Construction of multiplicative abstract schema for decimal-number numeration

This paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model.

Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Rejoinder to James Hamilton

Hamilton (2001) makes a number of comments on our paper (Harding and Pagan, 2002b). The objectives of this rejoinder are, firstly, to note the areas in which we agree; secondly, to define with greater clarity the areas in which we disagree; and, thirdly, to point to other papers, including a longer version of this response, where we have dealt with some of the issues that he raises. The core of our debate with him is whether one should use an algorithm with a specified set of rules for determining the turning points in economic activity or whether one should use a parametric model that features latent states. Hamilton begins his criticism by stating that there is a philosophical distinction between the two methods for dating cycles and concludes that the method we use “leaves vague and intuitive exactly what this algorithm is intended to measure”. Nothing is further from the truth. When seeking ways to decide on whether a turning point has occurred it is always useful to ask the question, what is a recession? Common usage suggests that it is a decline in the level of economic activity that lasts for some time. For this reason it has become standard to describe a recession as a decline in GDP that lasts for more than two quarters. Finding periods in which quarterly GDP declined for two periods is exactly what our approach does. What is vague about this?

Beyond charity : outlines of a jurisprudence for civil society

There is not a single, coherent, jurisprudence for civil society organisations. Pressure for a clearly enuciated body of law applying to the whole of this sector of society continues to increase. The rise of third sector scholarship, the retreat of the welfare state, the rediscovery of the concept of civil society and pressures to strengthen social capital have all contributed to an ongoing stream of inquiry into the laws that regulate and favour civil society organisations. There have been almost thirty inquiries over the last sixty years into the doctrine of charitable purpose in common law countries. Those inquiries have established that problems with the law applying to civil society organisations are rooted in the common law adopting a ‘technical’ definition of charitable purpose and the failure of this body of law to develop in response to societal changes. Even though it is now well recognised that problems with law reform stem from problems inherent in the doctrine of charitable purpose, statutory reforms have merely ‘bolted on’ additions to the flawed ‘technical’ definition. In this way the scope of operation of the law has been incrementally expanded to include a larger number of civil society organisations. This piecemeal approach continues the exclusion of most civil society organisations from the law of charities discourse, and fails to address the underlying jurisprudential problems. Comprehensive reform requires revisiting the foundational problems embedded in the doctrine of charitable purpose, being informed by recent scholarship, and a paradigm shift that extends the doctrine to include all civil society organisations. Scholarly inquiry into civil society organisations, particularly from within the discipline of neoclassical economics, has elucidated insights that can inform legal theory development. This theory development requires decoupling the two distinct functions performed by the doctrine of charitable purpose which are: setting the scope of regulation, and determining entitlement to favours, such as tax exemption. If the two different functions of the doctrine are considered separately in the light of theoretical insights from other disciplines, the architecture for a jurisprudence emerges that facilitates regulation, but does not necessarily favour all civil society organisations. Informed by that broader discourse it is argued that when determining the scope of regulation, civil society organisations are identified by reference to charitable purposes that are not technically defined. These charitable purposes are in essence purposes which are: Altruistic, for public Benefit, pursued without Coercion. These charitable puposes differentiate civil society organisations from organisations in the three other sectors namely; Business, which is manifest in lack of altruism; Government, which is characterised by coercion; and Family, which is characterised by benefits being private not public. When determining entitlement to favour, it is theorised that it is the extent or nature of the public benefit evident in the pursuit of a charitable purpose that justifies entitlement to favour. Entitlement to favour based on the extent of public benefit is the theoretically simpler – the greater the public benefit the greater the justification for favour. To be entitled to favour based on the nature of a purpose being charitable the purpose must fall within one of three categories developed from the first three heads of Pemsel’s case (the landmark categorisation case on taxation favour). The three categories proposed are: Dealing with Disadvantage, Encouraging Edification; and Facilitating Freedom. In this alternative paradigm a recast doctrine of charitable purpose underpins a jurisprudence for civil society in a way similar to the way contract underpins the jurisprudence for the business sector, the way that freedom from arbitrary coercion underpins the jurisprudence of the government sector and the way that equity within families underpins succession and family law jurisprudence for the family sector. This alternative architecture for the common law, developed from the doctrine of charitable purpose but inclusive of all civil society purposes, is argued to cover the field of the law applying to civil society organisations and warrants its own third space as a body of law between public law and private law in jurisprudence.

A constraints-led perspective to understanding skill acquisition and game play: A basis for integration of motor learning theory and physical education praxis?

Background: In order to design appropriate environments for performance and learning of movement skills, physical educators need a sound theoretical model of the learner and of processes of learning. In physical education, this type of modelling informs the organization of learning environments and effective and efficient use of practice time. An emerging theoretical framework in motor learning, relevant to physical education, advocates a constraints-led perspective for acquisition of movement skills and game play knowledge. This framework shows how physical educators could use task, performer and environmental constraints to channel acquisition of movement skills and decision making behaviours in learners. From this viewpoint, learners generate specific movement solutions to satisfy the unique combination of constraints imposed on them, a process which can be harnessed during physical education lessons. Purpose: In this paper the aim is to provide an overview of the motor learning approach emanating from the constraints-led perspective, and examine how it can substantiate a platform for a new pedagogical framework in physical education: nonlinear pedagogy. We aim to demonstrate that it is only through theoretically valid and objective empirical work of an applied nature that a conceptually sound nonlinear pedagogy model can continue to evolve and support research in physical education. We present some important implications for designing practices in games lessons, showing how a constraints-led perspective on motor learning could assist physical educators in understanding how to structure learning experiences for learners at different stages, with specific focus on understanding the design of games teaching programmes in physical education, using exemplars from Rugby Union and Cricket. Findings: Research evidence from recent studies examining movement models demonstrates that physical education teachers need a strong understanding of sport performance so that task constraints can be manipulated so that information-movement couplings are maintained in a learning environment that is representative of real performance situations. Physical educators should also understand that movement variability may not necessarily be detrimental to learning and could be an important phenomenon prior to the acquisition of a stable and functional movement pattern. We highlight how the nonlinear pedagogical approach is student-centred and empowers individuals to become active learners via a more hands-off approach to learning. Summary: A constraints-based perspective has the potential to provide physical educators with a framework for understanding how performer, task and environmental constraints shape each individual‟s physical education. Understanding the underlying neurobiological processes present in a constraints-led perspective to skill acquisition and game play can raise awareness of physical educators that teaching is a dynamic 'art' interwoven with the 'science' of motor learning theories.

The millennial adolescent

The Millennial Adolescent' offers contemporary, stimulating insights for those currently teaching as well as those preparing to teach. This book investigates the characteristics of Generation Y, using students own voices, generational theory and case studies. The text is structured around the principle that effective teachers need to know who they are teaching as well as what to teach, how to teach it, and how to assess the outcome. Using generational theory, 'The Millennial Adolescent' investigates the characteristics of Generation Y, or the Millennial Generation, and points out what all teachers need to know about working with this current generation of students who are described in a number of ways digital natives, team oriented, confident, multi-taskers, high achievers, and a generation unlike any other. The book contains well-known frameworks for developing understandings about adolescents, blended and contrasted with a contemporary socio-cultural construction of adolescence, set in our particular time, era and society. This book reflects the uniqueness of Australian contexts, while connecting with international trends and global patterns. Engaging and full of insights, this book is essential reading for all professionals dealing with adolescents.

Mobile learning, social learning

Understanding the future development of interaction design as it applies to learning and training scenarios is crucial to effective development of curriculum and appropriate application of social and mobile communication technologies. As Attewell & Saville-Smith have recognised (2004), the use of mobile communication devices for improved literacy and numeracy is a desirable prospect among young people who represent the average age of undergraduate students. Further, with the growing penetration of broadband internet access, the ubiquity of wireless access in educational locations, the rise of ultra-mobile portable computers and the proliferation of social software applications in educational contexts, there are a growing number of channels for facilitation of learning. Nevertheless, there has been insufficient consideration of the interaction design issues that affect the effective facilitation of such learning. This paper contends that there is a clear need to design mobile and social learning to accommodate the benefits of these diverse channels for interaction. Additionally, there is a need to implement suitable testing processes to ensure participants in mobile and social learning are contributing effectively and maximising their learning. Through the presentation of case studies in mobile and social learning, the paper attempts to demonstrate how considered interaction design techniques can improve the effectiveness of new learning channels.

Making the most of MiLK : harnessing the contemporary culture and interests of natural born cyborg

MiLK is a mobile learning kit that allows students and teachers to author their own place-based learning events using simple web and mobile technologies. We will demonstrate how MiLK has been used by a number of teachers in various contexts to connect students, curriculum and everyday environments. This workshop will introduce participants to the various MiLK tools and processes; including mapping, designing, playing and reviewing events, group journals, discussion forums, student profiles, and class profiles. We will focus on the role of place as a potential resource for curriculum design and delivery. The MiLK Team are looking for enthusiastic mobile technology champions to join us. No previous experience or training in this area is needed. This workshop is designed to be relevant to all KLAs. During this session teachers will have an opportunity to experiment with simple tools to create dynamic resources for their own classrooms.

Critical social theory and transformative learning : evidence in pre-service teachers' service-learning reflection logs

This paper reports on the opportunities for transformational learning experienced by a group of pre-service teachers who were engaged in service-learning as a pedagogical process with a focus on reflection. Critical social theory informed the design of the reflection process as it enabled a move away from knowledge transmission toward knowledge transformation. The structured reflection log was designed to illustrate the critical social theory expectations of quality learning that teach students to think critically: ideology critique and utopian critique. Butin's lenses and a reflection framework informed by the work of Bain, Ballantyne, Mills and Lester were used in the design of the service-learning reflection log. Reported data provide evidence of transformational learning and highlight how the students critique their world and imagine how they could contribute to a better world in their work as a beginning teacher.

Model round-trip engineering

In the quest for shorter time-to-market, higher quality and reduced cost, model-driven software development has emerged as a promising approach to software engineering. The central idea is to promote models to first-class citizens in the development process. Starting from a set of very abstract models in the early stage of the development, they are refined into more concrete models and finally, as a last step, into code. As early phases of development focus on different concepts compared to later stages, various modelling languages are employed to most accurately capture the concepts and relations under discussion. In light of this refinement process, translating between modelling languages becomes a time-consuming and error-prone necessity. This is remedied by model transformations providing support for reusing and automating recurring translation efforts. These transformations typically can only be used to translate a source model into a target model, but not vice versa. This poses a problem if the target model is subject to change. In this case the models get out of sync and therefore do not constitute a coherent description of the software system anymore, leading to erroneous results in later stages. This is a serious threat to the promised benefits of quality, cost-saving, and time-to-market. Therefore, providing a means to restore synchronisation after changes to models is crucial if the model-driven vision is to be realised. This process of reflecting changes made to a target model back to the source model is commonly known as Round-Trip Engineering (RTE). While there are a number of approaches to this problem, they impose restrictions on the nature of the model transformation. Typically, in order for a transformation to be reversed, for every change to the target model there must be exactly one change to the source model. While this makes synchronisation relatively “easy”, it is ill-suited for many practically relevant transformations as they do not have this one-to-one character. To overcome these issues and to provide a more general approach to RTE, this thesis puts forward an approach in two stages. First, a formal understanding of model synchronisation on the basis of non-injective transformations (where a number of different source models can correspond to the same target model) is established. Second, detailed techniques are devised that allow the implementation of this understanding of synchronisation. A formal underpinning for these techniques is drawn from abductive logic reasoning, which allows the inference of explanations from an observation in the context of a background theory. As non-injective transformations are the subject of this research, there might be a number of changes to the source model that all equally reflect a certain target model change. To help guide the procedure in finding “good” source changes, model metrics and heuristics are investigated. Combining abductive reasoning with best-first search and a “suitable” heuristic enables efficient computation of a number of “good” source changes. With this procedure Round-Trip Engineering of non-injective transformations can be supported.

Texting while driving : psychosocial influences on young people’s texting intentions and behaviour

Despite the dangers and illegality, there is a continued prevalence of texting while driving amongst young Australian drivers. The present study tested an extended theory of planned behaviour (TPB) to predict young drivers’ (17 to 24 years) intentions to [1] send and [2] read text messages while driving. Participants (N = 169 university students) completed measures of attitudes, subjective norm, perceived behavioural control, intentions, and the additional social influence measures of group norm and moral norm. One week later, participants reported on the number of texts sent and read while driving in the previous week. Attitude predicted intentions to both send and read texts while driving, and subjective norm and perceived behavioural control determined sending, but not reading, intentions. Further, intention, but not perceptions of control, predicted both texting behaviours 1 week later. In addition, both group norm and moral norm added predictive ability to the model. These findings provide support for the TPB in understanding students’ decisions to text while driving as well as the inclusion of additional normative influences within this context, suggesting that a multi-strategy approach is likely to be useful in attempts to reduce the incidence of these risky driving behaviours.

Holding and opportunity cost theory in a property development context

This paper focuses on the varying approaches and methodologies adopted when the calculation of holding costs is undertaken, focusing on greenfield development. Whilst acknowledging there may be some consistency in embracing first principles relating to holding cost theory, a review of the literature reveals considerable lack of uniformity in this regard. There is even less clarity in quantitative determination, especially in Australia where there has been only limited empirical analysis undertaken. Despite a growing quantum of research undertaken in relation to various elements connected with housing affordability, the matter of holding costs has not been well addressed regardless of its part in the highly prioritised Australian Government’s housing research agenda. The end result has been a modicum of qualitative commentary relating to holding costs. There have been few attempts at finer-tuned analysis that exposes a quantified level of holding cost calculated with underlying rigour. Holding costs can take many forms, but they inevitably involve the computation of “carrying costs” of an initial outlay that has yet to fully realise its ultimate yield. Although sometimes considered a “hidden” cost, it is submitted that holding costs prospectively represent a major determinate of value. If this is the case, then considered in the context of housing affordability, it is therefore potentially pervasive.

The mystery of polygamy

The economic literature on marriage identifies a number of benefits of marriage and discusses mechanisms that cause societies to prefer certain marital structures such as polygamy or monogamy. In principle, however, these benefits and mechanisms might lead societies towards polyandry and even cenogamy. The rareness of polyandry and the absence of cenogamy, however, clearly indicate that important aspects of marriage are omitted. This paper argues that the reproductive nature of marital arrangements must be taken into account when analyzing the foundations of marriage. Monogamy always achieves efficient parental investments in offspring. For polygamous arrangements this might be often true. It fails, however, in polyandry because paternity cannot be established with certainty. Cenogamy is shown to be an unstable arrangement.