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.

Photodissociation and chemistry of N2 in the circumstellar envelope of carbon-rich AGB stars

The envelopes of AGB stars are irradiated externally by ultraviolet photons; hence, the chemistry is sensitive to the photodissociation of N$_2$ and CO, which are major reservoirs of nitrogen and carbon, respectively. The photodissociation of N$_2$ has recently been quantified by laboratory and theoretical studies. Improvements have also been made for CO photodissociation. For the first time, we use accurate N$_2$ and CO photodissociation rates and shielding functions in a model of the circumstellar envelope of the carbon-rich AGB star, IRC +10216. We use a state-of-the-art chemical model of an AGB envelope, the latest CO and N$_2$ photodissociation data, and a new method for implementing molecular shielding functions in full spherical geometry with isotropic incident radiation. We compare computed column densities and radial distributions of molecules with observations. The transition of N$_2$ $\to$ N (also, CO $\to$ C $\to$ C$^+$) is shifted towards the outer envelope relative to previous models. This leads to different column densities and radial distributions of N-bearing species, especially those species whose formation/destruction processes largely depend on the availability of atomic or molecular nitrogen, for example, C$_n$N ($n$=1, 3, 5), C$_n$N$^-$ ($n$=1, 3, 5), HC$_n$N ($n$=1, 3, 5, 7, 9), H$_2$CN and CH$_2$CN. The chemistry of many species is directly or indirectly affected by the photodissociation of N$_2$ and CO, especially in the outer shell of AGB stars where photodissociation is important. Thus, it is important to include N$_2$ and CO shielding in astrochemical models of AGB envelopes and other irradiated environments. In general, while differences remain between our model of IRC +10216 and the observed molecular column densities, better agreement is found between the calculated and observed radii of peak abundance.

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.

The Application of Computational Chemistry and Chemometrics to Developing a Method for Online Monitoring of Polymer Degradation in the Manufacture of Bioresorbable Medical Implants

Bioresorbable polymers such as PLA have an important role to play in the development of temporary implantable medical devices with significant benefits over traditional therapies. However, development of new devices is hindered by high manufacturing costs associated with difficulties in processing the material. A major problem is the lack of insight on material degradation during processing. In this work, a method of quantifying degradation of PLA using IR spectroscopy coupled with computational chemistry and chemometric modeling is examined. It is shown that the method can predict the quantity of degradation products in solid-state samples with reasonably good accuracy, indicating the potential to adapt the method to developing an on-line sensor for monitoring PLA degradation in real-time during processing.

Facilitation of nucleoside and nucleotide chemistry by ball milling

Chemistry and Mechanism of Alizarin Red S and Methylene Blue Biosorption onto Olive Stone: Equilibrium and Kinetic

The biosorption process of anionic dye Alizarin Red S (ARS) and cationic dye methylene blue (MB) as a function of solution pH, initial concentration and contact time onto olive stone (OS) biomass has been investigated. The main objectives of the current study are to: (i) study the chemistry and the mechanism of ARS and MB biosorption onto olive stone and the type of OS–ARS, MB interactions occurring, (ii) study the biosorption equilibrium and kinetic experimental data required for the design and operation of column reactors. Equilibrium biosorption isotherms and kinetics were also examined. Experimental equilibrium data were fitted to four different isotherms by non-linear regression method, however, the biosorption experimental data for ARS and MB dyes were well interpreted by the Temkin and Langmuir isotherms, respectively. The maximum monolayer adsorption capacity for ARS and MB dyes were 109.0 and 102.6 mg/g, respectively. The kinetic data of the two dyes could be better described by the pseudo second-order model. The data showed that olive stone can be effectively used for removing dyes from wastewater.