The African Institute for Mathematical Sciences

Its mission is to promote Mathematics and Science in Africa and to provide a focal point for Mathematics university training in Africa. It offers scholarships for up to 50 students to come and study for a period of nine months. Of the 50 students, about 15 positions are reserved for females. In the 2006/2007 intake there were over 250 applicants. The students are housed and fed and their return travel from their home town is fully funded. Lecturers also stay at AIMS and share their meals with the students, so that a rapport quickly develops. The students are away from their families and friends for nine months and are absolutely committed to the discipline of Mathematics. When they first arrive, some of them have little ability in English but since all tuition is in English they quickly learn. Some find the transitions difficult but they all support one another and at the end of their time their English skills are very good. The students do a series of subjects that last for about three weeks each, consisting of 30 contact hours, as well as a thesis/project. Each course has a number of assignments associated with it and these get evaluated. AIMS has seven or eight teaching assistants who help with the tutorials, marking, advice, and who are a vital component of AIMS.

A mathematical model for genetic regulation of the lactose operon

In this paper we construct a mathematical model for the genetic regulatory network of the lactose operon. This mathematical model contains transcription and translation of the lactose permease (LacY) and a reporter gene GFP. The probability of transcription of LacY is determined by 14 binding states out of all 50 possible binding states of the lactose operon based on the quasi-steady-state assumption for the binding reactions, while we calculate the probability of transcription for the reporter gene GFP based on 5 binding states out of 19 possible binding states because the binding site O2 is missing for this reporter gene. We have tested different mechanisms for the transport of thio-methylgalactoside (TMG) and the effect of different Hill coefficients on the simulated LacY expression levels. Using this mathematical model we have realized one of the experimental results with different LacY concentrations, which are induced by different concentrations of TMG.

Thinking feeling

In “Thinking Feeling” a camera zooms in and around an animated constellation of words. There are ten words, each repeated one hundred times. The individual words independently pulse and orbit an invisible nucleus. The slow movements of the words and camera are reinforced by an airy, synthesised soundtrack. Over time, various phrasal combinations form and dissolve on screen. A bit like forcing oneself to sleep, “Thinking Feeling” picks at that fine line between controlling and letting go of thoughts. It creates small mantric loops that slip in and out of focus, playing with the liminal zones between the conscious and unconscious, between language and sensation, between gripping and releasing, and between calm and irritation.

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.

Re-thinking how we plan to address technically complex problems : drawing on planning theory to guide practice in revision of land use plans in coastal high hazard zones

Queensland's new State Planning Policy for Coastal Protection, released in March and approved in April 2011 as part of the Queensland Coastal Plan, stipulates that local governments prepare and implement adaptation strategies for built up areas projected to be subject to coastal hazards between present day and 2100. Urban localities within the delineated coastal high hazard zone (as determined by models incorporating a 0.8 meter rise in sea level and a 10% increase in the maximum cyclone activity) will be required to re-evaluate their plans to accommodate growth, revising land use plans to minimise impacts of anticipated erosion and flooding on developed areas and infrastructure. While implementation of such strategies would aid in avoidance or minimisation of risk exposure, communities are likely to face significant challenges in such implementation, especially as development in Queensland is so intensely focussed upon its coasts with these new policies directing development away from highly desirable waterfront land. This paper examines models of planning theory to understand how we plan when faced with technically complex problems towards formulation of a framework for evaluating and improving practice.

Investigative thinking and creativity : an empirical study of police detectives in Norway

This paper makes distinctions among four investigative thinking styles of detectives: method style, challenge style, skill style, and risk style. Based on previous research, this study empirically tested, to what extent there are cumulative relationships among these thinking styles. Furthermore, this research studied relationships between investigative thinking styles and creativity in police investigations. Significant relationships were found between the extent of the challenge and risk styles and the extent of creativity.

Complex modelling in the primary/middle school years

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual (Katehi, Pearson, & Feder, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to significant changes in the forms of mathematical and scientific thinking that are required beyond the classroom. Modelling, in its various forms, can develop and broaden children’s mathematical and scientific thinking beyond the standard curriculum. This paper first considers future competencies in the mathematical sciences within an increasingly complex world. Next, consideration is given to interdisciplinary problem solving and models and modelling. Examples of complex, interdisciplinary modelling activities across grades are presented, with data modelling in 1st grade, model-eliciting in 4th grade, and engineering-based modelling in 7th-9th grades.

Risk-informed thinking in airports: the application of business continuity management in airport infrastructure

Airports worldwide represent key forms of critical infrastructure in addition to serving as nodes in the international aviation network. While the continued operation of airports is critical to the functioning of reliable air passenger and freight transportation, these infrastructure systems face a number of sources of disturbance that threaten their operational viability. Recent examples of high magnitude events include the eruption of Iceland’s Eyjafjallajokull volcano eruption (Folattau and Schofield 2010), the failure of multiple systems at the opening of Heathrow’s Terminal 5 (Brady and Davies 2010) and the Glasgow airport 2007 terrorist attack (Crichton 2008). While these newsworthy events do occur, a multitude of lower-level more common disturbances also have the potential to cause significant discontinuity to airport operations. Regional airports face a unique set of challenges, particularly in a nation like Australia where they serve to link otherwise remote and isolated communities to metropolitan hubs (Wheeler 2005), often without the resources and political attention received by larger capital city airports. This paper discusses conceptual relationships between Business Continuity Management (BCM) and High Reliability Theory, and proposes BCM as an appropriate risk-based management process to ensure continued airport operation in the face of uncertainty. In addition, it argues that that correctly implemented BCM can lead to highly reliable organisations. This is framed within the broader context of critical infrastructures and the need for adequate crisis management approaches suited to their unique requirements (Boin and McConnell 2007).

Seeing the outer suburbs : addressing the urban bias in creative place thinking

Seeing the outer suburbs: addressing the urban bias in creative place thinking, Regional Studies. This paper draws upon quantitative and qualitative research into Australian cities to question the assumption that creative industries workers inherently seek to cluster in inner-urban areas. It challenges this foundational assumption by combining a critical application of the location quotient analysis of major Australian cities with qualitative research drawn from interviews with creative workers based in suburban Melbourne and Brisbane. The findings provide analyses as to why many creative industries workers prefer to locate themselves in outer suburban places. There is also discussion of the implications of these findings for future work on the cultural geography and policies of creative industries.

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.

Design and design thinking in business and management education and development

Design and design thinking have been identified as making valuable contributions to business and management and the numbers of higher education programs that teach design thinking to business students, managers and executives are growing. However multiple definitions of design thinking and the range of perspectives have created some confusion about potential pathways. This paper examines notions of design and design thinking and uses these definitions to identify themes in higher educational programs. We present the findings from an initial exploratory investigation of design and design thinking in higher education business programs and define four distinct educational approaches around human centred innovation, integrative thinking, design management and design as strategy. Potential directions for management education programs are presented.

Multiple perspectives of design thinking in business education

Business education leaders have expressed interest in learning more about design and design thinking and their contributions to better problem framing, problem solving and to generating new solutions. Many business schools have engaged in educational programs with students from multiple disciplines, applying design thinking to business problems around workplace issues. This paper investigates a range of educational programs that teach design thinking to students in business education, at undergraduate and postgraduate levels around the world. We identify four patterns of program delivery that are emerging: human-centered design, integrative thinking, design management and design as strategy and discuss contributions from each. We expect that these four patterns of program delivery will continue and predict an increasing focus on programs around design as strategy in the near future.