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.

Auditory sensory memory and working memory processes in children with normal hearing and cochlear implants.

There can be wide variation in the level of oral/aural language ability that prelingually hearing-impaired children develop after cochlear implantation. Automatic perceptual processing mechanisms have come under increasing scrutiny in attempts to explain this variation. Using mismatch negativity methods, this study explored associations between auditory sensory memory mechanisms and verbal working memory function in children with cochlear implants and a group of hearing controls of similar age. Whilst clear relationships were observed in the hearing children between mismatch activation and working memory measures, this association appeared to be disrupted in the implant children. These findings would fit with the proposal that early auditory deprivation and a degraded auditory signal can cause changes in the processes underpinning the development of oral/aural language skills in prelingually hearing-impaired children with cochlear implants and thus alter their developmental trajectory

Informational masking in young and elderly listeners for speech masked by simultaneous speech and noise

Three experiments measured the effects of age on informational masking of speech by competing speech. The experiments were designed to minimize the energetic contributions of the competing speech so that informational masking could be measured with no large corrections for energetic masking. Experiment 1 used a "speech-in-speech-in-noise" design, in which the competing speech was presented in noise at a signal-to-noise ratio (SNR) of -4 dB. This ensured that the noise primarily contributed the energetic masking but the competing speech contributed the informational masking. Equal amounts of informational masking (3 dB) were observed for young and elderly listeners, although less was found for hearing-impaired listeners. Experiment 2 tested a range of SNRs in this design and showed that informational masking increased with SNR up to about an SNR of -4 dB, but decreased thereafter. Experiment 3 further reduced the energetic contribution of the competing speech by filtering it into different frequency bands from the target speech. The elderly listeners again showed approximately the same amount of informational masking (4-5 dB), although some elderly listeners had particular difficulty understanding these stimuli in any condition. On the whole, these results suggest that young and elderly listeners were equally susceptible to informational masking. © 2009 Acoustical Society of America.

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.

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.

Does flexibility in secondary level mathematics curriculum affect degree performance?

The authors have much experience in developing mathematics skills of first-year engineering students and attempting to ensure a smooth transition from secondary school to university. Concerns exist due to there being flexibility in the choice of modules needed to obtain a secondary level (A-level) mathematics qualification. This qualification is based on some core (pure maths) modules and a selection from mechanics and statistics modules. A survey of aerospace and mechanical engineering students in Queen’s University Belfast revealed that a combination of both mechanics and statistics (the basic module in both) was by far the most popular choice and therefore only about one quarter of this cohort had studied mechanics beyond the basic module within school maths. Those students who studied the extra mechanics and who achieved top grades at school subsequently did better in two core, first-year engineering courses. However, students with a lower grade from school did not seem to gain any significant advantage in the first-year engineering courses despite having the extra mechanics background. This investigation ties in with ongoing and wider concerns with secondary level mathematics provision in the UK.

Mature students – participation in maths support and progression

Maths support at the Learning Development Service takes the form of drop-in contact, one-to-one appointments and workshops. Analysis over three years from 2010/11 to 2012/13 shows that 45% of one-to-one appointments involved a mature student, defined at Queen’s University Belfast (QUB) as one who has had a break in full-time study (normally a minimum of two years). This is a very high proportion given that 4% of students at QUB are mature. Considering engineering undergraduates only, the fraction of one-to-one appointments involving mature students was also 45%. This study can report a wide variation in terms of progression of mature students in engineering and aims to consider how more traditional undergraduate learners could be persuaded to adopt the attitudes of mature students in partaking of maths support.

Using Cooperative Learning to Engage Students in Science

Cooperative learning can actively engage students in school science, stimulating curiosity and improving attitudes and motivation. Allen Thurston discusses the roles teachers and students can play to maximize its potential.