Essential mathematics:a refresher course for business and social studies

Many students starting courses in business, accounting and similar areas want to update their mathematical skills, and are seeking a suitable text; this book addresses their needs. Written in an informal style, emphasising understanding and application of techniques rather than formal proofs, it covers all the mathematics needed by entrants to BTEC, undergraduate, MBA and related professional courses. Plentiful worked examples and exercises with solutions make the book a practical self-study aid for those wishing to revise before starting their course.

Are poor mathematics skills associated with visual deficits in temporal processing?

Developmental learning disabilities such as dyslexia and dyscalculia have a high rate of co-occurrence in pediatric populations, suggesting that they share underlying cognitive and neurophysiological mechanisms. Dyslexia and other developmental disorders with a strong heritable component have been associated with reduced sensitivity to coherent motion stimuli, an index of visual temporal processing on a millisecond time-scale. Here we examined whether deficits in sensitivity to visual motion are evident in children who have poor mathematics skills relative to other children of the same age. We obtained psychophysical thresholds for visual coherent motion and a control task from two groups of children who differed in their performance on a test of mathematics achievement. Children with math skills in the lowest 10% in their cohort were less sensitive than age-matched controls to coherent motion, but they had statistically equivalent thresholds to controls on a coherent form control measure. Children with mathematics difficulties therefore tend to present a similar pattern of visual processing deficit to those that have been reported previously in other developmental disorders. We speculate that reduced sensitivity to temporally defined stimuli such as coherent motion represents a common processing deficit apparent across a range of commonly co-occurring developmental disorders.

An iterative-style approach to constructing intelligent tutoring systems in mathematics

Mathematics is highly structured and also underpins most of science and engineering. For this reason, it has proved a very suitable domain for Intelligent Tutoring System (ITS) research, with the result that probably more tutoring systems have been constructed for the domain than any other. However, the literature reveals that there still exists no consensus on a credible approach or approaches for the design of such systems, despite numerous documented efforts. Current approaches to the construction of ITSs leave much to be desired. Consequently, existing ITSs in the domain suffer from a considerable number of shortcomings which render them 'unintelligent'. The thesis examines some of the reasons why this is the case. Following a critical review of existing ITSs in the domain, and some pilot studies, an alternative approach to their construction is proposed (the 'iterative-style' approach); this supports an iterative style, and also improves on at least some of the shortcomings of existing approaches. The thesis also presents an ITS for fractions which has been developed using this approach, and which has been evaluated in various ways. It has, demonstrably, improved on many of the limitations of existing ITSs; furthermore, it has been shown to be largely 'intelligent', at least more so than current tutors for the domain. Perhaps more significantly, the tutor has also been evaluated against real students with, so far, very encouraging results. The thesis thus concludes that the novel iterative-style approach is a more credible approach to the construction of ITSs in mathematics than existing techniques.

School mathematics and dyslexia: aspects of the interrelationship

This investigation sought to explore the nature and extent of school mathematical difficulties among the dyslexic population. Anecdotal reports have suggested that many dyslexics may have difficulties in arithmetic, but few systematic studies have previously been undertaken. The literature pertaining to dyslexia and school mathematics respectively is reviewed. Clues are sought in studies of dyscalculia. These seem inadequate in accounting for dyslexics' reported mathematical difficulties. Similarities between aspects of language and mathematics are examined for underlying commonalities that may partially account for concomitant problems in mathematics, in individuals with a written language dysfunction. The performance of children taught using different mathematics work-schemes is assessed to ascertain if these are associated with differential levels of achievement that may be reflected in the dyslexic population few are found. Findings from studies designed to assess the relationship between written language failure and achievement in mathematics are reported. Study 1 reveals large correlational differences between subtest scores (Wechsler Intelligence Scale for Children, Wechsler, 1976) and three mathematics tests, for young dyslexics and children without literacy difficulties. However, few differences are found between levels of attainment, at this age (6 ½ - 9 years). Further studies indicate that, for dyslexics, achievement in school mathematics, may be independent of measured intelligence, as is the case with their literacy skills. Studies 3 and 4 reveal that dyslexics' performances on a range of school mathematical topics gets relatively worse compared with that of Controls (age range 8 - 17 years), as they get older. Extensive item analyses reveal many errors relating strongly to known deficits in the dyslexics' learning style - poor short-term memory, sequencing skills and verbal labelling strategies. Subgroups of dyslexics are identified on the basis of mathematical performance. Tentative explanations, involving alternative neuropsychological approaches, are offered for the measured differences in attainment between these groups.

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Being Tamil, being Hindu:Tamil migrants’ negotiations of the absence of Tamil Hindu spaces in the West Midlands and South West of England

This paper considers the religious practices of Tamil Hindus who have settled in the West Midlands and South West of England in order to explore how devotees of a specific ethno-regional Hindu tradition with a well-established UK infrastructure in the site of its adherents’ population density adapt their religious practices in settlement areas which lack this infrastructure. Unlike the majority of the UK Tamil population who live in the London area, the participants in this study did not have ready access to an ethno-religious infrastructure of Tamil-orientated temples and public rituals. The paper examines two means by which this absence was addressed as well as the intersections and negotiations of religion and ethnicity these entailed: firstly, Tamil Hindus’ attendance of temples in their local area which are orientated towards a broadly imagined Hindu constituency or which cater to a non-Tamil ethno-linguistic or sectarian community; and, secondly, through the ‘DIY’ performance of ethnicised Hindu ritual in non-institutional settings.

Innovation in education. Commentary:teaching statistics using dance and movement and a case for neuroscience in mathematics education

Review: A commentary on Teaching statistics using dance and movement by Irving, L.T. (2015). Front. Psychol. 6:50. doi: 10.3389/fpsyg.2015.00050 A case for neuroscience in mathematics education by Susac, A., and Braeutigam, S. (2014). Front. Hum. Neurosci. 8:314. doi: 10.3389/fnhum.2014.00314