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.

Synchronous learner support for music sequencing software

In the field of music technology there is a distinct focus on networking between spatially disparate locales to improve teaching and learning through real-time communication. This article proposes a new delivery model for learner support based on a review of technical and learning services, pilot research using remote desktops to teach music-sequencing software, and recent education research regarding professional development. A 24/7 delivery model using remote desktops, mobile devices and shared calendars offers a flexible real-time addition to the learner support services already on offer. Treating every user of the service as a potential expert, the model aims to deliver universal support situated in a personalized context, which will serve the technical and education requirements of teachers and learners.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Designing participation in agile ridesharing with mobile social software

Growing participation is a key challenge for the viability of sustainability initiatives, many of which require enactment at a local community level in order to be effective. This paper undertakes a review of technology assisted carpooling in order to understand the challenge of designing participation and consider how mobile social software and interface design can be brought to bear. It was found that while persuasive technology and social networking approaches have roles to play, critical factors in the design of carpooling are convenience, ease of use and fit with contingent circumstances, all of which require a use-centred approach to designing a technological system and building participation. Moreover, the reach of technology platform-based global approaches may be limited if they do not cater to local needs. An approach that focuses on iteratively designing technology to support and grow mobile social ridesharing networks in particular locales is proposed. The paper contributes an understanding of HCI approaches in the context of other designing participation approaches.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Getting Excited About Software Programming

Invited one hour presentation at Microsoft Tech Ed 2009 about getting students interested in games programming at QUT.

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Elicitator : an expert elicitation tool for regression in ecology

Expert elicitation is the process of retrieving and quantifying expert knowledge in a particular domain. Such information is of particular value when the empirical data is expensive, limited, or unreliable. This paper describes a new software tool, called Elicitator, which assists in quantifying expert knowledge in a form suitable for use as a prior model in Bayesian regression. Potential environmental domains for applying this elicitation tool include habitat modeling, assessing detectability or eradication, ecological condition assessments, risk analysis, and quantifying inputs to complex models of ecological processes. The tool has been developed to be user-friendly, extensible, and facilitate consistent and repeatable elicitation of expert knowledge across these various domains. We demonstrate its application to elicitation for logistic regression in a geographically based ecological context. The underlying statistical methodology is also novel, utilizing an indirect elicitation approach to target expert knowledge on a case-by-case basis. For several elicitation sites (or cases), experts are asked simply to quantify their estimated ecological response (e.g. probability of presence), and its range of plausible values, after inspecting (habitat) covariates via GIS.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Introducing a Business Process and Software Centric Approach for Enterprise System Teaching

To meet new challenges of Enterprise Systems that essentially go beyond the initial implementation, contemporary organizations seek employees with business process experts with software skills. Despite a healthy demand from the industry for such expertise, recent studies reveal that most Information Systems (IS) graduates are ill-equipped to meet the challenges of modern organizations. This paper shares insights and experiences from a course that is designed to provide a business process centric view of a market leading Enterprise System. The course, designed for both undergraduate and graduate students, uses two common business processes in a case study that employs both sequential and explorative exercises. Student feedback gained through two longitudinal surveys across two phases of the course demonstrates promising signs of the teaching approach.

An adaptable framework for the teaching and assessment of software development across year levels

Few frameworks exist for the teaching and assessment of programming subjects that are coherent and logical. Nor are they sufficiently generic and adaptable to be used outside the particular tertiary institutions in which they were developed. This paper presents the Teaching and Assessment of Software Development (TASD) frame-work. We describe its development and implementation at an Australian university and demonstrate, with examples, how it has been used, with supporting data. Extracts of criteria sheets (grading rubrics) for a variety of assessment tasks are included. The numerous advantages of this new framework are discussed with comparisons made to those reported in the published literature.