Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Assessing a statistical inquiry

As statistical education becomes more firmly embedded in the school curriculum and its value across the curriculum is recognised, attention moves from knowing procedures, such as calculating a mean or drawing a graph, to understanding the purpose of a statistical investigation in decision making in many disciplines. As students learn to complete the stages of an investigation, the question of meaningful assessment of the process arises. This paper considers models for carrying out a statistical inquiry and, based on a four-phase model, creates a developmental squence that can be used for the assessment of outcomes from each of the four phases as well as for the complete inquiry. The developmental sequence is based on the SOLO model, focussing on the "observed" outcomes during the inquiry process.

Recurrence risk modelling of the genetic susceptibility to ankylosing spondylitis

Objectives - It has long been suspected that susceptibility to ankylosing spondylitis (AS) is influenced by genes lying distant to the major histocompatibility complex. This study compares genetic models of AS to assess the most likely mode of inheritance, using recurrence risk ratios in relatives of affected subjects. Methods - Recurrence risk ratios in different degrees of relatives were determined using published data from studies specifically designed to address the question. The methods of Risch were used to determine the expected recurrence risk ratios in different degrees of relatives, assuming equal first degree relative recurrence risk between models. Goodness of fit was determined by χ2 comparison of the expected number of affected subjects with the observed number, given equal numbers of each type of relative studied. Results - The recurrence risks in different degrees of relatives were: monozygotic (MZ) twins 63% (17/27), first degree relatives 8.2% (441/5390), second degree relatives 1.0% (8/834), and third degree relatives 0.7% (7/997). Parent-child recurrence risk (7.9%, 37/466) was not significantly different from the sibling recurrence risk (8.2%, 404/4924), excluding a significant dominance genetic component to susceptibility. Poor fitting models included single gene, genetic heterogeneity, additive, two locus multiplicative, and one locus and residual polygenes (χ2 > 32 (two degrees of freedom), p < 10-6 for all models). The best fitting model studied was a five locus model with multiplicative interaction between loci (χ2 = 1.4 (two degrees of freedom), p = 0.5). Oligogenic multiplicative models were the best fitting over a range of population prevalences and first degree recurrence risk rates. Conclusions - This study suggests that of the genetic models tested, the most likely model operating in AS is an oligogenic model with predominantly multiplicative interaction between loci.

Quantifying the state of populations and effects of disturbances at large spatio-temporal scales: The case of coral populations in the great barrier reef

This project was a step forward in applying statistical methods and models to provide new insights for more informed decision-making at large spatial scales. The model has been designed to address complicated effects of ecological processes that govern the state of populations and uncertainties inherent in large spatio-temporal datasets. Specifically, the thesis contributes to better understanding and management of the Great Barrier Reef.

Exploring accuracy factors in cost estimating practice towards implementing Building Information Modelling (BIM)

Cost estimating has been acknowledged as a crucial component of construction projects. Depending on available information and project requirements, cost estimates evolve in tandem with project lifecycle stages; conceptualisation, design development, execution and facility management. The premium placed on the accuracy of cost estimates is crucial to producing project tenders and eventually in budget management. Notwithstanding the initial slow pace of its adoption, Building Information Modelling (BIM) has successfully addressed a number of challenges previously characteristic of traditional approaches in the AEC, including poor communication, the prevalence of islands of information and frequent reworks. Therefore, it is conceivable that BIM can be leveraged to address specific shortcomings of cost estimation. The impetus for leveraging BIM models for accurate cost estimation is to align budgeted and actual cost. This paper hypothesises that the accuracy of BIM-based estimation, as more efficient, process-mirrors of traditional cost estimation methods, can be enhanced by simulating traditional cost estimation factors variables. Through literature reviews and preliminary expert interviews, this paper explores the factors that could potentially lead to more accurate cost estimates for construction projects. The findings show numerous factors that affect the cost estimates ranging from project information and its characteristic, project team, clients, contractual matters, and other external influences. This paper will make a particular contribution to the early phase of BIM-based project estimation.

Cost estimating practice incorporating Building Information Modelling (BIM): Malaysian Quantity Surveyors perspectives

Cost estimating is a key task within Quantity Surveyors’ (QS) offices. Provision of an accurate estimate is vital to ensure that the objectives of the client are met by staying within the client’s budget. Building Information Modelling (BIM) is an evolving technology that has gained attention in the construction industries all over the world. Benefits from the use of BIM include cost and time savings if the processes used by the procurement team are adapted to maximise the benefits of BIM. BIM can be used by QSs to automate aspects of quantity take-off and the preparation of estimates, decreasing turnaround time and assist in controlling errors and inaccuracies. The Malaysian government has decided to require the use of BIM for its projects beginning from 2016. However, slow uptake is reported in the use of BIM both within companies and to support collaboration within the Malaysian industry. It has been recommended that QSs to start evaluating the impact of BIM on their practices. This paper reviews the perspectives of QSs in Malaysia towards the use of BIM to achieve more dependable results in their cost estimating practice. The objectives of this paper include identifying strategies in improving practice and potential adoption drivers that lead QSs to BIM usage in their construction projects. From the expert interviews, it was found out that, despite still using traditional methods and not practising BIM, the interviewees still acquire limited knowledge related to BIM. There are some drivers that potentially motivate them to employ BIM in their practices. These include client demands, innovation in traditional methods, speed in estimating costs, reduced time and costs, improvement in practices and self-awareness, efficiency in projects, and competition from other companies. The findings of this paper identify the potential drivers in encouraging Malaysian Quantity Surveyors to exploit BIM in their construction projects.

Trans-scale granular modelling of cytoskeleton: A mini-review

Living cells are the functional unit of organs that controls reactions to their exterior. However, the mechanics of living cells can be difficult to characterize due to the crypticity of their microscale structures and associated dynamic cellular processes. Fortunately, multiscale modelling provides a powerful simulation tool that can be used to study the mechanical properties of these soft hierarchical, biological systems. This paper reviews recent developments in hierarchical multiscale modeling technique that aimed at understanding cytoskeleton mechanics. Discussions are expanded with respects to cytoskeletal components including: intermediate filaments, microtubules and microfilament networks. The mechanical performance of difference cytoskeleton components are discussed with respect to their structural and material properties. Explicit granular simulation methods are adopted with different coarse-grained strategies for these cytoskeleton components and the simulation details are introduced in this review.

Review and future options for computer modelling in the sugar industry

Computer modelling has been used extensively in some processes in the sugar industry to achieve significant gains. This paper reviews the investigations carried out over approximately the last twenty five years, including the successes but also areas where problems and delays have been encountered. In that time the capability of both hardware and software have increased dramatically. For some processes such as cane cleaning, cane billet preparation, and sugar drying, the application of computer modelling towards improved equipment design and operation has been quite limited. A particular problem has been the large number of particles and particle interactions in these…

Generalizing the use of geographical weights in biodiversity modelling

Aim Determining how ecological processes vary across space is a major focus in ecology. Current methods that investigate such effects remain constrained by important limiting assumptions. Here we provide an extension to geographically weighted regression in which local regression and spatial weighting are used in combination. This method can be used to investigate non-stationarity and spatial-scale effects using any regression technique that can accommodate uneven weighting of observations, including machine learning. Innovation We extend the use of spatial weights to generalized linear models and boosted regression trees by using simulated data for which the results are known, and compare these local approaches with existing alternatives such as geographically weighted regression (GWR). The spatial weighting procedure (1) explained up to 80% deviance in simulated species richness, (2) optimized the normal distribution of model residuals when applied to generalized linear models versus GWR, and (3) detected nonlinear relationships and interactions between response variables and their predictors when applied to boosted regression trees. Predictor ranking changed with spatial scale, highlighting the scales at which different species–environment relationships need to be considered. Main conclusions GWR is useful for investigating spatially varying species–environment relationships. However, the use of local weights implemented in alternative modelling techniques can help detect nonlinear relationships and high-order interactions that were previously unassessed. Therefore, this method not only informs us how location and scale influence our perception of patterns and processes, it also offers a way to deal with different ecological interpretations that can emerge as different areas of spatial influence are considered during model fitting.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Statistical literacy social media project for the masses

This article examines a social media assignment used to teach and practice statistical literacy with over 400 students each semester in large-lecture traditional, fully online, and flipped sections of an introductory-level statistics course. Following the social media assignment, students completed a survey on how they approached the assignment. Drawing from the authors’ experiences with the project and the survey results, this article offers recommendations for developing social media assignments in large courses that focus on the interplay between the social media tool and the implications of assignment prompts.

Robust iris recognition using decision fusion and degradation modelling

This thesis investigates the use of fusion techniques and mathematical modelling to increase the robustness of iris recognition systems against iris image quality degradation, pupil size changes and partial occlusion. The proposed techniques improve recognition accuracy and enhance security. They can be further developed for better iris recognition in less constrained environments that do not require user cooperation. A framework to analyse the consistency of different regions of the iris is also developed. This can be applied to improve recognition systems using partial iris images, and cancelable biometric signatures or biometric based cryptography for privacy protection.

Modelling of the evaporation of a droplet suspended in a binary atmosphere

The process of spray drying is applied in a number of contexts. One such application is the production of a synthetic rock used for storage of nuclear waste. To establish a framework for a model of the spray drying process for this application, we here develop a model describing evaporation from droplets of pure water, such that the model may be extended to account for the presence of colloid within the droplet. We develop a spherically-symmetric model and formulate continuum equations describing mass, momentum, and energy balance in both the liquid and gas phases from first principles. We establish appropriate boundary conditions at the surface of the droplet, including a generalised Clapeyron equation that accurately describes the temperature at the surface of the droplet. To account for experiment design, we introduce a simplified platinum ball and wire model into the system using a thin wire problem. The resulting system of equations is transformed in order to simplify a finite volume solution scheme. The results from numerical simulation are compared with data collected for validation, and the sensitivity of the model to variations in key parameters, and to the use of Clausius–Clapeyron and generalised Clapeyron equations, is investigated. Good agreement is found between the model and experimental data, despite the simplicity of the platinum phase model.

Spatio-temporal modelling of cancer data in Queensland using Bayesian methods

Cancer is the leading contributor to the disease burden in Australia. This thesis develops and applies Bayesian hierarchical models to facilitate an investigation of the spatial and temporal associations for cancer diagnosis and survival among Queenslanders. The key objectives are to document and quantify the importance of spatial inequalities, explore factors influencing these inequalities, and investigate how spatial inequalities change over time. Existing Bayesian hierarchical models are refined, new models and methods developed, and tangible benefits obtained for cancer patients in Queensland. The versatility of using Bayesian models in cancer control are clearly demonstrated through these detailed and comprehensive analyses.

Atheroma: Is calcium important or not? A modelling study of stress within the atheromatous fibrous cap in relation to position and size of calcium deposits

Atheromatous plaque rupture h the cause of the majority of strokes and heart attacks in the developed world. The role of calcium deposits and their contribution to plaque vulnerability are controversial. Some studies have suggested that calcified plaque tends to be more stable whereas others have suggested the opposite. This study uses a finite element model to evaluate the effect of calcium deposits on the stress within the fibrous cap by varying their location and size. Plaque fibrous cap, lipid pool and calcification were modeled as hyperelastic, Isotropic, (nearly) incompressible materials with different properties for large deformation analysis by assigning time-dependent pressure loading on the lumen wall. The stress and strain contours were illustrated for each condition for comparison. Von Mises stress only increases up to 1.5% when varying the location of calcification in the lipid pool distant to the fibrous cap. Calcification in the fibrous cap leads to a 43% increase of Von Mises stress when compared with that in the lipid pool. An increase of 100% of calcification area leads to a 15% stress increase in the fibrous cap. Calcification in the lipid pool does not increase fibrous cap stress when it is distant to the fibrous cap, whilst large areas of calcification close to or in the fibrous cap may lead to a high stress concentration within the fibrous cap, which may cause plaque rupture. This study highlights the application of a computational model on a simulation of clinical problems, and it may provide insights into the mechanism of plaque rupture.