Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

Australasian horror special issue editorial : putting Australian and New Zealand horror movies on the map of cinema studies

This Australasian horror special issue is an important step forward in putting Australian and New Zealand horror movies on the map of film and cinema studies as a subject worthy of intellectual debate. The journal issue is the first devoted solely to the academic discussion of Australasian horror movies. While an Australian horror movie tradition has produced numerous titles since the 1970s achieving commercial success and cult popularity worldwide, the horror genre is largely missing from Australian film history. While there have been occasional essays on standout titles such as Wolf Creek (Mclean, 2005), an increasing number of articles on ‘Ozploitation’ movies, and irregular discussion about Australian Gothic, overall the nature of Australian horror as a genre remains poorly understood. In terms of New Zealand, debate has tended to revolve around ‘Kiwi Gothic’ and of course Peter Jackon’s early splatter films, rather than Kiwi horror as a specific filmmaking tradition.

Complexity and learning behaviors in product innovation

Successful product innovation and the ability of companies to continuously improve their innovation processes are rapidly becoming essential requirements for competitive advantage and long-term growth in both manufacturing and service industries. It is now recognized that companies must develop innovation capabilities across all stages of the product development, manufacture, and distribution cycle. These Continuous Product Innovation (CPI) capabilities are closely associated with a company’s knowledge management systems and processes. Companies must develop mechanisms to continuously improve these capabilities over time. Using results of an international survey on CPI practices, sets of companies are identified by similarities in specific contingencies related to their complexity of product, process, technological, and customer interface. Differences between the learning behaviors found present in the company groups and in the levers used to develop and support these behaviors are identified and discussed. This paper also discusses appropriate mechanisms for firms with similar complexities, and some approaches they can use to improve their organizational learning and product innovation.

Managing process model complexity via abstract syntax modifications

As a result of the growing adoption of Business Process Management (BPM) technology different stakeholders need to understand and agree upon the process models that are used to configure BPM systems. However, BPM users have problems dealing with the complexity of such models. Therefore, the challenge is to improve the comprehension of process models. While a substantial amount of literature is devoted to this topic, there is no overview of the various mechanisms that exist to deal with managing complexity in (large) process models. It is thus hard to obtain comparative insight into the degree of support offered for various complexity reducing mechanisms by state-of-the-art languages and tools. This paper focuses on complexity reduction mechanisms that affect the abstract syntax of a process model, i.e. the structure of a process model. These mechanisms are captured as patterns, so that they can be described in their most general form and in a language- and tool-independent manner. The paper concludes with a comparative overview of the degree of support for these patterns offered by state-of-the-art languages and language implementations.

Introduction and Epilogue to Special Issue: Re-conceiving the artful in management development and education

The editorial focus of this issue is on artful, aesthetic and artistic endeavours in management. Being artful is not about arts-based quick fixes. In the context of this Special Issue, to be artful is to transform self through profound learning experiences that expand human consciousness, often facilitated by artistic processes. In management education and development this suggests a shift from instrumental management towards a paradigm of artful creation. Why the arts and artfulness? And why now? In what ways can the arts inform, inspire and leverage management development and education?

On the Classification of Recursive Languages

A one-sided classifier for a given class of languages converges to 1 on every language from the class and outputs 0 infinitely often on languages outside the class. A two-sided classifier, on the other hand, converges to 1 on languages from the class and converges to 0 on languages outside the class. The present paper investigates one-sided and two-sided classification for classes of recursive languages. Theorems are presented that help assess the classifiability of natural classes. The relationships of classification to inductive learning theory and to structural complexity theory in terms of Turing degrees are studied. Furthermore, the special case of classification from only positive data is also investigated.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

Multi-linear strategies for (re)presenting the complexity of young people in research

Within the current climate of unpredictability and constant change, young people at school are faced with a multitude of choices and contradictory influences. In this article, I argue that (re)presentations of young people in youth research need to reflect the complexity and multiplicity of their lives and changing priorities, and I attempt to (re)present a small group of young people in this particular milieu. I illustrate some of the competing influences in their lives, and I outline some specific strategies that are useful for (re)presenting these contextual worlds. The strategies I advocate disrupt the homogenous representations of ‘youth’ as a developmental phase and instead reflect the diverse spheres of influence which shape their subjectivities and practices.

Unraveling the complexity of driving while intoxicated: a study into the prevalence of psychiatric and substance abuse comorbidity

Objective Research is beginning to provide an indication of the co-occurring substance abuse and mental health needs for the driving under the influence (DUI) population. This study aimed to examine the extent of such psychiatric problems among a large sample size of DUI offenders entering treatment in Texas. Methods This is a study of 36,373 past year DUI clients and 308,714 non-past year DUI clients admitted to Texas treatment programs between 2005 and 2008. Data were obtained from the State's administrative dataset. Results Analysis indicated that non-past year DUI clients were more likely to present with more severe illicit substance use problems, while past year DUI clients were more likely to have a primary problem with alcohol. Nevertheless, a cannabis use problem was also found to be significantly associated with DUI recidivism in the last year. In regards to mental health status, a major finding was that depression was the most common psychiatric condition reported by DUI clients, including those with more than one DUI offence in the past year. This cohort also reported elevated levels of Bipolar Disorder compared to the general population, and such a diagnosis was also associated with an increased likelihood of not completing treatment. Additionally, female clients were more likely to be diagnosed with mental health problems than males, as well as more likely to be placed on medications at admission and more likely to have problems with methamphetamine, cocaine, and opiates. Conclusions DUI offenders are at an increased risk of experiencing comorbid psychiatric disorders, and thus, corresponding treatment programs need to cater for a range of mental health concerns that are likely to affect recidivism rates.