Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Study of industrially relevant boundary layer and axisymmetric flows, including swirl and turbulence

Micropolar and RNG-based modelling of industrially relevant boundary layer and recirculating swirling flows is described. Both models contain a number of adjustable parameters and auxiliary conditions that must be either modelled or experimentally determined, and the effects of varying these on the resulting flow solutions is quantified. To these ends, the behaviour of the micropolar model for self-similar flow over a surface that is both stretching and transpiring is explored in depth. The simplified governing equations permit both analytic and numerical approaches to be adopted, and a number of closed form solutions (both exact and approximate) are obtained using perturbation and order of magnitude analyses. Results are compared with the corresponding Newtonian flow solution in order to highlight the differences between the micropolar and classical models, and significant new insights into the behaviour of the micropolar model are revealed for this flow. The behaviour of the RNG-bas based models for swirling flow with vortex breakdown zones is explored in depth via computational modelling of two experimental data sets and an idealised breakdown flow configuration. Meticulous modeling of upstream auxillary conditions is required to correctly assess the behavior of the models studied in this work. The novel concept of using the results to infer the role of turbulence in the onset and topology of the breakdown zone is employed.

Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Discovering, applying and integrating self-knowledge : a grounded theory study of learning in life coaching

Professional coaching is a rapidly expanding field with interdisciplinary roots and broad application. However, despite abundant prescriptive literature, research into the process of coaching, and especially life coaching, is minimal. Similarly, although learning is inherently recognised in the process of coaching, and coaching is increasingly being recognised as a means of enhancing teaching and learning, the process of learning in coaching is little understood, and learning theory makes up only a small part of the evidence-based coaching literature. In this grounded theory study of life coaches and their clients, the process of learning in life coaching across a range of coaching models is examined and explained. The findings demonstrate how learning in life coaching emerged as a process of discovering, applying and integrating self-knowledge, which culminated in the development of self. This process occurred through eight key coaching processes shared between coaches and clients and combined a multitude of learning theory.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

A grounded theory study of technology appropriation in anaesthesia

The human-technology nexus is a strong focus of Information Systems (IS) research; however, very few studies have explored this phenomenon in anaesthesia. Anaesthesia has a long history of adoption of technological artifacts, ranging from early apparatus to present-day information systems such as electronic monitoring and pulse oximetry. This prevalence of technology in modern anaesthesia and the rich human-technology relationship provides a fertile empirical setting for IS research. This study employed a grounded theory approach that began with a broad initial guiding question and, through simultaneous data collection and analysis, uncovered a core category of technology appropriation. This emergent basic social process captures a central activity of anaesthestists and is supported by three major concepts: knowledge-directed medicine, complementary artifacts and culture of anaesthesia. The outcomes of this study are: (1) a substantive theory that integrates the aforementioned concepts and pertains to the research setting of anaesthesia and (2) a formal theory, which further develops the core category of appropriation from anaesthesia-specific to a broader, more general perspective. These outcomes fulfill the objective of a grounded theory study, being the formation of theory that describes and explains observed patterns in the empirical field. In generalizing the notion of appropriation, the formal theory is developed using the theories of Karl Marx. This Marxian model of technology appropriation is a three-tiered theoretical lens that examines appropriation behaviours at a highly abstract level, connecting the stages of natural, species and social being to the transition of a technology-as-artifact to a technology-in-use via the processes of perception, orientation and realization. The contributions of this research are two-fold: (1) the substantive model contributes to practice by providing a model that describes and explains the human-technology nexus in anaesthesia, and thereby offers potential predictive capabilities for designers and administrators to optimize future appropriations of new anaesthetic technological artifacts; and (2) the formal model contributes to research by drawing attention to the philosophical foundations of appropriation in the work of Marx, and subsequently expanding the current understanding of contemporary IS theories of adoption and appropriation.

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

Evaluating the effect of a patient education brochure on patients’ expectations and satisfaction with emergency department service

Introduction: The purpose of this study was to assess the capacity of a written intervention, in this case a patient information brochure, to improve patient satisfaction during an Emergency Department (ED) visit. For the purpose of measuring the effect of the intervention the ED journey was conceptualised as a series of distinct areas of service comprising waiting time, service by the triage nurse, care from doctors and nurses and information giving Background of study: Research into patient satisfaction has become a widespread activity endorsed by both governments and hospital administrations. The literature on ED patient satisfaction has consistently indicated three primary areas of patient dissatisfaction: waiting time, nursing care and communication. Recent developments in the literature on patient satisfaction studies however have highlighted the relationship between patients. expectations of a service encounter and their consequent assessment of the experience as dissatisfying or satisfying. Disconfirmation theory posits that the degree to which expectations are confirmed will affect subsequent levels of satisfaction. The conceptual framework utilised in this study is Coye.s (2004) model of disconfirmation. Coye while reiterating satisfaction is a consequence of the degree expectations are either confirmed or disconfirmed also posits that expectations can be modified by interventions. Coye.s work conceptualises these interventions as intra encounter experiences (cues) which function to adjust expectations. Coye suggests some cues are unintended and may have a negative impact which also reinforces the value of planned cues intended to meet or exceed consumer expectations. Consequently the brochure can be characterized as a potentially positive cue, encouraging the patient to understand processes and to orient them in what can be a confronting environment. Only a limited number of studies have examined the effect of written interventions within an ED. No studies could be located which have tested the effect of ED interventions using a conceptual framework which relates the effect of the degree to which expectations are confirmed or disconfirmed in terms of satisfaction with services. Method: Two studies were conducted. Study One used qualitative methods to explore patients. expectations of the ED from the perspective of both patients and health care professionals. Study One was used in part to direct the development of the intervention (brochure) in Study Two. The brochure was an intervention designed to modify patients. expectations thus increasing their satisfaction with the provision of ED service. As there was no existing tools to measure ED patients. expectations and satisfaction a new tool was also developed based on the findings and the literature of Study One. Study Two used a non-randomised, quasi-experimental approach using a non-equivalent post-test only comparison group design used to investigate the effect of the patient education brochure (Stommel and Wills, 2004). The brochure was disseminated to one of two study groups (the intervention group). The effect of the brochure was assessed by comparing the data obtained from both the intervention and control group. These two groups consisted of 150 participants each. It was expected that any differences in the relevant domains selected for examination would indicate the effect of the brochure both on expectation and potentially satisfaction. Results: Study One revealed several areas of common ground between patients and nurses in terms of relevant content for the written intervention, including the need for information on the triage system and waiting times. Areas of difference were also found with patients emphasizing communication issues, whereas focus group members expressed concern that patients were often unable to assimilate verbal information. The findings suggested the potential utility of written material to reinforce verbal communication particularly in terms of the triage process and other ED protocols. This material was synthesized within the final version of the written intervention. Overall the results of Study Two indicated no significant differences between the two groups. The intervention group did indicate a significant number of participants who viewed the brochure of having changed their expectations. The effect of the brochure may have been obscured by a lack of parity between the two groups as the control group presented with statistically significantly higher levels of acuity and experienced significantly shorter waiting times. In terms of disconfirmation theory this would suggest expectations that had been met or exceeded. The results confirmed the correlation of expectations with satisfaction. Several domains also indicated age as a significant predictor with older patients tending to score higher satisfaction results. Other significant predictors of satisfaction established were waiting time and care from nurses, reinforcing the combination of efficient service and positive interpersonal experiences as being valued by patients. Conclusions: Information presented in written form appears to benefit a significant number of ED users in terms of orientation and explaining systems and procedures. The degree to which these effects may interact with other dimensions of satisfaction however is likely to be limited. Waiting time and interpersonal behaviours from staff also provide influential cues in determining satisfaction. Written material is likely to be one element in a series of coordinated strategies to improve patient satisfaction during periods of peak demand.