Mathematical modelling of tumour-induced angiogenesis

The growth of solid tumours beyond a critical size is dependent upon angiogenesis, the formation of new blood vessels from an existing vasculature. Tumours may remain dormant at microscopic sizes for some years before switching to a mode in which growth of a supportive vasculature is initiated. The new blood vessels supply nutrients, oxygen, and access to routes by which tumour cells may travel to other sites within the host (metastasize). In recent decades an abundance of biological research has focused on tumour-induced angiogenesis in the hope that treatments targeted at the vasculature may result in a stabilisation or regression of the disease: a tantalizing prospect. The complex and fascinating process of angiogenesis has also attracted the interest of researchers in the field of mathematical biology, a discipline that is, for mathematics, relatively new. The challenge in mathematical biology is to produce a model that captures the essential elements and critical dependencies of a biological system. Such a model may ultimately be used as a predictive tool. In this thesis we examine a number of aspects of tumour-induced angiogenesis, focusing on growth of the neovasculature external to the tumour. Firstly we present a one-dimensional continuum model of tumour-induced angiogenesis in which elements of the immune system or other tumour-cytotoxins are delivered via the newly formed vessels. This model, based on observations from experiments by Judah Folkman et al., is able to show regression of the tumour for some parameter regimes. The modelling highlights a number of interesting aspects of the process that may be characterised further in the laboratory. The next model we present examines the initiation positions of blood vessel sprouts on an existing vessel, in a two-dimensional domain. This model hypothesises that a simple feedback inhibition mechanism may be used to describe the spacing of these sprouts with the inhibitor being produced by breakdown of the existing vessel's basement membrane. Finally, we have developed a stochastic model of blood vessel growth and anastomosis in three dimensions. The model has been implemented in C++, includes an openGL interface, and uses a novel algorithm for calculating proximity of the line segments representing a growing vessel. This choice of programming language and graphics interface allows for near-simultaneous calculation and visualisation of blood vessel networks using a contemporary personal computer. In addition the visualised results may be transformed interactively, and drop-down menus facilitate changes in the parameter values. Visualisation of results is of vital importance in the communication of mathematical information to a wide audience, and we aim to incorporate this philosophy in the thesis. As biological research further uncovers the intriguing processes involved in tumourinduced angiogenesis, we conclude with a comment from mathematical biologist Jim Murray, Mathematical biology is : : : the most exciting modern application of mathematics.

Contextualising the teaching and learning of measurement in Torres Strait Islander schools

This paper reports on a mathematics project conducted with six Torres Strait Islander schools and communities by the research team at the YuMi Deadly Centre at QUT. Data collected is from a small focus group of six teachers and two teacher aides. We investigated how measurement is taught and learned by students, their teachers and teacher aides in the community schools. A key focus of the project was that the teaching and learning of measurement be contextualised to the students’ culture, community and home languages. A significant finding from the project was that the teachers had differing levels of knowledge and understanding about how to contextualise measurement to support student learning. For example, an Indigenous teacher identified that mathematics and the environment are relational, that is, they are not discrete and in isolation from one another, rather they mesh together, thus affording the articulation and interchange among and between mathematics and Torres Strait Islander culture.

Understanding the very nature of Project Management : a praxiological approach

Foreword: In this paper I call upon a praxiological approach. Praxeology (early alteration of praxiology) is the study of human action and conduct. The name praxeology/praxiologyakes is root in praxis, Medieval Latin, from Greek, doing, action, from prassein to do, practice (Merriam-Webster Dictionary). Having been involved in project management education, research and practice for the last twenty years, I have constantly tried to improve and to provide a better understanding/knowledge of the field and related practice, and as a consequence widen and deepen the competencies of the people I was working with (and my own competencies as well!), assuming that better project management lead to more efficient and effective use of resources, development of people and at the end to a better world. For some time I have perceived a need to clarify the foundations of the discipline of project management, or at least elucidate what these foundations could be. An immodest task, one might say! But not a neutral one! I am constantly surprised by the way the world (i.e., organizations, universities, students and professional bodies) sees project management: as a set of methods, techniques, tools, interacting with others fields – general management, engineering, construction, information systems, etc. – bringing some effective ways of dealing with various sets of problems – from launching a new satellite to product development through to organizational change.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

…Where did I lose you? Accessing the literacy demands of assessment

In this study we sought to find out how teachers could make assessment fairer for Indigenous students in learning mathematics, given the context of the high stakes of the National Assessment Program Literacy and Numeracy (NAPLAN). Today, teachers are experiencing the full range of demands from their own students who require individual attention, through to system level expectations of improved performances for all students. Many staff experience reform fatigue with limited time for critical reflection and a reduction in support for the use and the analysis of the overwhelming amount of data that has become available in recent years. Over the past three years we worked with teachers in seven schools to gradually refine our research focus to centre on how we might best support teachers in this demanding context with the important outcome of improved teaching and learning of mathematics with particular consideration of how to respond to the cultural needs of Indigenous (Aboriginal and Torres Strait Islander) students.

Jabberwocky : the complexities of mathematical English

Mathematical English is a unique language based on ordinary English, with the addition of highly stylised formal symbol systems. Some words have a redefined status. Mathematical English has its own lexicon, syntax, semantics and literature. It is more difficult to understand than ordinary English. Ability in basic interpersonal communication does not necessarily result in proficiency in the use of mathematical English. The complex nature of mathematical English may impact upon the ability of students to succeed in mathematical and numeracy assessment. This article presents a review of the literature about the complexities of mathematical English. It includes examples of more than fifty language features that have been shown to add to the challenge of interpreting mathematical texts. Awareness of the complexities of mathematical English is an essential skill needed by mathematics teachers when teaching and when designing assessment tasks.

Australia at the crossroads : a review of school science practical work

In Australia we are at a crossroad in science education. We have come from a long history of adopting international curricula, through to blending international and Australian developed materials, to the present which is a thoroughly unique Australian curriculum in science. This paper documents Australia’s journey over the past 200 years, as we prepare for the unveiling of our first truly Australian National Curriculum. One of the unique aspects of this curriculum is the emphasis on practical work and inquiry-based learning. This paper identifies seven forms of practical work currently used in Australian schools and the purposes aligned with each form by 138 pre-service and experienced in-service teachers. The paper explores the question “What does the impending national curriculum, with its emphasis on practical inquiry mean to the teachers now, are they ready?” The study suggests that practical work in Australian schools is multifaceted, and the teacher aligned purposes are dependent not only upon the age of the student, but also on the type of practical work being undertaken. It was found that most teachers are not ready to teach using inquiry-based pedagogy and cite lack of content knowledge, behaviour management, and lack of physical resources and availability of classroom space as key issues which will hinder their implementation of the inquiry component of Australia’s pending curriculum in science.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

'Going live' : establishing the creative attributes of the live multi-camera television professional

In my capacity as a television professional and teacher specialising in multi-camera live television production for over 40 years, I was drawn to the conclusion that opaque or inadequately formed understandings of how creativity applies to the field of live television, have impeded the development of pedagogies suitable to the teaching of live television in universities. In the pursuit of this hypothesis, the thesis shows that television degrees were born out of film studies degrees, where intellectual creativity was aligned to single camera production, and the 'creative roles' of producers, directors and scriptwriters. At the same time, multi-camera live television production was subsumed under the 'mass communication' banner, leading to an understanding that roles other than producer and director are simply technical, and bereft of creative intent or acumen. The thesis goes on to show that this attitude to other television production personnel, for example, the vision mixer, videotape operator and camera operator, relegates their roles to that of 'button pusher'. This has resulted in university teaching models with inappropriate resources and unsuitable teaching practices. As a result, the industry is struggling to find people with the skills to fill the demands of the multi-camera live television sector. In specific terms the central hypothesis is pursued through the following sequenced approach. Firstly, the thesis sets out to outline the problems, and traces the origins of the misconceptions that hold with the notion that intellectual creativity does not exist in live multi-camera television. Secondly, this more adequately conceptualised rendition, of the origins particular to the misconceptions of live television and creativity, is then anchored to the field of examination by presentation of the foundations of the roles involved in making live television programs, using multicamera production techniques. Thirdly, this more nuanced rendition of the field sets the stage for a thorough analysis of education and training in the industry, and teaching models at Australian universities. The findings clearly establish that the pedagogical models are aimed at single camera production, a position that deemphasises the creative aspects of multi-camera live television production. Informed by an examination of theories of learning, qualitative interviews, professional reflective practice and observations, the roles of four multi-camera live production crewmembers (camera operator, vision mixer, EVS/videotape operator and director's assistant), demonstrate the existence of intellectual creativity during live production. Finally, supported by the theories of learning, and the development and explication of a successful teaching model, a new approach to teaching students how to work in live television is proposed and substantiated.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Mathematics learning in prep

Most teachers recognise the importance of mathematics teaching and learning in early years but there is not consensus on how and when this learning should occur. Young-Loveridge (cited in de Vries, Thomas, and Warren, 2010) suggests that quality early mathematical experiences are a key determinant to later achievement.

Time-varying bispectral analysis of visually evoked multi-channel EEG

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

The impact of construction organisations’ learning capabilities on collaborative projects

Dynamic capability theory asserts that the learning capabilities of construction organisations influence the degree to which value-for-money (VfM) is achieved on collaborative projects. However, there has been little study conducted to verify this relationship. The evidence is particularly limited within the empirical context of infrastructure delivery in Australia. Primarily drawing on the theoretical perspectives of the resource-based view of the firm (e.g. Barney 1991), dynamic capabilities (e.g. Helfat et al. 2007), absorptive capacity (e.g. Lane et al. 2006) and knowledge management (e.g. Nonaka 1994), this paper conceptualises learning capability as a knowledge-based dynamic capability. Learning capability builds on the micro-foundations of high-order learning routines, which are deliberately developed by construction organisations for managing collaborative projects. Based on this conceptualisation of learning capability, an exploratory case study was conducted. The study investigated the operational and higher-order learning routines adopted by a project alliance team to successfully achieve VfM. The case study demonstrated that the learning routines of the alliance project were developed and modified by the continual joint learning activities of participant organisations. Project-level learning routines were found to significantly influence the development of organisational-level learning routines. In turn, the learning outcomes generated from the alliance project appeared to significantly influence the development of project management routines and contractual arrangements applied by the participant organisations in subsequent collaborative projects. The case study findings imply that the higher-order learning routines that underpin the learning capability of construction organisations have the potential to influence the VfM achieved on both current and future collaborative projects.

Community Partnerships for Fostering Student Interest and Engagement in STEM

The foundations of Science, Technology, Engineering and Mathematics (STEM) education begins in the early years of schooling when students encounter formal learning experiences primarily in mathematics and science. Politicians, economists and industrialists recognise the importance of STEM in society, and therefore a number of strategies have been implemented to foster interest. Similarly, most students see the importance of science and mathematics in their lives, but school science and mathematics is usually seen as irrelevant, particularly by students in developed countries. This paper reports on the establishment and implementation of partnerships with industry experts from one jurisdiction which have, over a decade, attempted to reconcile the interests of youth and the contemporary world of science. Four case studies are presented and qualitative findings analyzed in terms of program outcomes and student engagement. The key finding is that the formation of relationships and partnerships, in which students have high degree of autonomy and sense of responsibility, is paramount to positive dispositions towards STEM. Those features of successful partnerships are also discussed. The findings raise some hope that innovative schools and partnerships can foster innovation and connect youth with the real world.