Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Influencing pre-service teachers, skills and attitudes towards diversity. Is DOL the Answer?

Abstract: This paper reports on a preliminary investigation into the success of an undergraduate course, in helping preservice teachers at a regional university develop the skills and attitudes necessary to design inclusive learning environments that cater for, and celebrate, difference. The study is particularly relevant given recommendations by the Education Queensland Ministerial Taskforce (Queensland Government, 2004) that all pre-service teacher education programs must ensure that inclusive education is a pervasive theme. The paper starts by providing an overview of inclusive contexts and a rationale for inclusive education including critical elements. This leads into an overview of the undergraduate course EDED11400 Managing Diversity and discussion, based on feedback from the teaching team, on the capacity for the course to help pre-service teachers develop inclusive curriculum and pedagogical practices. The pedagogical framework Dimensions of Learning* is then discussed, with consideration given to whether this framework with its focus on critical thinking and habits of mind, might improve future learning outcomes in the course EDED11400 Managing Diversity. (*Dimensions of Learning is a pedagogical framework designed to teach thinking skills (Marzano et al., 1988). It explores five types of thinking represented in the framework by five dimensions of learning.)

Clinical strategies for the alleviation of contractures from a predictive mathematical model of dermal repair

Hypertrophic scars arise when there is an overproduction of collagen during wound healing. These are often associated with poor regulation of the rate of programmed cell death(apoptosis) of the cells synthesizing the collagen or by an exuberant inflammatory response that prolongs collagen production and increases wound contraction. Severe contractures that occur, for example, after a deep burn can cause loss of function especially if the wound is over a joint such as the elbow or knee. Recently, we have developed a morphoelastic mathematical model for dermal repair that incorporates the chemical, cellular and mechanical aspects of dermal wound healing. Using this model, we examine pathological scarring in dermal repair by first assuming a smaller than usual apoptotic rate for myofibroblasts, and then considering a prolonged inflammatory response, in an attempt to determine a possible optimal intervention strategy to promote normal repair, or terminate the fibrotic scarring response. Our model predicts that in both cases it is best to apply the intervention strategy early in the wound healing response. Further, the earlier an intervention is made, the less aggressive the intervention required. Finally, if intervention is conducted at a late time during healing, a significant intervention is required; however, there is a threshold concentration of the drug or therapy applied, above which minimal further improvement to wound repair is obtained.

Developing and enhancing independent learning skills : using video tutorials as a means of helping students help themselves

Purpose – The purpose of this paper is to examine the use of short video tutorials in a post-graduate accounting subject, as a means of helping students develop and enhance independent learning skills. Design/methodology/approach – In total, five short (approximately five to 10 minutes) video tutorials were introduced in an effort to shift the reliance for learning from the lecturer to the student. Data on students’ usage of online video tutorials, and comments by students in university questionnaires were collated over three semesters from 2008 to 2009. Interviews with students were then conducted in late 2009 to more comprehensively evaluate the use and perceived benefits of video tutorials. Findings – Findings reveal preliminary but positive outcomes in terms of both more efficient and effective teaching and learning. Research limitations/implications – The shift towards more independent learning through the use of video tutorials has positive implications for educators, employers, and professional accounting bodies; each of whom has identified the need for this skill in accounting graduates. Practical implications – The use of video tutorials has the potential for more rewarding teaching and more effective learning. Originality/value – This study is one of the first to examine the use and benefits of video tutorials as a means of developing independent learning skills in accountancy students – addressing a key concern within the profession.

Do balanced skills help nascent entrepreneurs to make progress in the venture creation process?

We apply Lazear’s jack-of-all-trades theory to investigate the effect of nascent entrepreneurs´ balanced skill set across various functional areas on the performance of nascent projects. Analyzing longitudinal data on innovative nascent projects, we find that nascent entrepreneurs with a more balanced skill set are more successful in that they progress faster in the venture creation process.

Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

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.

Balanced skills among nascent entrepreneurs

This paper examines the effects and origins of balanced skills among nascent entrepreneurs. In a first step we apply Lazear’s jack-of-all-trades theory to investigate performance effects of a balanced skill set. Second, we investigate potential sources of balanced skills, thereby testing the investment hypothesis against the endowment hypothesis. Analyzing data on high-potential nascent projects, we find support for the notion that balanced skills are important for making progress in the venture creation process. Regarding the origins of balanced skills, the data support both hypotheses. In line with the investment hypothesis an early interest in an entrepreneurial career, prior managerial and entrepreneurial experience are significantly related with a more balanced skill set. Supporting the endowment hypothesis, an entrepreneurial personality profile indicating entrepreneurial talent is correlated with a balanced skill set. Our results thus hint at the need for theories on the origins of a balanced skill set that integrate both views.

Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

Alternatives to the behavioural technicist approaches to study skills

The content and approach of study skills courses are critiqued and alternatives are suggested. It is proposed that an approach providing students with knowledge about the cognitive processes involved in mastering complex material would make the study skills teacher an agent of social change aiming for the enlightenment and emancipation of students and lecturers.

ACE research vignette 016 : balanced skills - effects and origins

This series of research vignettes is aimed at sharing current and interesting research findings from our team of international Entrepreneurship researchers. In this vignette, post-doctoral research fellow Dr Michael Stuetzer considers the effects and origins of balanced skills.

Creativity in policing: building the necessary skills to solve complex and protracted investigations

Despite an increased focus on proactive policing in recent years, criminal investigation is still perhaps the most important task of any law enforcement agency. As a result, the skills required to carry out a successful investigation or to be an ‘effective detective’ have been subjected to much attention and debate (Smith and Flanagan, 2000; Dean, 2000; Fahsing and Gottschalk, 2008:652). Stelfox (2008:303) states that “The service’s capacity to carry out investigations comprises almost entirely the expertise of investigators.” In this respect, Dean (2000) highlighted the need to profile criminal investigators in order to promote further understanding of the cognitive approaches they take to the process of criminal investigation. As a result of his research, Dean (2000) produced a theoretical framework of criminal investigation, which included four disparate cognitive or ‘thinking styles’. These styles were the ‘Method’, ‘Challenge’, ‘Skill’ and ‘Risk’. While the Method and Challenge styles deal with adherence to Standard Operating Procedures (SOPs) and the internal ‘drive’ that keeps an investigator going, the Skill and Risk styles both tap on the concept of creativity in policing. It is these two latter styles that provide the focus for this paper. This paper presents a brief discussion on Dean’s (2000) Skill and Risk styles before giving an overview of the broader literature on creativity in policing. The potential benefits of a creative approach as well as some hurdles which need to be overcome when proposing the integration of creativity within the policing sector are then discussed. Finally, the paper concludes by proposing further research into Dean’s (2000) skill and risk styles and also by stressing the need for significant changes to the structure and approach of the traditional policing organisation before creativity in policing is given the status it deserves.

Evaluation of the skills for preventing injury in youth program : impact on health risk behaviors, injury and school connectedness

Injury is the leading cause of death among young people, and involvement in health risk behaviors, such as alcohol use and transport-related risks, is related to increased risk for injury. Effective health promotion programs for adolescents focus on multiple levels, including relationships with peers and parents, student knowledge, behavior and attitudes, and school-level factors such as school connectedness. This study describes the pilot evaluation of a comprehensive, multi-level injury prevention program for 13-14 year old adolescents, targeting change in injury associated with transport and alcohol risks. The program, called Skills for Preventing Injury in Youth (SPIY), incorporates two primary elements: an 8-week, teacher delivered attitude and behavior change curriculum with peer protection and first aid messages; and professional development for program teachers focusing on strategies to increase students’ connectedness to school. Five Australian high schools were recruited for the pilot evaluation research, with three being assigned to receive intervention components and two assigned as curriculum-as-usual controls. In the intervention schools, 118 Year 8 students participated in surveys at baseline, with 105 completing surveys at follow up, six months following the intervention. In the control schools, 196 Year 8 students completed surveys at baseline and 207 at follow up. Survey measures included self-reported injury, risk taking behavior and school connectedness. Results showed that students in the control schools were significantly more likely to report riding bikes without helmets, riding with dangerous drivers, having driven cars on the road, and using alcohol six months after the program, while the intervention group showed no such increase in these behaviors. Additionally, students in the control schools were significantly more likely to report having had pedestrian-related injuries at follow up than they were at the baseline measurement, while intervention school students showed no change. There was also a trend observed in terms of a decrease in bicycle related injuries among intervention school students, compared with a slight increasing trend in bicycle injuries among control students. Overall, scores on the school connectedness scale decreased significantly from baseline to follow up for both intervention and control students, however measurement limitations may have impacted on results relating to students’ connectedness. Overall, the SPIY program has shown promising results in regards to prevention of students’ health risk behavior and injuries. Evidence suggests that the curriculum component was important; however there was limited evidence to suggest that teacher training in school connectedness strategies contributed to these promising results. While school connectedness may be an important factor to target in risk and injury prevention programs, programs may need to incorporate whole-of-school strategies or target a broader range of teachers than were selected for the current research.