Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Enhancing professional ethics : service-learning in teacher education

The ethical conduct of professionals has been the focus of increasing scrutiny over the past several decades as members of the public, the media, professional bodies, and legislative authorities have struggled to define ethical behaviour in times of governmental change, increasing internationalisation, globalised communications, threats of terrorism, and the challenges of developments in science and medicine (e.g., Demmke & Bossaert, 2004). National governments and transnational bodies have responded to these concerns about ethics and corruption through measures such as the United Nations Convention Against Corruption (United Nations Office on Drugs and Crime, 2004), Transparency International’s annual corruption index (2010) and Queensland’s Public Sector Ethics Act 1994 (Queensland Parliament 1994). Similarly, academic interest in ethics and its application across a range of domains(e.g., business, health care, social welfare, criminal justice, law, journalism, defence, environment, and media) has also increased. To illustrate, in 1993, a non-partisan, non-profit national umbrella organisation, the Australian Association for Professional and Applied Ethics, was formed following a conference concerned with the teaching of ethics (http://www.arts.unsw.edu.au./aapae/about_aapae/about_aapae.htm), while a recent review of the Excellence in Research for Australian rankings of national and international academic journals revealed that 16 journals related to ethics had received the top ratings of A* or A (Australian Research Council, 2009). In this chapter we examine professional ethics and argue, with specific reference to the context of pre-service teacher education, that Service-learning is one way of enhancing emerging professionals’ understanding of ethics.

Mentoring across the professions : some issues and challenges

Mentoring has been identified as a valuable learning activity for beginners and more experienced personnel across a range of professions. For example, education, nursing, medicine, law, accounting , and public administration are among those professions that have utilised mentoring programs as a way of socialising and developing the skills and competencies of new professionals. The definition of mentoring used in this paper comes from Hansford, Tennent, and Ehrich (2002, 2003) that describes mentoring as a process whereby a more experienced practitioner works with, supports, guides and provides professional development to a less experienced practitioner. Mentoring, then, is often used to develop novice or less experienced professionals at two important phases in their career: (i) during their initial university training; and (ii) after graduation from university. For example, within the field experience components of many university degrees in education, nursing, medicine, social work, and other human service programs, students are assigned workplace mentors who assist them in transferring important skills and knowledge learned at university into practical setting. For concentrated periods of time during their degree, pre-service teachers, pre-service nurses and medical students work in the field alongside a workplace mentor.

Introduction : bringing back theory

In a report in the New York Times about a public symposium on the future of theory held at University of Chicago in 2002, staff writer Emily Eakin suggests that theory appears to have taken a back seat to more pressing current affairs – the Bush Administration, Al Qaeda, Iraq. Further, she reports that the symposium’s panel of high-profile theorists and scholars, including Homi Bhabha, Stanley Fish, Fredric Jameson, seemed reticent to offer their views on what is often touted as the demise or irrelevance of theory. The symposium and other commentaries on the topic of theory have prompted the view that the ‘Golden Age of Theory’ has passed and we are now in a ‘Post-Theory Age’. Given these pronouncements, we need to ask – Does theory matter any longer? Is it time for the obituary? Or are reports of the death of theory greatly exaggerated? The question remains whether to mourn or celebrate the demise of theory, and whether the body has in fact breathed its last. The title of this Introduction – ‘Bringing back theory’ – suggests a resurrection, or perhaps a haunting, as if the funeral has passed and, like Banquo’s ghost, theory returns to unsettle or disturb the celebration. It also suggests an entreaty, or perhaps a return performance. Rather than settle on one meaning, one interpretation, we are happy for all possibilities to coexist. The coexistence of different theories, different approaches, different interpretations also reflects the state of literary and cultural studies generally and children’s literature criticism in particular. No single theory or viewpoint predominates or vies for hegemony. Yet, one further question lingers – what is theory?

Post-disaster housing reconstruction : challenges for community participation

The extant literature suggests that community participation is an important ingredient for the successful delivery of post-disaster housing reconstruction projects. Even though policy-makers, international funding bodies and non-governmental organisations broadly appreciate the value of community participation, post-disaster reconstruction practices systematically fail to follow, or align with, existing policy statements. Research into past experiences has led many authors to argue that post-disaster reconstruction is the least successful physically visible arena of international cooperation. Why is the principle of community participation not evident in the veracity of reconstructions already carried out on the ground? This paper discusses and develops the concepts of, and challenges to, community participation and the subsequent negative and positive effects on post-disaster reconstruction projects outcomes.

What aspects of the scoliosis correction are most important to the teenager who has keyhole scoliosis correction surgery? A prospective series of 100 patients

Introduction. Surgical treatment of scoliosis is assessed in the spine clinic by the surgeon making numerous measurements on X-Rays as well as the rib hump. But it is important to understand which of these measures correlate with self-reported improvements in patients’ quality of life following surgery. The objective of this study was to examine the relationship between patient satisfaction after thoracoscopic (keyhole) anterior scoliosis surgery and standard deformity correction measures using the Scoliosis Research Society (SRS) adolescent questionnaire. Methods. A series of 100 consecutive adolescent idiopathic scoliosis patients received a single anterior rod via a keyhole approach at the Mater Children’s Hospital, Brisbane. Patients completed SRS outcomes questionnaires before surgery and again at 24 months after surgery. Multiple regression and t-tests were used to investigate the relationship between SRS scores and deformity correction achieved after surgery. Results. There were 94 females and 6 males with a mean age of 16.1 years. The mean Cobb angle improved from 52º pre-operatively to 21º for the instrumented levels post-operatively (59% correction) and the mean rib hump improved from 16º to 8º (51% correction). The mean total SRS score for the cohort was 99.4/120 which indicated a high level of satisfaction with the results of their scoliosis surgery. None of the deformity related parameters in the multiple regressions were significant. However, the twenty patients with the smallest Cobb angles after surgery reported significantly higher SRS scores than the twenty patients with the largest Cobb angles after surgery, but there was no difference on the basis of rib hump correction. Discussion. Patients undergoing thoracoscopic (keyhole) anterior scoliosis correction report good SRS scores which are comparable to those in previous studies. We suggest that the absence of any statistically significant difference in SRS scores between patients with and without rod or screw complications is because these complications are not associated with any clinically significant loss of correction in our patient group. The Cobb angle after surgery was the only significant predictor of patient satisfaction when comparing subgroups of patients with the largest and smallest Cobb angles after surgery.

The measurement of applied forces during anterior single rod surgical correction of adolescent idiopathic scoliosis

INTRODUCTION. Following anterior thoracoscopic instrumentation and fusion for the treatment of thoracic AIS, implant related complications have been reported as high as 20.8%. Currently the magnitudes of the forces applied to the spine during anterior scoliosis surgery are unknown. The aim of this study was to measure the segmental compressive forces applied during anterior single rod instrumentation in a series of adolescent idiopathic scoliosis patients. METHODS. A force transducer was designed, constructed and retrofitted to a surgical cable compression tool, routinely used to apply segmental compression during anterior scoliosis correction. Transducer output was continuously logged during the compression of each spinal joint, the output at completion converted to an applied compression force using calibration data. The angle between adjacent vertebral body screws was also measured on intra-operative frontal plane fluoroscope images taken both before and after each joint compression. The difference in angle between the two images was calculated as an estimate for the achieved correction at each spinal joint. RESULTS. Force measurements were obtained for 15 scoliosis patients (Aged 11-19 years) with single thoracic curves (Cobb angles 47˚- 67˚). In total, 95 spinal joints were instrumented. The average force applied for a single joint was 540 N (± 229 N)ranging between 88 N and 1018 N. Experimental error in the force measurement, determined from transducer calibration was ± 43 N. A trend for higher forces applied at joints close to the apex of the scoliosis was observed. The average joint correction angle measured by fluoroscope imaging was 4.8˚ (±2.6˚, range 0˚-12.6˚). CONCLUSION. This study has quantified in-vivo, the intra-operative correction forces applied by the surgeon during anterior single rod instrumentation. This data provides a useful contribution towards an improved understanding of the biomechanics of scoliosis correction. In particular, this data will be used as input for developing patient-specific finite element simulations of scoliosis correction surgery.

Self-defence against terrorism in the post 9/11 world

In 1986 the then United States Secretary of State George Shultz asserted that: It is absurd to argue that international law prohibits us from capturing terrorists in international waters or airspace; from attacking them on the soil of other nations, even for the purpose of rescuing hostages; or from using force against states that support, train and harbor terrorists or guerrillas. At that time the United States’ claim of a right to use military force in self-defence against terrorism2 received little support from other states.3 The predominant view then was that terrorist attacks committed by private or non-state actors were a form of criminal activity to be combated through domestic and international criminal justice mechanisms. The notion that such terrorist acts should be treated as ‘armed attacks’ triggering a victim state’s right of self-defence was not accepted by the majority of states. To suggest, as Shultz had done, that a state not directly responsible for terrorist acts could have its territorial integrity violated by military action targeting terrorists located within that state, was a controversial proposition in 1986. However, some fifteen years later, when the United States and a coalition of allies launched a military campaign in Afghanistan following the 11 September 2001 (hereafter ‘9/11’) terrorist attacks, there was virtually unanimous international support for the use of force.

The last post? Tracking the Australasian to Aussie Post, 1864-2002

Aussie Post, the flagship of ocker Australiana, folded in January 2002. Post began life as the Australasian, a middlebrow magazine steeped in a nineteenth century civics of stable citizenship with a modicum of diversionary leisure. The transformation began when the Australasian became Australasian Post in 1946 under George Johnston's brief 15-week editorship. Johnston's idealistic vision of Post as a voice of post-war Australian modernity was soon overtaken by commercial imperatives as Post's identity wavered between its civic antecedents and a new low-brow populism, a niche it had finally settled into by the mid-1950s. This tension between staid civics and risqué populism shaped the magazine's long evolution into its final realisation of the pictorial general interest genre. This paper, based on a close examination of the magazines themselves, tracks Post's generic evolution and focuses on the struggle to redefine the magazine’s identity during the post-war period when the axis of Australian identity was reluctantly shifting from the staid traditions of Rule Britannia to the flashy modernity of Pax Americana.

Legal ethics in a post-Westphalian world : building the international rule of law and otehr tasks

The emergence of strong sovereign states after the Treaty of Westphalia turned two of the most cosmopolitan professions (law and arms) into two of the least cosmopolitan. Sovereign states determined the content of the law within their borders – including which, if any, ecclesiastical law was to be applied; what form of economic regulation was adopted; and what, if any, international law applied. Similarly, states sought to ensure that all military force was at their disposal in national armies. The erosion of sovereignty in a post-Westphalian world may significantly reverse these processes. The erosion of sovereignty is likely to have profound consequences for the legal profession and the ethics of how, and for what ends, it is practised. Lawyers have played a major role in the civilization of sovereign states through the articulation and institutionalisation of key governance values – starting with the rule of law. An increasingly global profession must take on similar tasks. The same could be said of the military. This essay will review the concept of an international rule of law and its relationship to domestic conceptions and outline the task of building the international rule of law and the role that lawyers can and should play in it.