Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Benefits of e-learning benchmarks : Australian case studies

In 2004, the Australian Flexible Learning Framework developed a suite of quantitative and qualitative indicators on the uptake, use and impact of e-learning in the Vocational Education and Training (VET) sector. These indicators were used to design items for a survey to gather quantitative data for benchmarking. A series of four surveys gathered data from VET providers, teachers, students and their employers. The data formed baseline indicators that were used to establish organisational goals and benchmarks for e-learning. These indicators were the first know set for benchmarking e-learning in Australia. The case studies in this paper illustrate ways in which VET providers have approached e-learning benchmarking, the benefits achieved and the lessons that they learned. The cases exemplify how VET providers have adapted the baseline indicators, how the indicators informed organisational plans and e-learning outcomes. The benefits of benchmarking are categorised under three purposes: reporting, performance management, and service improvement. A set of practical strategies is derived from the cases for consideration by other organisations interested in benchmarking e-learning services.

A reflective model for colour studies learning

In a university context how should colour be taught in order to engage students? Entwistle states, ‘What we learn depends on how we learn, and why we have to learn it.’ Therefore, there is a need to address the accumulating evidence that highlights the effects of learning environments on the quality of student learning when considering colour education. It is necessary to embrace the contextual demands while ensuring that the student knowledge of colour and the joy of discovering its characteristics in practice are enhanced. Institutional policy is forcing educators to re-evaluate traditional studio’s effectiveness and the intensive 'hands-on' interactive approach that is embedded in such an approach. As curriculum development involves not only theory and project work, the classroom culture and physical environment also need to be addressed. The increase in student numbers impacting the number of academic staff/student ratio, availability of teaching support as well as increasing variety of student age, work commitments, learning styles and attitudes have called for positive changes to how we teach. The Queensland University of Technology’s restructure in 2005 was a great opportunity to re-evaluate and redesign the approach to teaching within the design units of Interior Design undergraduate program –including colour. The resultant approach “encapsulates a mode of delivery, studio structure, as well as the learning context in which students and staff interact to facilitate learning”1 with a potential “to be integrated into a range of Interior Design units as it provides an adaptive educational framework rather than a prescriptive set of rules”.

My "middle way" media studies

I would argue that the problems that contemporary capitalism gives rise to are not the result of the classic exercise of power and hegemony characteristic of the monopoly phase of capitalism but of the “creative destruction” of such a phase. Schumpeter’s famous phrase is reflective of Lash and Urry’s (1987) notion of “disorganised capitalism” or of Robert Reich’s (2007) claim that large corporations have significantly less power now than three decades ago. The consequence is that there is a need to explore an economic “middle way” in debates about the narrative of the relationship between culture and economy, between the Scylla of total explanatory political economy and the Charybdis of tedium-by-case-study. This involves a Schumpeterian emphasis on entrepreneurial or enterprise economics (Cunningham, Banks, and Potts 2008). Schumpeter, in 1962, in Capitalism, Socialism and Democracy, argued that Marx had “no adequate theory of enterprise” and failed to “distinguish the entrepreneur from the capitalist” (quoted in McCraw 2007: 349). Schumpeter, his most recent biographer, Thomas McCraw, “told of capitalism in the way most people experience it: as consumer desires aroused by endless advertising; as forcible jolts up and down the social pecking order; as goals reached, shattered, altered, then reached once more as people try, try again.” He knew that “creative destruction fosters economic growth but also that it undercuts cherished human values” (p. 6). Schumpeter’s most recent biographer, Thomas McCraw, says that he elucidated what capitalism “really feels like” (as quoted in McCraw 2007: 349, 6).

The distribution and spread of citrus canker in Emerald, Australia

Citrus canker is a disease of citrus and closely related species, caused by the bacterium Xanthomonas citri subsp. citri. This disease, previously exotic to Australia, was detected on a single farm [infested premise-1, (IP1). IP is the terminology used in official biosecurity protocols to describe a locality at which an exotic plant pest has been confirmed or is presumed to exist. IP are numbered sequentially as they are detected] in Emerald, Queensland in July 2004. During the following 10 months the disease was subsequently detected on two other farms (IP2 and IP3) within the same area and studies indicated the disease first occurred on IP1 and spread to IP2 and IP3. The oldest, naturally infected plant tissue observed on any of these farms indicated the disease was present on IP1 for several months before detection and established on IP2 and IP3 during the second quarter (i.e. autumn) 2004. Transect studies on some IP1 blocks showed disease incidences ranged between 52 and 100% (trees infected). This contrasted to very low disease incidence, less than 4% of trees within a block, on IP2 and IP3. The mechanisms proposed for disease spread within blocks include weather-assisted dispersal of the bacterium (e.g. wind-driven rain) and movement of contaminated farm equipment, in particular by pivot irrigator towers via mechanical damage in combination with abundant water. Spread between blocks on IP2 was attributed to movement of contaminated farm equipment and/or people. Epidemiology results suggest: (i) successive surveillance rounds increase the likelihood of disease detection; (ii) surveillance sensitivity is affected by tree size; and (iii) individual destruction zones (for the purpose of eradication) could be determined using disease incidence and severity data rather than a predefined set area.

Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Incomplete pregnancy and risk of ovarian cancer : results from two Australian case-control studies and systematic review

Although full-term pregnancies reduce the risk of ovarian cancer, it has not been conclusively established whether incomplete pregnancies also influence risk. We investigated the relationship between a history of incomplete pregnancy and incident epithelial ovarian cancer among over 4,500 women who participated in two large Australian population-based case-control studies in 1990-1993 and 2002-2005. They provided responses to detailed questions about their reproductive histories and other personal factors. Summary odds ratios (OR) and confidence intervals (CI) derived from each study using the same covariates were aggregated. We found no significant associations between the number of incomplete pregnancies and ovarian cancer, for parous (OR = 0.98, 95% CI: 0.89, 1.08) or nulliparous (OR = 1.06, 95% CI: 0.75, 1.48) women, nor for the number of spontaneous or induced abortions and ovarian cancer for parous women (OR = 0.95, 95% CI 0.82, 1.09; OR = 1.08, 95% CI: 0.86, 1.36) or nulliparous women (OR = 1.2, 95% CI: 0.6, 2.4; OR = 0.8, 95% CI: 0.47, 1.38), respectively. A systematic review of 37 previous studies of the topic confirmed our findings that a history of incomplete pregnancy does not influence a woman’s risk of epithelial ovarian cancer.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).