(INA)(2)(OH2)]center dot DMF by further LAG with non-aqueous liquids such as methanol or DMF. Overall, the mechanochemical dehydrations are more effective than heating or immersion in bulk solvents. The work demonstrates a two-step mechanochemical synthesis of coordination networks via discrete aquo complexes which may be preferable to single step reactions or grinding-annealing procedures in some cases. For example, the two step method was the only way to prepare [Cd(INA)(2)(OH2)]center dot DMF mechanochemically and the porous network Cu(INA)(2) could not be obtained from the aquo complex by heating.

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.

VEDA:Variation-aware energy-efficient discrete Wavelet Transform architecture

In this paper, we present a unified approach to an energy-efficient variation-tolerant design of Discrete Wavelet Transform (DWT) in the context of image processing applications. It is to be noted that it is not necessary to produce exactly correct numerical outputs in most image processing applications. We exploit this important feature and propose a design methodology for DWT which shows energy quality tradeoffs at each level of design hierarchy starting from the algorithm level down to the architecture and circuit levels by taking advantage of the limited perceptual ability of the Human Visual System. A unique feature of this design methodology is that it guarantees robustness under process variability and facilitates aggressive voltage over-scaling. Simulation results show significant energy savings (74% - 83%) with minor degradations in output image quality and avert catastrophic failures under process variations compared to a conventional design. © 2010 IEEE.

Finding the Most Descriptive Substructures in Graphs with Discrete and Numeric Labels

Many graph datasets are labelled with discrete and numeric attributes. Most frequent substructure discovery algorithms ignore numeric attributes; in this paper we show how they can be used to improve search performance and discrimination. Our thesis is that the most descriptive substructures are those which are normative both in terms of their structure and in terms of their numeric values. We explore the relationship between graph structure and the distribution of attribute values and propose an outlier-detection step, which is used as a constraint during substructure discovery. By pruning anomalous vertices and edges, more weight is given to the most descriptive substructures. Our method is applicable to multi-dimensional numeric attributes; we outline how it can be extended for high-dimensional data. We support our findings with experiments on transaction graphs and single large graphs from the domains of physical building security and digital forensics, measuring the effect on runtime, memory requirements and coverage of discovered patterns, relative to the unconstrained approach.

Rapid design of discrete orthonormal wavelet transforms using silicon IP components

A rapid design methodology for orthonormal wavelet transform cores has been developed. This methodology is based on a generic, scaleable architecture utilising time-interleaved coefficients for the wavelet transform filters. The architecture has been captured in VHDL and parameterised in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is embedded within the cores and allows them to be cascaded without any interface glue logic for any desired level of decomposition. Case studies for stand alone and cascaded silicon cores for single and multi-stage wavelet analysis respectively are reported. The design time to produce silicon layout of a wavelet based system has been reduced to typically less than a day. The cores are comparable in area and performance to handcrafted designs. The designs are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

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.

Perceptual Watermarking for Discrete Shearlet Transform

This paper presents a new perceptual watermarking model for Discrete Shearlet transform (DST). DST provides the optimal representation [10] of the image features based on multi-resolution and multi-directional analysis. This property can be exploited on for watermark embedding to achieve the watermarking imperceptibility by introducing the human visual system using Chou’s model. In this model, a spatial JND profile is adapted to fit the sub-band structure. The combination of DST and the Just-Noticeable Distortion (JND) profile improves the levels of robustness against certain attacks while minimizing the distortion; by assigning a visibility threshold of distortion to each DST sub-band coefficient in the case of grey scale image watermarking.

A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Discrete cyclic di-GMP-dependent control of bacterial predation versus axenic growth in Bdellovibrio bacteriovorus

Bdellovibrio bacteriovorus is a Delta-proteobacterium that oscillates between free-living growth and predation on Gram-negative bacteria including important pathogens of man, animals and plants. After entering the prey periplasm, killing the prey and replicating inside the prey bdelloplast, several motile B. bacteriovorus progeny cells emerge. The B. bacteriovorus HD100 genome encodes numerous proteins predicted to be involved in signalling via the secondary messenger cyclic di-GMP (c-di-GMP), which is known to affect bacterial lifestyle choices. We investigated the role of c-di-GMP signalling in B. bacteriovorus, focussing on the five GGDEF domain proteins that are predicted to function as diguanylyl cyclases initiating c-di-GMP signalling cascades. Inactivation of individual GGDEF domain genes resulted in remarkably distinct phenotypes. Deletion of dgcB (Bd0742) resulted in a predation impaired, obligately axenic mutant, while deletion of dgcC (Bd1434) resulted in the opposite, obligately predatory mutant. Deletion of dgcA (Bd0367) abolished gliding motility, producing bacteria capable of predatory invasion but unable to leave the exhausted prey. Complementation was achieved with wild type dgc genes, but not with GGAAF versions. Deletion of cdgA (Bd3125) substantially slowed predation; this was restored by wild type complementation. Deletion of dgcD (Bd3766) had no observable phenotype. In vitro assays showed that DgcA, DgcB, and DgcC were diguanylyl cyclases. CdgA lacks enzymatic activity but functions as a c-di-GMP receptor apparently in the DgcB pathway. Activity of DgcD was not detected. Deletion of DgcA strongly decreased the extractable c-di-GMP content of axenic Bdellovibrio cells. We show that c-di-GMP signalling pathways are essential for both the free-living and predatory lifestyles of B. bacteriovorus and that obligately predatory dgcC- can be made lacking a propensity to survive without predation of bacterial pathogens and thus possibly useful in anti-pathogen applications. In contrast to many studies in other bacteria, Bdellovibrio shows specificity and lack of overlap in c-di-GMP signalling pathways.