Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.

A constraints-led perspective to understanding skill acquisition and game play: A basis for integration of motor learning theory and physical education praxis?

Background: In order to design appropriate environments for performance and learning of movement skills, physical educators need a sound theoretical model of the learner and of processes of learning. In physical education, this type of modelling informs the organization of learning environments and effective and efficient use of practice time. An emerging theoretical framework in motor learning, relevant to physical education, advocates a constraints-led perspective for acquisition of movement skills and game play knowledge. This framework shows how physical educators could use task, performer and environmental constraints to channel acquisition of movement skills and decision making behaviours in learners. From this viewpoint, learners generate specific movement solutions to satisfy the unique combination of constraints imposed on them, a process which can be harnessed during physical education lessons. Purpose: In this paper the aim is to provide an overview of the motor learning approach emanating from the constraints-led perspective, and examine how it can substantiate a platform for a new pedagogical framework in physical education: nonlinear pedagogy. We aim to demonstrate that it is only through theoretically valid and objective empirical work of an applied nature that a conceptually sound nonlinear pedagogy model can continue to evolve and support research in physical education. We present some important implications for designing practices in games lessons, showing how a constraints-led perspective on motor learning could assist physical educators in understanding how to structure learning experiences for learners at different stages, with specific focus on understanding the design of games teaching programmes in physical education, using exemplars from Rugby Union and Cricket. Findings: Research evidence from recent studies examining movement models demonstrates that physical education teachers need a strong understanding of sport performance so that task constraints can be manipulated so that information-movement couplings are maintained in a learning environment that is representative of real performance situations. Physical educators should also understand that movement variability may not necessarily be detrimental to learning and could be an important phenomenon prior to the acquisition of a stable and functional movement pattern. We highlight how the nonlinear pedagogical approach is student-centred and empowers individuals to become active learners via a more hands-off approach to learning. Summary: A constraints-based perspective has the potential to provide physical educators with a framework for understanding how performer, task and environmental constraints shape each individual‟s physical education. Understanding the underlying neurobiological processes present in a constraints-led perspective to skill acquisition and game play can raise awareness of physical educators that teaching is a dynamic 'art' interwoven with the 'science' of motor learning theories.

Complex modelling of open system design for sustainable architecture

This paper argues a model of complex system design for sustainable architecture within a framework of entropy evolution. The spectrum of sustainable architecture consists of the efficient use of energy and material resource in life-cycle of buildings, the active involvement of the occupants in micro-climate control within buildings, and the natural environmental context. The interactions of the parameters compose a complex system of sustainable architectural design, of which the conventional linear and fragmented design technologies are insufficient to indicate holistic and ongoing environmental performance. The complexity theory of dissipative structure states a microscopic formulation of open system evolution, which provides a system design framework for the evolution of building environmental performance towards an optimization of sustainability in architecture.

Modelling Wages and Prices in Australia

This paper estimates a simultaneous-equation model of wages and prices for Australia, underpinned by a competing claims framework of imperfect competition. Two separate co-integrating relationships for wages and prices are identified by imposing the economic hypotheses implied by the theory. The steady-state relationships for wages and prices are then embedded in a parsimonious, dynamic wage-price model. The final model is both simple and parsimonious and able to describe the process of wage and price inflation in Australia

Are organ donation communication decisions reasoned or reactive? A test of the utility of an augmented Theory of Planned Behaviour with the Prototype/Willingness Model

Objectives: To explore whether people's organ donation consent decisions occur via a reasoned and/or social reaction pathway. --------- Design: We examined prospectively students' and community members' decisions to register consent on a donor register and discuss organ donation wishes with family. --------- Method: Participants completed items assessing theory of planned behaviour (TPB; attitude, subjective norm, perceived behavioural control (PBC)), prototype/willingness model (PWM; donor prototype favourability/similarity, past behaviour), and proposed additional influences (moral norm, self-identity, recipient prototypes) for registering (N=339) and discussing (N=315) intentions/willingness. Participants self-reported their registering (N=177) and discussing (N=166) behaviour 1 month later. The utility of the (1) TPB, (2) PWM, (3) augmented TPB with PWM, and (4) augmented TPB with PWM and extensions was tested using structural equation modelling for registering and discussing intentions/willingness, and logistic regression for behaviour. --------- Results: While the TPB proved a more parsimonious model, fit indices suggested that the other proposed models offered viable options, explaining greater variance in communication intentions/willingness. The TPB, augmented TPB with PWM, and extended augmented TPB with PWM best explained registering and discussing decisions. The proposed and revised PWM also proved an adequate fit for discussing decisions. Respondents with stronger intentions (and PBC for registering) had a higher likelihood of registering and discussing. --------- Conclusions: People's decisions to communicate donation wishes may be better explained via a reasoned pathway (especially for registering); however, discussing involves more reactive elements. The role of moral norm, self-identity, and prototypes as influences predicting communication decisions were highlighted also.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

Modelling the process of dialogic communication in public relations: a role-based approach

This paper takes Kent and Taylor’s (2002) call to develop a dialogic theory of public relations and suggests that a necessary first step is the modelling of the process of dialogic communication in public relations. In order to achieve this, extant literature from a range of fields is reviewed, seeking to develop a definition of dialogic communication that is meaningful to the practice of contemporary public relations. A simple transmission model of communication is used as a starting point. This is synthesised with concepts relating specifically to dialogue, taken here in its broadest sense rather than defined as any one particular outcome. The definition that emerges from this review leads to the conclusion that dialogic communication in public relations involves the interaction of three roles – those of sender, receiver, and responder. These three roles are shown to be adopted at different times by both participants involved in dialogic communication. It is further suggested that variations occur in how these roles are conducted: the sender and receiver roles can be approached in a passive or an active way, while the responder role can be classified as being either resistant or responsive to the information received in dialogic communication. The final modelling of the definition derived provides a framework which can be tested in the field to determine whether variations in the conduct of the roles in dialogic communication actually exist, and if so, whether they can be linked to the different types of outcome from dialogic communication identified previously in the literature.

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.

Beyond statistical procedures for predictive modelling: Data mining algorithms and support for university research at QUT

In a seminal data mining article, Leo Breiman [1] argued that to develop effective predictive classification and regression models, we need to move away from the sole dependency on statistical algorithms and embrace a wider toolkit of modeling algorithms that include data mining procedures. Nevertheless, many researchers still rely solely on statistical procedures when undertaking data modeling tasks; the sole reliance on these procedures has lead to the development of irrelevant theory and questionable research conclusions ([1], p.199). We will outline initiatives that the HPC & Research Support group is undertaking to engage researchers with data mining tools and techniques; including a new range of seminars, workshops, and one-on-one consultations covering data mining algorithms, the relationship between data mining and the research cycle, and limitations and problems with these new algorithms. Organisational limitations and restrictions to these initiatives are also discussed.

Widening the gap between measurement and modelling of secondary organic aerosol properties?

The link between measured sub-saturated hygroscopicity and cloud activation potential of secondary organic aerosol particles produced by the chamber photo-oxidation of α-pinene in the presence or absence of ammonium sulphate seed aerosol was investigated using two models of varying complexity. A simple single hygroscopicity parameter model and a more complex model (incorporating surface effects) were used to assess the detail required to predict the cloud condensation nucleus (CCN) activity from the subsaturated water uptake. Sub-saturated water uptake measured by three hygroscopicity tandem differential mobility analyser (HTDMA) instruments was used to determine the water activity for use in the models. The predicted CCN activity was compared to the measured CCN activation potential using a continuous flow CCN counter. Reconciliation using the more complex model formulation with measured cloud activation could be achieved widely different assumed surface tension behavior of the growing droplet; this was entirely determined by the instrument used as the source of water activity data. This unreliable derivation of the water activity as a function of solute concentration from sub-saturated hygroscopicity data indicates a limitation in the use of such data in predicting cloud condensation nucleus behavior of particles with a significant organic fraction. Similarly, the ability of the simpler single parameter model to predict cloud activation behaviour was dependent on the instrument used to measure sub-saturated hygroscopicity and the relative humidity used to provide the model input. However, agreement was observed for inorganic salt solution particles, which were measured by all instruments in agreement with theory. The difference in HTDMA data from validated and extensively used instruments means that it cannot be stated with certainty the detail required to predict the CCN activity from sub-saturated hygroscopicity. In order to narrow the gap between measurements of hygroscopic growth and CCN activity the processes involved must be understood and the instrumentation extensively quality assured. It is impossible to say from the results presented here due to the differences in HTDMA data whether: i) Surface tension suppression occurs ii) Bulk to surface partitioning is important iii) The water activity coefficient changes significantly as a function of the solute concentration.