Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

Automated proof for formal indistinguishability and its applications

Bana et al. proposed the relation formal indistinguishability (FIR), i.e. an equivalence between two terms built from an abstract algebra. Later Ene et al. extended it to cover active adversaries and random oracles. This notion enables a framework to verify computational indistinguishability while still offering the simplicity and formality of symbolic methods. We are in the process of making an automated tool for checking FIR between two terms. First, we extend the work by Ene et al. further, by covering ordered sorts and simplifying the way to cope with random oracles. Second, we investigate the possibility of combining algebras together, since it makes the tool scalable and able to cover a wide class of cryptographic schemes. Specially, we show that the combined algebra is still computationally sound, as long as each algebra is sound. Third, we design some proving strategies and implement the tool. Basically, the strategies allow us to find a sequence of intermediate terms, which are formally indistinguishable, between two given terms. FIR between the two given terms is then guaranteed by the transitivity of FIR. Finally, we show applications of the work, e.g. on key exchanges and encryption schemes. In the future, the tool should be extended easily to cover many schemes. This work continues previous research of ours on use of compilers to aid in automated proofs for key exchange.

Exploring the role of the governing body (board) in information technology governance : a study of Australian universities

In this thesis, I advance the understanding of information technology (IT) governance research and corporate governance research by considering the question “How do boards govern IT?” The importance of IT to business has increased over the last decade, but there has been little academic research which has focused on boards and their role in the governance of IT (Van Grembergen, De Haes and Guldentops, 2004). Most of the research on information technology governance (ITG) has focused on advancing the understanding and measurement of the components of the ITG model (Buckby, Best & Stewart, 2008; Wilkin & Chenhall, 2010), a model recommended by the IT Governance Institute (2003) as ‘best practice’ for boards to use in governing IT. IT governance is considered to be the responsibility of the board and is said to form an important subset of an organisation’s corporate governance processes (Borth & Bradley, 2008). Boards need to govern IT as a result of the large capital investment in IT resources and high dependency on IT by organisations. Van Grembergen, De Haes and Guldentops (2004) and De Haes & Van Grembergen (2009) indicate that corporate governance matters are not able to be effectively discharged unless IT is being governed properly, and call for further specific research on the role of the board in ITG. Researchers also indicate that the link between corporate governance and IT governance has been neglected (Borth & Bradley, 2008; Musson & Jordan, 2005; Bhattacharjya & Chang, 2008). This thesis will address this gap in the ITG literature by providing the bridge between the ITG and corporate governance literatures. My thesis uses a critical realist epistemology and a mixed method approach to gather insights into my research question. In the first phase of my research I develop a survey instrument to assess whether boards consider the components of the ITG model in governing IT. The results of this first study indicated that directors do not conceptualise their role in governing IT using the elements of the ITG model. Thus, I moved to focus on whether prominent corporate governance theories might elucidate how boards govern IT. In the second phase of the research, I used a qualitative inductive case based study to assess whether agency, stewardship and resource dependence theories explain how boards govern IT in Australian universities. As the first in-depth study of university IT governance processes, my research contributes to the ITG research field by revealing that Australian university board governance of IT is characterized by a combination of agency theory and stewardship theory behaviours and processes. The study also identified strong links between a university’s IT structure and evidence of agency and stewardship theories. This link provides insight into the structures element of the emerging enterprise governance of IT framework (Van Grembergen, De Haes & Guldentops, 2004; De Haes & Van Grembergen, 2009; Van Grembergen & De Haes, 2009b; Ko & Fink, 2010). My research makes an important contribution to governance research by identifying a key link between corporate and ITG literatures and providing insight into board IT governance processes. The research conducted in my thesis should encourage future researchers to continue to explore the links between corporate and IT governance research.

Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Comment

The support vector machine (SVM) has played an important role in bringing certain themes to the fore in computationally oriented statistics. However, it is important to place the SVM in context as but one member of a class of closely related algorithms for nonlinear classification. As we discuss, several of the “open problems” identified by the authors have in fact been the subject of a significant literature, a literature that may have been missed because it has been aimed not only at the SVM but at a broader family of algorithms. Keeping the broader class of algorithms in mind also helps to make clear that the SVM involves certain specific algorithmic choices, some of which have favorable consequences and others of which have unfavorable consequences—both in theory and in practice. The broader context helps to clarify the ties of the SVM to the surrounding statistical literature.

Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

The contribution of leadership attributes to large scale, complex project success

Mismanagement of large-scale, complex projects has resulted in spectacular failures, cost overruns, time blowouts, and stakeholder dissatisfaction. We focus discussion on the interaction of key management and leadership attributes which facilitate leaders’ adaptive behaviors. These behaviors should in turn influence adaptive team member behavior, stakeholder engagement and successful project outcomes, outputs and impacts. An understanding of this type of management will benefit from a perspective based in managerial and organizational cognition. The research question we explore is whether successful leaders of large-scale complex projects have an internal process leading to a display of administrative, adaptive, and enabling behaviors that foster adaptive processes and enabling behaviors within their teams and with external stakeholders. At the core of the model we propose interactions of key attributes, namely cognitive flexibility, affect, and emotional intelligence. The result of these cognitive-affective attribute interactions is leadership leading to enhanced likelihood of complex project success.

Music selection using a touch screen interface : effect of auditory and visual feedback on driving and usability

This study aimed to examine the effects on driving, usability and subjective workload of performing music selection tasks using a touch screen interface. Additionally, to explore whether the provision of visual and/or auditory feedback offers any performance and usability benefits. Thirty participants performed music selection tasks with a touch screen interface while driving. The interface provided four forms of feedback: no feedback, auditory feedback, visual feedback, and a combination of auditory and visual feedback. Performance on the music selection tasks significantly increased subjective workload and degraded performance on a range of driving measures including lane keeping variation and number of lane excursions. The provision of any form of feedback on the touch screen interface did not significantly affect driving performance, usability or subjective workload, but was preferred by users over no feedback. Overall, the results suggest that touch screens may not be a suitable input device for navigating scrollable lists.

Understanding user experience of mobile video : framework, measurement, and optimization

Since users have become the focus of product/service design in last decade, the term User eXperience (UX) has been frequently used in the field of Human-Computer-Interaction (HCI). Research on UX facilitates a better understanding of the various aspects of the user’s interaction with the product or service. Mobile video, as a new and promising service and research field, has attracted great attention. Due to the significance of UX in the success of mobile video (Jordan, 2002), many researchers have centered on this area, examining users’ expectations, motivations, requirements, and usage context. As a result, many influencing factors have been explored (Buchinger, Kriglstein, Brandt & Hlavacs, 2011; Buchinger, Kriglstein & Hlavacs, 2009). However, a general framework for specific mobile video service is lacking for structuring such a great number of factors. To measure user experience of multimedia services such as mobile video, quality of experience (QoE) has recently become a prominent concept. In contrast to the traditionally used concept quality of service (QoS), QoE not only involves objectively measuring the delivered service but also takes into account user’s needs and desires when using the service, emphasizing the user’s overall acceptability on the service. Many QoE metrics are able to estimate the user perceived quality or acceptability of mobile video, but may be not enough accurate for the overall UX prediction due to the complexity of UX. Only a few frameworks of QoE have addressed more aspects of UX for mobile multimedia applications but need be transformed into practical measures. The challenge of optimizing UX remains adaptations to the resource constrains (e.g., network conditions, mobile device capabilities, and heterogeneous usage contexts) as well as meeting complicated user requirements (e.g., usage purposes and personal preferences). In this chapter, we investigate the existing important UX frameworks, compare their similarities and discuss some important features that fit in the mobile video service. Based on the previous research, we propose a simple UX framework for mobile video application by mapping a variety of influencing factors of UX upon a typical mobile video delivery system. Each component and its factors are explored with comprehensive literature reviews. The proposed framework may benefit in user-centred design of mobile video through taking a complete consideration of UX influences and in improvement of mobile videoservice quality by adjusting the values of certain factors to produce a positive user experience. It may also facilitate relative research in the way of locating important issues to study, clarifying research scopes, and setting up proper study procedures. We then review a great deal of research on UX measurement, including QoE metrics and QoE frameworks of mobile multimedia. Finally, we discuss how to achieve an optimal quality of user experience by focusing on the issues of various aspects of UX of mobile video. In the conclusion, we suggest some open issues for future study.