The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eye’s ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

Young Children and the Environment : Early Learning for Sustainability

This world-first text book on early childhood edcuation for sustainabilty tackles one of the biggest contemporary issues of our times - the changing environmment - and demonstrates how early education can contribute to sustainable living. An essential text for students in early childhood teacher education and a practcial resource for child care practitioners and primary school teachers, it is designed to promote edcuation for sustainabilty from birth to eight years. the text refers to national and international initiatives such as 'sustainable Schools', 'Child Friendly Cities' and 'Health Promoting Schools' and explores their existing and potential links with early childhood education. Groundbreaking content draws on recent literature in the areas of organisational, educational and cultural chnage, and environmental sustainabilty. Specific chapters explore ethical challenges and the use of ICT to advance learning. Case studies and vignettes exemplify leadership in practice and 'provocations' are integrated throughout to inspire new ways of thinking about the environment, the wider world, young children and the transformative power of early edcuation.

A short-term evaluation of a school-based early adolescent injury prevention program

This paper reports on the development of a school-based intervention to reduce risk-taking and associated injuries. There is limited but important evidence that intervention design should ensure participation does not lead to an increase in target risk behaviors with some studies in alcohol and drug prevention finding unexpected negative effects. The short-term evaluation of Skills for Preventing Injury in Youth (SPIY) examined change in interpersonal violence, alcohol and transport-related risks. Intervention (n = 360) and comparison (n = 180) students were surveyed pre/post-intervention. A qualitative analysis based on focus groups (70 students) explored experiences of change. Findings indicate significant positive changes reinforced by students’ reports. A decrease in reported risk-taking for the intervention group and an increase in the comparison group were observed. These findings endorse SPIY as a useful curriculum approach to reducing injuries and lend support to the future conduct of a long-term outcome evaluation.

Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Modelling sustainable and optimal solutions for building services integration in early architectural design : confronting the software and professional interoperability deficit

Decisions made in the earliest stage of architectural design have the greatest impact on the construction, lifecycle cost and environmental footprint of buildings. Yet the building services, one of the largest contributors to cost, complexity, and environmental impact, are rarely considered as an influence on the design at this crucial stage. In order for efficient and environmentally sensitive built environment outcomes to be achieved, a closer collaboration between architects and services engineers is required at the outset of projects. However, in practice, there are a variety of obstacles impeding this transition towards an integrated design approach. This paper firstly presents a critical review of the existing barriers to multidisciplinary design. It then examines current examples of best practice in the building industry to highlight the collaborative strategies being employed and their benefits to the design process. Finally, it discusses a case study project to identify directions for further research.

Delirium in early-stage Alzheimer's disease : enhancing cognitive reserve as a possible preventive measure

Delirium is a disorder of acute onset with fluctuating symptoms and is characterized by inattention, disorganized thinking, and altered levels of consciousness. The risk for delirium is greatest in individuals with dementia, and the incidence of both is increasing worldwide because of the aging of our population. Although several clinical trials have tested interventions for delirium prevention in individuals without dementia, little is known about the mechanisms for the prevention of delirium in early-stage Alzheimer’s disease (AD). The purpose of this article is to explore ways of preventing delirium and slowing the rate of cognitive decline in early-stage AD by enhancing cognitive reserve. An agenda for future research on interventions to prevent delirium in individuals with early-stage AD is also presented.

Effectiveness of community-based nonpharmacological interventions for early-stage dementia : conclusions and recommendations

In 2007, a comprehensive review of the extant research on nonpharmacological interventions for persons with early-stage dementia was conducted. More than 150 research reports, centered on six major domains, were included: early-stage support groups, cognitive training and enhancement programs, exercise programs, exemplar programs, health promotion programs, and “other” programs not fitting into previous categories. Theories of neural regeneration and plasticity were most often used to support the tested interventions. Recommendations for practice, research, and health policy are outlined, including evidence-based, nonpharmacological treatment protocols for persons with mild cognitive impairment and early-stage dementia. A tested, community-based, multimodal treatment program is also described. Overall, findings identify well-supported nonpharmacological treatments for persons with early-stage dementia and implications for a national health care agenda to optimize outcomes for this growing population of older adults.

Healthy children, healthy planet : the case for transformative education in schools and early childhood from an Australian perspective

Climate change is an urgent global public health issue with substantial predicted impacts in the coming decades. Concurrently, global burden of disease studies highlight problems such as obesity, mental health problems and a range of other chronic diseases, many of which have origins in childhood. There is a unique opportunity to engage children in both health promotion and education for sustainability during their school years to help ameliorate both environmental and health issues. Evidence exists for the most effective ways to do this, through education that is empowering, action orientated and relevant to children’s day to day interests and concerns, and by tailoring such education to different educational sectors. The aim of this discussion paper is to argue the case for sustainability education in schools that links with health promotion and that adopts a practical approach to engaging children in these important public health and environmental issues. We describe two internationally implemented whole-school reform movements, Health Promoting Schools (HPS) and Sustainable Schools (SS) which seek to operationalise transformative educational processes. Drawing on international evidence and Australian case examples, we contend that children’s active involvement in such processes is not only educationally engaging and rewarding, it also contributes to human and environmental resilience and health. Further, school settings can play an important ecological public health role, incubating and amplifying the socially transformative changes urgently required to create pathways to healthy, just and sustainable human futures, on a viable planet.

Characteristics of sustainable entrepreneurship : some early explorations from the CAUSEE study

Principal Topic: For forward thinking companies, the environment may represent the ''biggest opportunity for enterprise and invention the industrial world has ever seen'' (Cairncross 1990). Increasing awareness of environmental and sustainability issues through media including the promotion of Al Gore's ''An Inconvenient Truth'' has seen increased awareness of environmental and sustainability issues and increased demand for business processes that reduce detrimental environmental impacts of global development (Dean & McMullen 2007). The increased demand for more environmentally sensitive products and services represents an opportunity for the development of ventures that seek to satisfy this demand through entrepreneurial action. As a consequence, increasing recent market developments in renewable energy, carbon emissions, fuel cells, green building, and other sectors suggest an increasing importance of opportunities for environmental entrepreneurship (Dean and McMullen 2007) and increasingly important area of business activity (Schaper 2005). In the last decade in particular, big business has sought to develop a more ''sustainability/ green friendly'' orientation as a response to public pressure and increased government legislation and policy to improve environmental performance (Cohen and Winn 2007). Whilst much of the literature and media is littered with examples of sustainability practices of large firms, nascent and young sustainability firms have only recently begun generating strong research and policy interest (Shepherd, Kuskova and Patzelt 2009): not only for their potential to generate above average financial performance and returns owing to a greater popularity and demand towards sustainability products and services offerings, but also for their intent to lessen environmental impacts, and to provide a more accurate reflection of the ''true cost'' of market offerings taking into account carbon and environmental impacts. More specifically, researchers have suggested that although the previous focus has been on large firms and their impact on the environment, the estimated collective impact of entries and exits of nascent and young firms in development is substantial and could outweigh the combined environmental impact of large companies (Hillary, 2000). Therefore, it may be argued that greater attention should be paid to nascent and young firms and researching sustainability practices, for both their impact in reducing environmental impacts and potential higher financial performance. Whilst acknowledging this research only uses the first wave of a four year longitudinal study of nascent and young firms, it can still begin to provide initial analysis on which to continue further research. The aim of this paper therefore is to provide an overview of the emerging literature in sustainable entrepreneurship and to present some selected preliminary results from the first wave of the data collection, with comparison, where appropriate, of sustainable and firms that do not fulfil this criteria. ''One of the key challenges in evaluating sustainability entrepreneurship is the lack of agreement in how it is defined'' (Schaper, 2005: 10). Some evaluate sustainable entrepreneurs simply as one category of entrepreneurs with little difference between them and traditional entrepreneurs (Dees, 1998). Other research recognises values-based sustainable enterprises requiring a unique perspective (Parrish, 2005). Some see the environmental or sustainable entrepreneurship is a subset of social entrepreneurship (Cohen & Winn, 2007; Dean & McMullen, 2007) whilst others see it as a separate, distinct theory (Archer 2009). Following one of the first definitions of sustainability developed by the Brundtland Commission (1987) we define sustainable entrepreneurship as firms which ''seek to meet the needs and aspirations of the present without compromising the ability to meet those of the future''. ---------- Methodology/Key Propositions: In this exploratory paper we investigate sustainable entrepreneurship using Cohen et al.'s (2008) framework to identify strategies of nascent and young entrepreneurial firms. We use data from The Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE). This study shares the general empirical approach with PSED studies in the US (Reynolds et al 1994; Reynolds & Curtin 2008). The overall study uses samples of 727 nascent (not yet operational) firms and another 674 young firms, the latter being in an operational stage but less than four years old. To generate the sub sample of sustainability firms, we used content analysis techniques on firm titles, descriptions and product descriptions provided by respondents. Two independent coders used a predefined codebook developed from our review of the sustainability entrepreneurship literature (Cohen et al. 2009) to evaluate the content based on terms such as ''sustainable'' ''eco-friendly'' ''renewable energy'' ''environment'' amongst others. The inter-rater reliability was checked and the Kappa's co-efficient was found to be within the acceptable range (0.746). 85 firms fulfilled the criteria given for inclusion in the sustainability cohort. ---------- Results and Implications: The results for this paper are based on Wave one of the CAUSEE survey which has been completed and the data is available for analysis. It is expected that the findings will assist in beginning to develop an understanding of nascent and young firms that are driven to contribute to a society which is sustainable, not just from an economic perspective (Cohen et al 2008), but from an environmental and social perspective as well. The CAUSEE study provides an opportunity to compare the characteristics of sustainability entrepreneurs with entrepreneurial firms without a stated environmental purpose, which constitutes the majority of the new firms created each year, using a large scale novel longitudinal dataset. The results have implications for Government in the design of better conditions for the creation of new business, firms who assist sustainability in developing better advice programs in line with a better understanding of their needs and requirements, individuals who may be considering becoming entrepreneurs in high potential arenas and existing entrepreneurs make better decisions.

What is early childhood education for sustainability?

Julie Davis canvasses the literature to explain why sustainability issues are important for young children and why early childhood educators should become engaged with EfS. She outlines the short history of ECEfS in Australasia and internationally, emphasising its marginalised and fragile early phase that is now beginning to coalesce into a robust international movement. She then highlights two recent studies undertaken in child care centres that illustrate the learning and actions that are possible when education for sustainability is incorporated into early childhood curriculum and pedagogy. Julie ends the chapter by identifying the qualities that might characterise early childhood education for sustainability, stressing its requirement to be transformative education that builds the capabilities of young children as agents of change for sustainability. In so doing, she draws together theoretical strands from both early childhood education and EfS, beginning the process of constructing a theoretical framework for ECEfS.

Creating deep and broad change through research and systems approaches in early childhood education for sustainability

The co-authors raise two matters they consider essential for the future development of ECEfS. The first is the need to create deep foundations based in research. At a time of increasing practitioner interest, research in ECEfS is meagre. A robust research community is crucial to support quality in curriculum and pedagogy, and to promote learning and innovation in thinking and practice. The second 'essential' for the expansion and uptake of ECEfS is broad systemic change. All level within the early childhood education system - individual teachers and classrooms, whole centres and schools, professional associations and networks, accreditation and employing authorities, and teacher educators - must work together to create and reinforce the cultural and educational changes required for sustainability. This chapter provides explanations of processes to engender systemic change. It illustrates a systems approach, with reference to a recent study focused on embedding EfS into teacher education. This study emphasises the apparent contradiction that the answer to large-scale reform lies with small-scale reforms that build capacity and make connections.