The official school mathematics curriculum - textbooks, teacher's handbooks, and syllabus - has a powerful influence on classroom practice in a developing country like Ghana, where many teachers with low teaching qualifications hardly ever have access to other sources of information and activity for their teaching. The official mathematics curriculum for Ghanaian primary schools was originally written with the small intellectual elite, who will proceed to secondary and further education, in mind. Concerns have been raised internationally for countries still using such curricula to adjust them, but the Ghanaian official school mathematics curriculum has remained in use in the nation's schools since their introduction in 1975 with no significant revision. The study, on the one hand, involved an investigation of the extent to which primary teachers in Ghana translate the contents of the official mathematics curriculum into classroom reality. On the other hand, it addressed issues related to the nature, and appropriateness, of the current official primary mathematics curriculum, which was an adaptation of the products of the `new-math' project spearheaded by the West African Regional Mathematics Programme in the 1970s. The study used a range of methods for data collection. These include an extensive content and curriculum analysis of the official primary mathematics curriculum materials, and a questionnaire survey of teachers' coverage of the content and teaching methods prescribed by the official curriculum. The questionnaire survey of teachers' coverage of teaching methods involved the observation of teachers in classroom settings. Tape recordings of lessons and instructions from teacher's handbooks were transcribed to provide both qualitative and quantitative data on classroom practice. The analysis of the curriculum revealed several inefficiencies in the Ghanaian primary mathematics curriculum. Though there was rhetoric in the introduction of the curriculum materials on the use of teaching skills that suggest discovery methods, the analysis indicated that learning/teaching activities that would encourage the use of such teaching skills in the materials were not included. It emerged from the findings that neither what the teachers really taught, nor what the official mathematics curriculum prescribed, was found to be adequate enough to meet the full mathematical needs of pupils. It was found that a very substantial part of the content of the curriculum was taught by the teachers, and both the official curriculum and the teachers, who implement it, emphasised expository teaching methods. It was argued in this light that the low pupils' attainment observed in the subject could not be seen simply as a reflection of the teachers' poor coverage of the curriculum, but as a reflection of inefficiencies within it. The findings of this study corroborate what is known about curriculum adaptation in school mathematics. It showed that coverage of textbooks does influence the emphasis on topics presented by teachers in their instruction, and also that topics in arithmetic are the most emphasised by both official mathematics curriculum materials and in teachers' actual classroom practice.

Bibliography : p. 161-176. / Propositional systems are deductively closed sets of sentences phrased in the language of some propositional logic. The set of systems of a given logic is turned into an algebra by endowing it with a number of operations, and into a relational structure by endowing it with a number of relations. Certain operations and relations on systems arise from some corresponding base operation or relation, either on sentences in the logic or on propositional valuations. These operations and relations on systems are called power constructs. The aim of this thesis is to investigate the use of power constructs in propositional systems. Some operations and relations on systems that arise as power constructs include the Tarskian addition and product operations, the contraction and revision operations of theory change, certain multiple- conclusion consequence relations, and certain relations of verisimilitude and simulation. The logical framework for this investigation is provided by the definition and comparison of a number of multiple-conclusion logics, including a paraconsistent three-valued logic of partial knowledge.

No description available.

Future photometric surveys will provide vastly more supernovae than have presently been observed, the majority of which will not be spectroscopically typed. Key to extracting information from these future datasets will be the efficient use of light-curves. In the first part of this thesis we introduce two methods for distinguishing type Ia supernovae from their contaminating counterparts, kernel density estimation and boosting. In the second half of this thesis we shift focus from classification to the related problem of type probability estimation, and ask how best to use type probabilities.

Bibliography: leaves 84-88 / We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.

No description available.

No description available.

No description available.

The theory of large deviations can help to shed light on systems in non-equilibrium statistical mechanics and, more generically, on non-reversible stochastic processes. For this purpose, we target trajectories in space time rather than static configurations and study time-extensive observables. This suggests that the details of the evolution law such as the presence of time correlations take on a major role. In this thesis, we investigate selected models with stochastic dynamics that incorporate memory by means of different mechanisms, devise a numerical approach for such models, and quantify to what extent the memory affects the large deviation functionals. The results are relevant for real-world situations, where simplified memoryless (Markovian) models may not always be appropriate. After an original introduction to the mathematics of stochastic processes, we explore, analytically and numerically, an open-boundary zero-range process which incorporates memory by means of hidden variables that affect particle congestion. We derive the exact solution for the steady state of the one-site system, as well as a mean-field approximation for larger one-dimensional lattices. Then, we focus on the large deviation properties of the particle current in such a system. This reveals that the time correlations can be apparently absorbed in a memoryless description for the steady state and the small fluctuation regime. However, they can dramatically alter the probability of rare currents. Different regimes are separated by dynamical phase transitions. Subsequently, we address systems in which the memory cannot be encoded in hidden variables or the waiting-time distributions depend on the whole trajectory. Here, the difficulty in obtaining exact analytical results is exacerbated. To tackle these systems, we have proposed a version of the so-called 'cloning' algorithm for the evaluation of large deviations that can be applied consistently for both Markovian and non-Markovian dynamics. The efficacy of this approach is confirmed by numerical results for some of the rare non-Markovian models whose large deviation functions can be obtained exactly. We finally adapt this machinery to a technological problem, specifically the performance evaluation of communication systems, where temporal correlations and large deviations are important.

This thesis set out to investigate the electrophysiological correlates of maths anxiety (MA). Research has shown that those with high MA (HMA) tend to have poorer accuracy and increased reaction time on maths based tasks and that high maths anxious individuals avoid situations where they might have to use maths. This can impact on their future by restricting their degree or job prospects. Previous research has identified the behavioural cognitive and psychological effects of MA and recently studies have begun to examine the associated underlying mechanisms in the brain. Chapter one outlines the background MA behavioural and measurement research before evaluating the neurophysiological methods used in cognitive neuroscience and the use of electroencephalography (EEG) in chapter two. Chapter three continues by outlining previous research concerning the neurophysiological processing of maths and number before evaluating relevant neurophysiological research concerning MA. Four experimental studies are conducted, exploring the neurophysiological underpinnings of MA research using EEG. Each of these recruits 30 participants and measures of electro-cortical (Event Related Potentials (ERPs), Global Field Power, Frequency etc.) and questionnaire measures are implemented. The first study aimed to identify whether the behavioural effects of MA (poorer accuracy and increased reaction time) are consistent with ERP differences (component amplitude and latency differences) in the brain and to understand why these effects are experienced. This revealed no significant comparisons between ERP components and behavioural responses involving low and high maths anxious individuals, but this may have been due to the lack of an anxious response by using a verification task, rather than requiring calculation. Study two introduces the measurement of gamma activity as a neurophysiological measure of anxiety and threat processing and brings three core areas of anxiety research together: Previous studies outline high anxiety in connection with gamma modulation, also showing gamma band activity is associated with the amygdala and finally, that the amygdala is responsible for the processing of threat perception and anxiety. This research has not been brought together when studying MA. Results produced similar ERP findings to the previous study but the introduction of gamma activity into the research provided the first differences between high and low MA (LMA) groups, showing significantly greater gamma activity levels in HMA individuals. However, this study only used numerically-based tasks, thus the third study implemented a non-numerical condition to act as a control. Study three replicates the findings showing a reduced level of gamma activity in high MA individuals for the non-numerical based task, however, this was also reduced for the simple maths task. It was theorised that it is more likely to be the initial threat perception that represents the anxious response and gamma activity increases. To test this and remove any working memory demands, the fourth study implements the presentation of single digit observation (using single digit numbers and letters). Even though there was no demand on working memory, high maths anxious participants displayed similar levels of gamma activity as low maths anxious individuals during letter observation. However, they had significantly greater levels during the observation of number. Findings suggest that HMA individuals may not only struggle with the processing of maths stimuli, but may have a threat-related response to the simple observation of numerical stimuli. This implies that HMA individuals consistently apply an avoidance technique due to a threat response associated with increased levels of gamma activity. The findings of the each study are finally discussed in terms of their contribution to the neurophysiological underpinnings of MA, the first exploration of this using gamma activity, future research and the extent that number anxiety may act as a precursor or sine qua non to MA.