Multiresolution and wavelets

Wavelets may possibly provide a useful basis for the numerical solution of differential or integral equations, in particular when they model processes which operate on very different space- or time-scales (turbulence, boundary layers, shocks, for instance). Our aim in this report is to provide a self-contained introduction to the basic theory of multiresolution and wavelets, accessible to the numerical analyst who knows nothing of signal processing, quantum theory, or any of the other established fields of application

Developing student teachers' understanding of teaching and pupils' learning : the role of support and challenge in the mentoring of student teachers

This study focuses on initial teacher education and results from the shift from college-based to school-based training in recent years. Specifically, the course involved is a post-graduate School Based Teacher Training Scheme (SCITT) in which the main participants are school-based training managers and mentors who hold the major responsibility for training trainee teachers. The study incorporates largely ethnographic research drawn from the participants taking part in several one year P. G. C. E. teacher training courses run by a non profit making Consortium, which is comprised of a partnership of secondary, primary and special schools together with colleges of Further Education. The data is obtained from introductory questionnaires, analysis of documentation including the trainees' course and subject handbooks and training documents for mentors, and finally audio-recorded interviews with six mentor-trainee teacher pairs. The study lays a particular emphasis on the role of support and challenge in mentoring and the effect of mentoring on student teachers' professional growth, specifically their understanding of learning to teach and of pupils' learning. The study is constructed around four themes:- A. Mentoring and Teacher Professional Development. B. Teachers' and Student Teachers' Beliefs about Teaching. C. Student Teachers' Subject Knowledge. D. Mentoring and Children's Learning. The importance of the study is the need for more research into the complex relationship between support and challenge in the training of student teachers, when the primary training role is that of the school-based teacher-mentor. The findings are as follows:- The study highlights the effectiveness of school-centred initial teacher training schemes in producing competent, thoughtful and highly motivated professionals who place children's learning at the centre of their teaching. It also emphasises the importance of the mentor's role in the student's training and professional growth. In the hands of skilful, experienced mentors the process offers the chance that students can become more rounded professionals providing that mentors are adequately trained. Trainees were more concerned with immediate classroom skills in early stages of their training. In general, the study found unequal amounts of support and challenge from mentors with the focus largely on support for the student, particularly early in the training. Students tend to lack awareness of being challenged. However, the study concludes that to achieve students' optimum professional growth, high levels of support and challenge are necessary. Support not only to engender improvement in classroom skills but also to enable students to have the confidence to express their personal beliefs about teaching and learning. The study's findings have important implications for mentor training, namely that if mentors were required to be conversant with theories of knowledge advocated by the SCITT and with the social, moral and ethical issues of teaching, they may be more inclined to challenge students' thinking on these issues. Furthermore, students' beliefs are more likely to be challenged by more skilled and knowledgeable mentors who could then help to clarify these beliefs and perceptions of teaching. Consequently, students may be encouraged to reflect critically on children's learning beyond the aim of enhancing their understanding of subject matter and obtaining academic success,to engage the pupils with these public forms of knowledge

A systematic evaluation of the cognitive behavioural model of tinnitus distress

Introduction & Aims Tinnitus has long been known to be a much more distressing problem to some people than to others, and understanding the reasons for this is crucial to the development of tinnitus therapy. McKenna et al. (2014) developed a Cognitive Behavioural Model of Tinnitus Distress based on psychological theory- in particular, the Cognitive Model of Insomnia (Harvey, 2002)- existing evidence, and clinical experience. It attempts to explain how tinnitus distress arises and is then maintained in certain individuals. It proposes that interaction between negative thoughts, arousal and distress, attention and monitoring, behaviour and underlying beliefs makes tinnitus a psychologically distressing experience. A strength of this model is that it consists of several testable hypotheses. It makes a series of predictions about what the individual components of tinnitus distress are and how they relate to one another. The primary aim of this project was to test all these predictions using questionnaire data gathered from people with tinnitus and thereby to evaluate whether and to what extent the Cognitive Behavioural Model is supported by evidence. In some contexts, the model is used as a therapeutic tool to help people understand their own experience of tinnitus. The secondary aim of this project was therefore to investigate whether and to what extent people with tinnitus feel the model applies to them and whether they find it easy to understand. Methods Two studies were conducted in order to investigate the two project aims. In the first, volunteers with tinnitus were asked to fill in a survey online or on paper which consisted of a series of questionnaires (or parts of questionnaires) each of which was designed to assess an individual component of the Cognitive Behavioural Model. Questionnaire data were used first to conduct factor analysis of each questionnaire individually. The resulting factor scores were then used to evaluate the full model using path analysis. A series of models based on the original, theoretical model were created and tested and results were compared. In the second study, tinnitus patients who had the Cognitive Behavioural Model explained to them in a therapy group were interviewed about their impressions of it. A focus group discussion about the model was also held with tinnitus therapists who were familiar with it. Interviews and the focus group were audio recorded, transcribed, and analysed using thematic analysis. Results Three hundred and forty-two adults with tinnitus completed the survey. Eleven tinnitus patients were interviewed and five therapists attended the focus group. Examination of mean questionnaire scores indicated a strong correlation between each of the measures used and overall tinnitus distress, with the exception of a modified version of the illness perception questionnaire, which was used to measure tinnitus control beliefs. A robust factor structure was identified for all but one of the questionnaires used in the survey; the Fear of Tinnitus Questionnaire. This questionnaire was excluded from further analysis. Path analysis indicated that a number of configurations of the Cognitive Behavioural Model were a fairly good fit to the data obtained. The two best fitting models differed principally in the placement of tinnitus magnitude, which was seen as a product of attention in the first and as an independent variable in the second. Key fit indices for the two best fitting models were RMSEA = 0.061, 90% CI = 0.047-0.076, CFI = 0.984 and RMSEA = 0.055, 90% CI = 0.035-0.075, CFI = 0.993. Results of qualitative analysis indicated that people with tinnitus are able to understand the Cognitive Behavioural Model and for the most part feel it broadly reflects their experience, although some people did not identify with certain parts of it. There were differing opinions amongst both patients and therapists as to how useful a part of tinnitus therapy it might be. Conclusion The Cognitive Behavioural Model of Tinnitus Distress is empirically supported by data obtained from a sample of people with tinnitus. Questions remain as to whether beliefs are important and what kind of beliefs influence tinnitus experience. The fact that different configurations of the model fit the data equally well and that people with tinnitus do not necessarily think that the model is a perfect reflection of their experience, indicate that there may in fact not be one universal model of tinnitus distress but several, some of which apply more to certain sub-groups of people with tinnitus than others. Further investigation of this is needed. This notwithstanding, this project indicates that the Cognitive Behavioural Model is a firm, evidence-based foundation on which to build psychological tinnitus therapies

What if and What More: disturbing habits of thought about playwork ‘re-search’

This short article reports on a presentation given at an International Journal of Playwork Practice seminar in 2018. It describes an approach to evaluating the work of an adventure playground using Participative Action Research and a critical cartographic method for producing documentation that shows the unique nature of playwork

Confirmatory factor analysis of Clinical Outocmes in Routine Evaluation (CORE-OM) used as a measure of emotional distress in people with tinnitus

BACKGROUND: People with troublesome tinnitus often experience emotional distress. Therefore a psychometrically sound instrument which can evaluate levels of distress and change over time is necessary to understand this experience. Clinical Outcomes in Routine Evaluation (CORE-OM) is a measure of emotional distress which has been widely used in mental health research. Although originally designed as a 4-factor questionnaire, factor analyses have not supported this structure and a number of alternative factor structures have been proposed in different samples. The aims of this study were to test the factor structure of the CORE-OM using a large representative tinnitus sample and to use it to investigate levels of emotional distress amongst people with a range of tinnitus experience. METHODS: The CORE-OM was completed by 342 people experiencing tinnitus who self-rated their tinnitus on a 5-point scale from ‘not a problem’ to ‘a very big problem’. Confirmatory factor analysis was used to test all ten factor models which have been previously derived across a range of population samples. Model fit was assessed using fit criterion and theoretical considerations. Mean scores on the full questionnaire and its subscales were compared between tinnitus problem categories using one-way ANOVA. RESULTS: The best fitting model included 33 of the 34 original items and was divided into three factors: negatively worded items, positively worded items and risk. The full questionnaire and each factor were found to have good internal consistency and factor loadings were high. There was a statistically significant difference in total CORE-OM scores across the five tinnitus problem categories. However there was no significant difference between those who rated their tinnitus ‘not a problem’, and ‘a small problem’ or ‘a moderate problem.’ CONCLUSION: This study found a 3-factor structure for the CORE-OM to be a good fit for a tinnitus population. It also found evidence of a relationship between emotional distress as measured by CORE-OM and perception of tinnitus as a problem. Its use in tinnitus clinics is to be recommended, particularly when emotional distress is a target of therapy

Particle tracking methods for residence time calculations in incompressible flow

Numerical methods are presented for the calculation of residence time distributions in steady incompressible fluid flow using a given set of normal fluid fluxes, defined across the cell faces of a cartesian tensor product mesh. A particle tracking approach is adopted involving the construction of a piecewise polynomial representation of the velocity distribution, and subsequent integration of this representation for the determination of individual particle trajectories