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.

Prognostic modelling options for remaining useful life estimation by industry

Over recent years a significant amount of research has been undertaken to develop prognostic models that can be used to predict the remaining useful life of engineering assets. Implementations by industry have only had limited success. By design, models are subject to specific assumptions and approximations, some of which are mathematical, while others relate to practical implementation issues such as the amount of data required to validate and verify a proposed model. Therefore, appropriate model selection for successful practical implementation requires not only a mathematical understanding of each model type, but also an appreciation of how a particular business intends to utilise a model and its outputs. This paper discusses business issues that need to be considered when selecting an appropriate modelling approach for trial. It also presents classification tables and process flow diagrams to assist industry and research personnel select appropriate prognostic models for predicting the remaining useful life of engineering assets within their specific business environment. The paper then explores the strengths and weaknesses of the main prognostics model classes to establish what makes them better suited to certain applications than to others and summarises how each have been applied to engineering prognostics. Consequently, this paper should provide a starting point for young researchers first considering options for remaining useful life prediction. The models described in this paper are Knowledge-based (expert and fuzzy), Life expectancy (stochastic and statistical), Artificial Neural Networks, and Physical models.

Porous zirconia scaffold modified with mesoporous bioglass coating

Porous yttria-stabilized zirconia (YSZ) has been regarded as a potential candidate for bone substitute as its high mechanical strength. However, porous YSZ bodies are biologically inert to bone tissue. It is therefore necessary to introduce bioactive coatings onto the walls of the porous structures to enhance the bioactivity. In this study, the porous zirconia scaffolds were prepared by infiltration of Acrylonitrile Butadiene Styrene (ABS) scaffolds with 3 mol% yttria stabilized zirconia slurry. After sintering, a method of sol-gel dip coating was involved to make coating layer of mesoporous bioglass (MBGs). The porous zirconia without the coating had high porosities of 60.1% to 63.8%, and most macropores were interconnected with pore sizes of 0.5-0.8mm. The porous zirconia had compressive strengths of 9.07-9.90MPa. Moreover, the average coating thickness was about 7μm. There is no significant change of compressive strength for the porous zirconia with mesoporous biogalss coating. The bone marrow stromal cell (BMSC) proliferation test showed both uncoated and coated zirconia scaffolds have good biocompatibility. The scanning electron microscope (SEM) micrographs and the compositional analysis graphs demonstrated that after testing in the simulated body fluid (SBF) for 7 days, the apatite formation occurred on the coating surface. Thus, porous zirconia-based ceramics were modified with bioactive coating of mesoporous bioglass for potential biomedical applications.

A vibrational spectroscopic study of the mixed anion mineral sanjuanite Al2(PO4)(SO4)(OH)•9H2O

The mineral sanjuanite Al2(PO4)(SO4)(OH)•9H2O has been characterised by Raman spectroscopy complimented by infrared spectroscopy. The mineral is characterised by an intense Raman band at 984 cm-1, assigned to the (PO4)3- ν1 symmetric stretching mode. A shoulder band at 1037 cm-1 is attributed to the (SO4)2- ν1 symmetric stretching mode. Two Raman bands observed at 1102 and 1148 cm-1 are assigned to (PO4)3- and (SO4)2- ν3 antisymmetric stretching modes. Multiple bands provide evidence for the reduction in symmetry of both anions. This concept is supported by the multiple sulphate and phosphate bending modes. Raman spectroscopy shows that there are more than one non-equivalent water molecules in the sanjuanite structure. There is evidence that structural disorder exists, shown by the complex set of overlapping bands in the Raman and infrared spectra. At least two types of water are identified with different hydrogen bond strengths. The involvement of water in the sanjuanite structure is essential for the mineral stability.

Raman spectroscopic study of the minerals diadochite and destinezite Fe3+2(PO4,SO4)2(OH)•6H2O – implications for soil science

The two minerals diadochite and destinezite of formula Fe2(PO4,SO4)2(OH)•6H2O have been characterised by Raman spectroscopy and complimented with infrared spectroscopy. These two minerals are both found in soils and are identical except for their morphology. Diadochite is amorphous whereas destinezite is highly crystalline. The spectra of diadochite are broad and ill-defined, whereas the spectra of destinezite are intense and well defined. Bands are assigned to phosphate and sulphate stretching and bending modes. Two symmetric stretching modes for both the phosphate and sulphate symmetric stretching modes support the concept of non-equivalent phosphate and sulphate units in the mineral structure. Multiple water bending and stretching modes imply that non-equivalent water molecules in the structure exist with different hydrogen bond strengths.

From Deep North to international governance exemplar : Fitzgerald's impact on the international anti-corruption movement

In pre-Fitzgerald Queensland, the existence of corruption was widely known but its extent and modes of operation were not fully evident. The Fitzgerald Report identified the need for reform of the structure, procedures and efficiency in public administration in Queensland. What was most striking in the Queensland reform process was that a new model for combatting corruption had been developed. Rather than rely upon a single law and a single institution, existing institutions were strengthened and new institutions were introduced to create a set of mutually supporting and mutually checking institutions, agencies and laws that jointly sought to improve governmental standards and combat corruption. Some of the reforms were either unique to Queensland or very rare. One of the strengths of this approach was that it avoided creating a single over-arching institution to fight corruption. There are many powerful opponents of reform. Influential institutions and individuals resist any interference with their privileges. In order to cause a mass exodus from an entrenched corruption system, a seminal event or defining process is needed to alter expectations and incentives that are sufficient to encourage significant numbers of individuals to desert the corruption system and assist the integrity system in exposing and destroying it. The Fitzgerald Inquiry was such an event. This article also briefly addresses methods for destroying national corruption systems where they emerge and exist.

From deep North to global governance exemplar : Fitzgerald's impact on the International Anti-corruption Movement

In pre-Fitzgerald Queensland, the existence of corruption was widely known but its extent and modes of operation were not fully evident. The Fitzgerald Report identified the need for reform of the structure, procedures and efficiency in public administration in Queensland. What was most striking in the Queensland reform process was that a new model for combating corruption had been developed. Rather than rely upon a single law and a single institution, existing institutions were strengthened and new institutions were instituted to create a set of mutually supporting and mutually checking institutions, agencies and laws that jointly sought to improve governmental standards and combat corruption. Some of the reforms were either unique to Queensland or very rare. One of the strengths of this approach was that it avoided creating a single overarching institution to fight corruption. There are many powerful opponents of reform. Influential institutions and individuals resist any interference with their privileges. In order to cause a mass exodus from an entrenched corruption system, a seminal event or defining process is needed to alter expectations and incentives that are sufficient to encourage significant numbers of individuals to desert the corruption system and assist the integrity system in exposing and destroying it. The Fitzgerald Inquiry was such an event. The article also briefly addresses methods for destroying national corruption system where they emerge and exist.

Quantifying variability within technique and performance in elite fast bowlers : is technical variability dysfunctional or functional?

In fast bowling, cricketers are expected to produce a range of delivery lines and lengths while maximising ball speed. From a coaching perspective, technique consistency has been typically associated with superior performance in these areas. However, although bowlers are required to bowl consistently, at the elite level they must also be able to vary line, length and speed to adapt to opposition batters’ strengths and weaknesses. The relationship between technique and performance variability (and consistency) has not been investigated in previous fast bowling research. Consequently, the aim of this study was to quantify both technique (bowling action and coordination) and performance variability in elite fast bowlers from Australian Junior and National Pace Squads. Technique variability was analysed to investigate whether it could be classified as functional or dysfunctional in relation to speed and accuracy.

Co-constructing self-efficacy narratives : a study of four mature age university students

This thesis reports on a study in which research participants, four mature aged females starting an undergraduate degree at a regional Australian university, collaborated with the researcher in co-constructing a self-efficacy narrative. For the purpose of the study, self-efficacy was conceptualized as a means by which an individual initiates action to engage in a task or set of tasks, applies effort to perform the task or set of tasks, and persists in the face of obstacles encountered in order to achieve successful completion of the task or set of tasks. Qualitative interviews were conducted with the participants, initially investigating their respective life histories for an understanding of how they made the decision to embark on their respective academic program. Additional data were generated from a written exercise, prompting participants to furnish specific examples of self-efficacy. These data were incorporated into the individual's self-efficacy narrative, produced as the outcome of the "narrative analysis". Another aspect of the study entailed "analysis of narrative" in which analytic procedures were used to identify themes common to the self-efficacy narratives. Five main themes were identified: (a) participants' experience of schooling . for several participants their formative experience of school was not always positive, and yet their narratives demonstrated their agency in persevering and taking on university-level studies as mature aged persons; (b) recognition of family as an early influence . these influences were described as being both positive, in the sense of being supportive and encouraging, as well as posing obstacles that participants had to overcome in order to pursue their goals; (c) availability of supportive persons – the support of particular persons was acknowledged as a factor that enabled participants to persist in their respective endeavours; (d) luck or chance factors were recognised as placing participants at the right place at the right time, from which circumstances they applied considerable effort in order to convert the opportunity into a successful outcome; and (e) self-efficacy was identified as a major theme found in the narratives. The study included an evaluation of the research process by participants. A number of themes were identified in respect of the manner in which the research process was experienced as a helpful process. Participants commented that: (a) the research process was helpful in clarifying their respective career goals; (b) they appreciated opportunities provided by the research process to view their life from a different perspective and to better understand what motivated them, and what their preferred learning styles were; (c) their past successes in a range of different spheres were made more evident to them as they were guided in self-reflection, and their self-efficacious behaviour was affirmed; and (d) the opportunities provided by their participation in the research process to identify strengths of which they had not been consciously aware, to find confirmation of strengths they knew they possessed, and in some instances to rectify misconceptions they had held about aspects of their personality. The study made three important contributions to knowledge. Firstly, it provided a detailed explication of a qualitative narrative method in exploring self-efficacy, with the potential for application to other issues in educational, counselling and psychotherapy research. Secondly, it consolidated and illustrated social cognitive theory by proposing a dynamic model of self-efficacy, drawing on constructivist and interpretivist paradigms and extending extant theory and models. Finally, the study made a contribution to the debate concerning the nexus of qualitative research and counselling by providing guidelines for ethical practice in both endeavours for the practitioner-researcher.

History in the Australian Curriculum F-10 : providing answers without asking questions

This paper examines the most recent version of the Australian Curriculum: History F-10. It does so in two ways. First, it explores some of the strengths and weaknesses of this curriculum with reference to the decision to frame aspects of Australian history within the context of a world history approach. Whilst the positioning of Indigenous Histories is applauded, the curriculum’s lack of attention to the significance of the recent history of Australia’s Asian neighbours, and Australia’s relationship with them, is critiqued. This part of the paper also emphasises the need for comparative approaches and calls for greater emphasis on providing students with opportunities to critique and contest the construction of narratives about the past. Second, the paper introduces four invited articles that examine different aspects of the Australian Curriculum: History. Collectively these papers reiterate the significance of the richness of integrated and child-centred approaches and the importance of developing historical thinking, empathy and the historical imagination in the classroom.

Early intervention music therapy : reporting on a 3-year project to address needs with at-risk families

Sing & Grow is an early intervention music therapy project presented to families with additional needs, or those at risk of experiencing disadvantage due to social and/or economic circumstances that may impact on their parenting experiences. The aim of the project is to provide short term music therapy programs to families in communities where access to such services may be limited. The program is strengths-based and focuses on building upon a parent’s capacity to relate to and respond to their child’s emotional and developmental needs.

Action inquiry into the use of standardized evaluation tools for music therapy : a real life journey within a parent-child community program

Sing & Grow is an early intervention music therapy project that provides community group music therapy programs to families with young children who encounter risk factors that may impact on parenting and optimal child develop variety of evaluation tools were devised and used over the first 3 years of the project. Upon the subsequent funding and expansion of the project at the end of this period, it was necessary to find, test and devise more rigorous, valid and reliable measures to withstand the scrutiny of researchers, and to combat the concerns and criticisms associated with the previous methods of data collection. An action inquiry project was therefore undertaken with two groups of project participants to trial the use of the Parenting Stress Index and Depression, Anxiety and Stress Scales, both recommended by leading psychologists. Key findings that will be discussed include the friction between the deficit-focussed nature of many psychometric tools and the strengths-based approach taken in service delivery, the level of difficulty in terms of literacy and comprehension for vulnerable respondents, and the lack of one tool with the ability to comprehensively measure all aspects of a broad scoping program. Keywords: music therapy, evaluation, PSI, DASS, action inquiry.

Conceptualising and teaching discursive and performative reflection in higher education

The importance of reflection in higher education, and across disciplinary fields is widely recognised. It is generally embedded in university graduate attributes, professional standards and course objectives. Furthermore, reflection is commonly included in assessment requirements in higher education subjects, often without necessary scaffolding or clear expectations for students. It is essential that academic staff have substantive knowledge and clear expectations about the aims of reflective activities, the most effective mode of representation, and appropriate teaching strategies to support students in deep, critical reflection. The paper argues the case for reflection to be represented in different modes, using discursive (language) or performative (symbolic practice) forms of expression according to disciplinary context and individual communicative strengths. It introduces key discursive and expressive elements that constitute different modes of representation in reflective tasks. This functional analysis of textual elements provides explicit knowledge for teaching and assessing multiple modes of reflection in higher education.

Evidence for three tumor suppressor loci on chromosome 9p involved in melanoma development

Cytogenetic and loss of heterozygosity (LOH) studies have long indicated the presence of a tumor suppressor gene (TSG) on 9p involved in the development of melanoma. Although LOH at 9p has been reported in approximately 60% of melanoma tumors, only 5-10% of these tumors have been shown to carry CDKN2A mutations, raising the possibility that another TSG involved in melanoma maps to chromosome 9p. To investigate this possibility, a panel of 37 melanomas derived from 35 individuals was analyzed for CDKN2A mutations by single-strand conformation polymorphism analysis and sequencing. The melanoma samples were then typed for 15 markers that map to 9p13-24 to investigate LOH trends in this region. In those tumors demonstrating retention of heterozygosity at markers flanking CDKN2A and LOH on one or both sides of the gene, multiplex microsatellite PCR was performed to rule out homozygous deletion of the region encompassing CDKN2A. CDKN2A mutations were found in tumors from 5 patients [5 (14%) of 35], 4 of which demonstrated LOH across the entire region examined. The remaining tumor with no observed LOH carried two point mutations, one on each allele. Although LOH was identified at one or more markers in 22 (59%) of 37 melanoma tumors corresponding to 20 (57%) of 35 individuals, only 11 tumors from 9 individuals [9 (26%) of 35] demonstrated LOH at D9S942 and D9S1748 the markers closest to CDKN2A. Of the remaining 11 tumors with LOH 9 demonstrated LOH at two or more contiguous markers either centromeric and/or telomeric to CDKN2A while retaining heterozygosity at several markers adjacent to CDKN2A. Multiplex PCR revealed one tumor carried a homozygous deletion extending from D9S1748 to the IFN-alpha locus. In the remaining eight tumors, multiplex PCR demonstrated that the observed heterozygosity was not attributable to homozygous deletion and stromal contamination at D9S1748, D9S942, or D9S974, as measured by comparative amplification strengths, which indicates that retention of heterozygosity with flanking LOH does not always indicate a homozygous deletion. This report supports the conclusions of previous studies that a least two TSGs involved in melanoma development in addition to CDKN2A may reside on chromosome 9p.

SAP webflow made configurable: unifying workflow templates into a configurable model

To facilitate the implementation of workflows, enterprise and workflow system vendors typically provide workflow templates for their software. Each of these templates depicts a variant of how the software supports a certain business process, allowing the user to save the effort of creating models and links to system components from scratch by selecting and activating the appropriate template. A combination of the strengths from different templates is however only achievable by manually adapting the templates which is cumbersome. We therefore suggest in this paper to combine different workflow templates into a single configurable workflow template. Using the workflow modeling language of SAP’s WebFlow engine, we show how such a configurable workflow modeling language can be created by identifying the configurable elements in the original language. Requirements imposed on configurations inhibit invalid configurations. Based on a default configuration such configurable templates can be used as easy as the traditional templates. The suggested approach is also applicable to other workflow modeling languages