Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.

Simulation and development of a mock circulation loop with variable compliance

Heart disease is attributed as the highest cause of death in the world. Although this could be alleviated by heart transplantation, there is a chronic shortage of donor hearts and so mechanical solutions are being considered. Currently, many Ventricular Assist Devices (VADs) are being developed worldwide in an effort to increase life expectancy and quality of life for end stage heart failure patients. Current pre-clinical testing methods for VADs involve laboratory testing using Mock Circulation Loops (MCLs), and in vivo testing in animal models. The research and development of highly accurate MCLs is vital to the continuous improvement of VAD performance. The first objective of this study was to develop and validate a mathematical model of a MCL. This model could then be used in the design and construction of a variable compliance chamber to improve the performance of an existing MCL as well as form the basis for a new miniaturised MCL. An extensive review of literature was carried out on MCLs and mathematical modelling of their function. A mathematical model of a MCL was then created in the MATLAB/SIMULINK environment. This model included variable features such as resistance, fluid inertia and volumes (resulting from the pipe lengths and diameters); compliance of Windkessel chambers, atria and ventricles; density of both fluid and compressed air applied to the system; gravitational effects on vertical columns of fluid; and accurately modelled actuators controlling the ventricle contraction. This model was then validated using the physical properties and pressure and flow traces produced from a previously developed MCL. A variable compliance chamber was designed to reproduce parameters determined by the mathematical model. The function of the variability was achieved by controlling the transmural pressure across a diaphragm to alter the compliance of the system. An initial prototype was tested in a previously developed MCL, and a variable level of arterial compliance was successfully produced; however, the complete range of compliance values required for accurate physiological representation was not able to be produced with this initial design. The mathematical model was then used to design a smaller physical mock circulation loop, with the tubing sizes adjusted to produce accurate pressure and flow traces whilst having an appropriate frequency response characteristic. The development of the mathematical model greatly assisted the general design of an in vitro cardiovascular device test rig, while the variable compliance chamber allowed simple and real-time manipulation of MCL compliance to allow accurate transition between a variety of physiological conditions. The newly developed MCL produced an accurate design of a mechanical representation of the human circulatory system for in vitro cardiovascular device testing and education purposes. The continued improvement of VAD test rigs is essential if VAD design is to improve, and hence improve quality of life and life expectancy for heart failure patients.

Theoretical and numerical investigation of plasmon nanofocusing in metallic tapered rods and grooves

Effective focusing of electromagnetic (EM) energy to nanoscale regions is one of the major challenges in nano-photonics and plasmonics. The strong localization of the optical energy into regions much smaller than allowed by the diffraction limit, also called nanofocusing, offers promising applications in nano-sensor technology, nanofabrication, near-field optics or spectroscopy. One of the most promising solutions to the problem of efficient nanofocusing is related to surface plasmon propagation in metallic structures. Metallic tapered rods, commonly used as probes in near field microscopy and spectroscopy, are of a particular interest. They can provide very strong EM field enhancement at the tip due to surface plasmons (SP’s) propagating towards the tip of the tapered metal rod. A large number of studies have been devoted to the manufacturing process of tapered rods or tapered fibers coated by a metal film. On the other hand, structures such as metallic V-grooves or metal wedges can also provide strong electric field enhancements but manufacturing of these structures is still a challenge. It has been shown, however, that the attainable electric field enhancement at the apex in the V-groove is higher than at the tip of a metal tapered rod when the dissipation level in the metal is strong. Metallic V-grooves also have very promising characteristics as plasmonic waveguides. This thesis will present a thorough theoretical and numerical investigation of nanofocusing during plasmon propagation along a metal tapered rod and into a metallic V-groove. Optimal structural parameters including optimal taper angle, taper length and shape of the taper are determined in order to achieve maximum field enhancement factors at the tip of the nanofocusing structure. An analytical investigation of plasmon nanofocusing by metal tapered rods is carried out by means of the geometric optics approximation (GOA), which is also called adiabatic nanofocusing. However, GOA is applicable only for analysing tapered structures with small taper angles and without considering a terminating tip structure in order to neglect reflections. Rigorous numerical methods are employed for analysing non-adiabatic nanofocusing, by tapered rod and V-grooves with larger taper angles and with a rounded tip. These structures cannot be studied by analytical methods due to the presence of reflected waves from the taper section, the tip and also from (artificial) computational boundaries. A new method is introduced to combine the advantages of GOA and rigorous numerical methods in order to reduce significantly the use of computational resources and yet achieve accurate results for the analysis of large tapered structures, within reasonable calculation time. Detailed comparison between GOA and rigorous numerical methods will be carried out in order to find the critical taper angle of the tapered structures at which GOA is still applicable. It will be demonstrated that optimal taper angles, at which maximum field enhancements occur, coincide with the critical angles, at which GOA is still applicable. It will be shown that the applicability of GOA can be substantially expanded to include structures which could be analysed previously by numerical methods only. The influence of the rounded tip, the taper angle and the role of dissipation onto the plasmon field distribution along the tapered rod and near the tip will be analysed analytically and numerically in detail. It will be demonstrated that electric field enhancement factors of up to ~ 2500 within nanoscale regions are predicted. These are sufficient, for instance, to detect single molecules using surface enhanced Raman spectroscopy (SERS) with the tip of a tapered rod, an approach also known as tip enhanced Raman spectroscopy or TERS. The results obtained in this project will be important for applications for which strong local field enhancement factors are crucial for the performance of devices such as near field microscopes or spectroscopy. The optimal design of nanofocusing structures, at which the delivery of electromagnetic energy to the nanometer region is most efficient, will lead to new applications in near field sensors, near field measuring technology, or generation of nanometer sized energy sources. This includes: applications in tip enhanced Raman spectroscopy (TERS); manipulation of nanoparticles and molecules; efficient coupling of optical energy into and out of plasmonic circuits; second harmonic generation in non-linear optics; or delivery of energy to quantum dots, for instance, for quantum computations.

Dancing the Thesis : Potentials and Pitfalls in Practice-led Research

Practice-led or multi modal theses (describing examinable outcomes of postgraduate study which comprise the practice of dancing/choreography with an accompanying exegesis) are an emerging strength of dance scholarship; a form of enquiry that has been gaining momentum for over a decade, particularly in Australia and the United Kingdom. It has been strongly argued that, in this form of research, legitimate claims to new knowledge are embodied predominantly within the practice itself (Pakes, 2003) and that these findings are emergent, contingent and often interstitial, contained within both the material form of the practice and in the symbolic languages surrounding the form. In a recent study on ‘dancing’ theses Phillips, Stock, Vincs (2009) found that there was general agreement from academics and artists that ‘there could be more flexibility in matching written language with conceptual thought expressed in practice’. The authors discuss how the seemingly intangible nature of danced / embodied research, reliant on what Melrose (2003) terms ‘performance mastery’ by the ‘expert practitioner’ (2006, Point 4) involving ‘expert’ intuition (2006, Point 5), might be accessed, articulated and validated in terms of alternative ways of knowing through exploring an ongoing dialogue in which the danced practice develops emergent theory. They also propose ways in which the danced thesis can be ‘converted’ into the required ‘durable’ artefact which the ephemerality of live performance denies, drawing on the work of Rye’s ‘multi-view’ digital record (2003) and Stapleton’s ‘multi-voiced audio visual document’(2006, 82). Building on a two-year research project (2007-2008) Dancing Between Diversity and Consistency: Refining Assessment in Postgraduate Degrees in Dance, which examined such issues in relation to assessment in an Australian context, the three researchers have further explored issues around interdisciplinarity, cultural differences and documentation through engaging with the following questions:  How do we represent research in which understandings, meanings and findings are situated within the body of the dancer/choreographer?  Do these need a form of ‘translating’ into textual form in order to be accessed as research?  What kind of language structures can be developed to effect this translation: metaphor, allusion, symbol?  How important is contextualising the creative practice?  How do we incorporate differing cultural inflections and practices into our reading and evaluation?  What kind of layered documentation can assist in producing a ‘durable’ research artefact from a non-reproduce-able live event?

Modernist 16-19 Business Education in a Postmodern world - critical evidence of business practice and business education in the cultural industries

This article examines the continued relevance of the 16-19 business education curriculum in the UK, stimulated by doubts expressed by Thomas (1996), over its continued relevance. We express a concern that business education needs, but is struggling, to respond to significant societal shifts in consumption and production strategies that do not sit easily within traditional theories of business practice currently underpinning 16-19 business education. We examine firstly, the extent to which a formal body of knowledge couched in a modernist discourse of facts and objectivity can cope with the changing and fluid developments in much current business practice that is rooted in the cultural and symbolic. Secondly, the extent to which both academic and vocational competences provide the means for students to develop a framework of critical understanding that can respond effectively to rapidly changing business environments.Findings are based on research conducted jointly by the University of Manchester and the Manchester Institute for Popular Culture at Manchester Metropolitan University. The growth of dynamism of the cultural industries sector - largely micro-businesses and small and medium sized enterprises (SMEs) -encapsulates forms of business knowledge, business language and business practice which may not immediately fit with the models provided within business education. Results suggest increasingly reflexive forms of consumption being met by similarly reflexive and flexible modes of production.Our evidence suggests that whilst modernist business knowledge is often the foundation for many 16-19 business education courses, these programmes of study/training do not usually reflect the activities of SME and micro-business practitioners in the cultural industries. Given the importance of cultural industries in terms of the production strategies required to meet increasingly reflexive markets, it is suggested that there may be a need to incorporate a postmodern approach to the current content and pedagogy; one that is contextual, cultural and discursive.

Generating rules with predicates, terms and variables from the pruned neural networks

Artificial neural networks (ANN) have demonstrated good predictive performance in a wide range of applications. They are, however, not considered sufficient for knowledge representation because of their inability to represent the reasoning process succinctly. This paper proposes a novel methodology Gyan that represents the knowledge of a trained network in the form of restricted first-order predicate rules. The empirical results demonstrate that an equivalent symbolic interpretation in the form of rules with predicates, terms and variables can be derived describing the overall behaviour of the trained ANN with improved comprehensibility while maintaining the accuracy and fidelity of the propositional rules.

Finding hy-Brazil : eugenics and modernism in the Pacific

In the 1930s a number of Australian women writers took issue with material and symbolic aspects of public health discourse and in particular challenged institutional endorsement of eugenicist movements. This paper discusses the response of inter-war women writers to the national discussion of science and medicine and, in particular, eugenics.

Cosmoscapes and the promotion of uncosmopolitan values

Globality generates increasingly diffuse networks of human and non-human innovators, carriers and icons of exotic, polyethnic cosmopolitan difference; and this diffusion is increasingly hard to ignore or police (Latour 1993). In fact, such global networks of material-symbolic exchange can frequently have the unintended consequence of promoting status systems and cultural relationships founded on uncosmopolitan values such as cultural appropriation and status-based social exclusion. Moreover, this materialsymbolic engagement with cosmopolitan difference could also be rather mundane, engaged in routinely without any great reflexive consciousness or capacity to destabilise current relations of cultural power, or interpreted unproblematically as just one component of a person’s social environment. Indeed, Beck’s (2006) argument is that cosmopolitanism, in an age of global risk, is being forced upon us unwillingly, so there should be no surprise if it is a bitter pill for some to swallow. Within these emergent cosmopolitan networks, which we call ‘cosmoscapes’, there is no certainty about the development of ethical or behavioural stances consistent with claims foundational to the current literature on cosmopolitanism. Reviewing historical and contemporary studies of globality and its dynamic generative capacity, this paper considers such literatures in the context of studies of cultural consumption and social status. When one positions these diverse bodies of literature against one another, it becomes clear that the possibility of widespread cosmopolitan cultural formations is largely unpromising.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Changing musical emotion : a computational rule system for modifying score and performance

When communicating emotion in music, composers and performers encode their expressive intentions through the control of basic musical features such as: pitch, loudness, timbre, mode, and articulation. The extent to which emotion can be controlled through the systematic manipulation of these features has not been fully examined. In this paper we present CMERS, a Computational Music Emotion Rule System for the control of perceived musical emotion that modifies features at the levels of score and performance in real-time. CMERS performance was evaluated in two rounds of perceptual testing. In experiment I, 20 participants continuously rated the perceived emotion of 15 music samples generated by CMERS. Three music works, each with five emotional variations were used (normal, happy, sad, angry, and tender). The intended emotion by CMERS was correctly identified 78% of the time, with significant shifts in valence and arousal also recorded, regardless of the works’ original emotion.

Theoretical investigation of mechanisms of formation and interaction of nanoparticles

In this thesis an investigation into theoretical models for formation and interaction of nanoparticles is presented. The work presented includes a literature review of current models followed by a series of five chapters of original research. This thesis has been submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by publication and therefore each of the five chapters consist of a peer-reviewed journal article. The thesis is then concluded with a discussion of what has been achieved during the PhD candidature, the potential applications for this research and ways in which the research could be extended in the future. In this thesis we explore stochastic models pertaining to the interaction and evolution mechanisms of nanoparticles. In particular, we explore in depth the stochastic evaporation of molecules due to thermal activation and its ultimate effect on nanoparticles sizes and concentrations. Secondly, we analyse the thermal vibrations of nanoparticles suspended in a fluid and subject to standing oscillating drag forces (as would occur in a standing sound wave) and finally on lattice surfaces in the presence of high heat gradients. We have described in this thesis a number of new models for the description of multicompartment networks joined by a multiple, stochastically evaporating, links. The primary motivation for this work is in the description of thermal fragmentation in which multiple molecules holding parts of a carbonaceous nanoparticle may evaporate. Ultimately, these models predict the rate at which the network or aggregate fragments into smaller networks/aggregates and with what aggregate size distribution. The models are highly analytic and describe the fragmentation of a link holding multiple bonds using Markov processes that best describe different physical situations and these processes have been analysed using a number of mathematical methods. The fragmentation of the network/aggregate is then predicted using combinatorial arguments. Whilst there is some scepticism in the scientific community pertaining to the proposed mechanism of thermal fragmentation,we have presented compelling evidence in this thesis supporting the currently proposed mechanism and shown that our models can accurately match experimental results. This was achieved using a realistic simulation of the fragmentation of the fractal carbonaceous aggregate structure using our models. Furthermore, in this thesis a method of manipulation using acoustic standing waves is investigated. In our investigation we analysed the effect of frequency and particle size on the ability for the particle to be manipulated by means of a standing acoustic wave. In our results, we report the existence of a critical frequency for a particular particle size. This frequency is inversely proportional to the Stokes time of the particle in the fluid. We also find that for large frequencies the subtle Brownian motion of even larger particles plays a significant role in the efficacy of the manipulation. This is due to the decreasing size of the boundary layer between acoustic nodes. Our model utilises a multiple time scale approach to calculating the long term effects of the standing acoustic field on the particles that are interacting with the sound. These effects are then combined with the effects of Brownian motion in order to obtain a complete mathematical description of the particle dynamics in such acoustic fields. Finally, in this thesis, we develop a numerical routine for the description of "thermal tweezers". Currently, the technique of thermal tweezers is predominantly theoretical however there has been a handful of successful experiments which demonstrate the effect it practise. Thermal tweezers is the name given to the way in which particles can be easily manipulated on a lattice surface by careful selection of a heat distribution over the surface. Typically, the theoretical simulations of the effect can be rather time consuming with supercomputer facilities processing data over days or even weeks. Our alternative numerical method for the simulation of particle distributions pertaining to the thermal tweezers effect use the Fokker-Planck equation to derive a quick numerical method for the calculation of the effective diffusion constant as a result of the lattice and the temperature. We then use this diffusion constant and solve the diffusion equation numerically using the finite volume method. This saves the algorithm from calculating many individual particle trajectories since it is describes the flow of the probability distribution of particles in a continuous manner. The alternative method that is outlined in this thesis can produce a larger quantity of accurate results on a household PC in a matter of hours which is much better than was previously achieveable.

Men's intimate partner abuse and control : reconciling paradoxical masculinities and social contradictions

Intimate partner abuse and control is one of the most common forms of violence against women, and is considered an international problem of social, political, legal and human rights significance. Yet few studies have attempted to understand this problem from the perspective of male perpetrators. This gap is addressed by conducting in-depth interviews with 16 able-bodied men of white European ancestry born and educated in New Zealand or Australia, who have been physically violent and/or emotionally, intellectually, sexually or financially controlling of a live-in female partner. This thesis extends and deepens the dominant ways of thinking about men’s intimate partner abuse by utilising a new theoretical framework compatible with contemporary feminist scholarship. A synthesis of Connell’s theory of masculinities and Bourdieu’s field theory is utilised for the purpose of exploring more nuanced, complex understandings of manliness and men’s relationships with men, women and social structures. Through such an analysis, this thesis finds that men’s perpetration of power and control over women is driven by a need to avoid the stigma of appearing weak. As a consequence, their desire and ability to show love, care and empathy is suppressed in favour of a presumed honourable manliness, and their female partners are used as weapons in the pursuit of symbolic capital in the form of recognition, prestige and acceptance from real and/or imagined men. This research also uncovers the complex interplay between masculine practices and particular social contexts. For example, the norms of practice encountered from those in authority, such as teachers, sports coaches, police, court judges and workplace management, influences the decision making of the men in this study, to use, or not to use, physical violence, psychological abuse and structural control. The principal conclusion is that there is a repertoire of paradoxical masculinities and contradictory social messages available to the men in this study. But gender policing by other men, complicit women and those in authority provides little room for legitimate complexity in masculine practices. Perpetrators in this study reconcile these conflicts of interest by generally avoiding subordinated masculinity and possible ostracism, and instead practicing more heroic hegemonic masculinities by abusing and controlling women and particular other men. This thesis concludes that for intimate partner abuse and control to cease, changes in power structures have to occur at all levels of society.