Chromatic dependence of first-order optical properties of the eye

Abstract: Many first-order optical properties depend on chromatic dispersion and, hence, on frequency of light. The purpose of this theoretical study is to investigate the dependence of first-order optical properties of model eyes on frequency. In this study we are purposefully not concerned with subjective measurements. Instead, definitions are obtained that are general for optical systems that have astigmatic and decentred elements, and then simplified for Gaussian systems. In linear optics the transference is a matrix that is a complete representation of the effects of the system on a ray traversing it. Almost all of the familiar optical properties of the system can be obtained from the transference. From the transference S we obtain the four fundamental properties namely dilation A, disjugacy B, divergence C and divarication D, submatrices of S. Transferences are symplectic and do not define a linear space. Linear spaces are amenable to statistical analyses and therefore a number of mappings to linear spaces are investigated, including the Cayley and logarithmic mappings to Hamiltonian space and the four characteristic matrices. In each case, the individual entries of the transform are studied for their dependence on frequency and then the chromatic dependence relationship between the entries is compared graphically.M.Phil. (Optometry

Public History in Australia

This article charts the peaks and troughs of public history inside and outside academia in Australia and the promise of the establishment of a new network of public historians in Australia and Aotearoa New Zealand. It reveals the value of Australian creative engagements with the past. It concludes by suggesting that networks and team-based work are vital for the successful practice of public history in Australasia and elsewhere. &nbsp

A Study of the New Zealand Mathematics Curriculum

Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics' curriculum in the context of the first stage of a study. The emphasis is on the importance of research design that begins with an explicit, evidence-based hypothesis. To that end, we describe evidence that informs and identifies the study's hypothesised problem and causes. The study itself will show whether or not the hypothesis is justified; that is, is the absence of standardised prescribed content in New Zealand mathematics' curriculum the reason for the country's declining mathematics rankings? The study aims to increase understanding in the field of mathematics education by exploring the effects on New Zealand year 7 public school teachers' mathematics curriculum selection and design practices, teaching practices, and subsequently student achievement.Comment: Submitted to the New Zealand Journal of Educational Studies, 12 June 202

Predicting how a disrupted semester during the COVID-19 pandemic impacted student learning

Tertiary education faced unprecedented disruption resulting from COVID-19 driven lockdowns around the world, leaving educators with little understanding of how the pandemic and consequential shift to online environments would impact students′ learning. Utilising the theoretical framework of a student′s affective field, this study aimed to investigate how student achievement, achievement-related affect, and self-perceived well-being contributed to predicting how their learning was impacted. Questionnaire responses and academic achievement measures from students (N = 208) in a New Zealand second-year, tertiary mathematics course were analysed. Despite a return to in-person teaching after eliminating community-transmission of the virus, students reported larger impacts of the disruption to semester on both their learning and well-being at the end of the term than during the lockdown. Hierarchical multiple regression revealed that gender, prior achievement, performance on low-stakes assessment, as well as exam-related self-efficacy and hope, made significant, independent contributions to explaining students′ perceived learning impact. Even when controlling for achievement and achievement-related affect, students′ perceived impact to their well-being made a significant and substantial contribution to the impact on their learning. The findings provide motivation to further investigate whether attempts to address student achievement-related affect can help mitigate the effects of major life disruptions on studying. We suggest that frequent, low-stakes assessment can identify students who are more likely to report greater negative impacts to their learning. We finally conclude that student well-being is paramount to how students perceive their own learning, even when controlling for actual measures of and about their achievement

Inquiry-based mathematics education: a call for reform in tertiary education seems unjustified

In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting substantial funding from US government agencies. This resulted in the successful mobilization of regional consortia in many states, uniting over 800 mathematics education practitioners working to reform undergraduate education. Inquiry-based learning is characterized by the fundamental premise that learners should be allowed to learn 'new to them' mathematics without being taught. This progressive idea is based on the assumption that it is best to advance learners to the level of experts by engaging learners in mathematical practices similar to those of practicing mathematicians: creating new definitions, conjectures and proofs - that way, learners are thought to develop 'deep mathematical understanding'. However, concerted efforts to radically reform mathematics education must be systematically scrutinized in view of available evidence and theoretical advances in the learning sciences. To that end, this scoping review sought to consolidate the extant research literature from cognitive science and educational psychology, offering a critical commentary on the effectiveness of inquiry-based learning. Our analysis of research articles and books pertaining to the topic revealed that the call for a major reform by the IBME advocates is not justified. Specifically, the general claim that students would learn better (and acquire superior conceptual understanding) if they were not taught is not supported by evidence. Neither is the general claim about the merits of IBME for addressing equity issues in mathematics classrooms

Traditional lectures versus active learning – A false dichotomy?

Traditional lectures are commonly understood to be a teacher-centered mode of instruction where the main aim is a provision of explanations by an educator to the students. Recent literature in higher education overwhelmingly depicts this mode of instruction as inferior compared to the desired student-centered models based on active learning techniques. First, using a four-quadrant model of educational environments, we address common confusion related to a conflation of two prevalent dichotomies by focusing on two key dimensions: (1) the extent to which students are prompted to engage actively and (2) the extent to which expert explanations are provided. Second, using a case study, we describe an evolution of tertiary mathematics education, showing how traditional instruction can still play a valuable role, provided it is suitably embedded in a student-centered course design. We support our argument by analyzing the teaching practice and learning environment in a third-year abstract algebra course through the lens of Stanislas Dehaene's theoretical framework for effective teaching and learning. The framework, comprising "four pillars of learning", is based on a state-of-the-art conception of how learning can be facilitated according to cognitive science, educational psychology and neuroscience findings. In the case study, we illustrate how, over time, the unit design and the teaching approach have evolved into a learning environment that aligns with the four pillars of learning. We conclude that traditional lectures can and do evolve to optimize learning environments and that the erection of the dichotomy "traditional instruction versus active learning" is no longer relevant

Australia, the healthiest nation: death, hospital and cost savings of the Preventative Health Taskforce target reductions for alcohol, 2007 to 2020

Background - The National Preventative Health Taskforce has set a 30% target reduction in the proportion of risky and high risk drinkers by 2020. This study estimated the potential saving in deaths, hospitalisations and associated economic cost savings to premature mortality and health of achieving the target. Method - Past national estimates of alcohol-attributable hospitalisations and deaths were used to forecast trends from 2007 to 2020. Estimated potential savings in deaths and hospitalisations were based on incremental decline in the prevalence of risky/high-risk drinking reaching a total of 30% by 2020 (about 2.3% per year). Associated economic costs of premature death were estimated using the Value of Statistical Life method (willingness to pay). Hospital costs were estimated from known trends in annual national costs for recent past years and taking inflation into account. Results - A 30% reduction in risky/high-risk drinkers would avoid an estimated 7,200 deaths and some 94,000 person-years-of-life lost due to premature death by 2020. The estimated benefit to the health sector would include 330,000 fewer hospitalisations and 1.5 million associated bed days. The net present value of these benefits is AUD 22.7 billion from deaths avoided and AUD 1.7 billion from fewer hospital separations totalling AUD 24.4 billion. Conclusion - The potential savings in premature deaths, health and associated financial costs of a 30% reduction in risky and high-risk drinking by 2020 across the Australian population are considerable

Chromatic properties of astigmatic eyes

Background: Chromatic differences in power, refractive compensation, position and magnification have been described in the literature for Gaussian eyes. Aim: This article explores these definitions and defines chromatic properties for eyes that have astigmatic and decentred or tilted elements. Setting: Linear optics. Methods: The optical model is linear optics and makes use of the ray transference T. Results: Results are presented as either 2 × 2 matrices or 2 × 1 vectors. The dependence of the chromatic properties on the position of an object and the limiting aperture is explored and results are presented as independent of, or dependent on, object and aperture position. Apertures undergo both longitudinal and transverse shifts in position. The results are general and apertures may include pupils or pinholes, either surgically inserted inside the eye or held in front of the eye. Numerical examples are provided for Le Grand’s four-surface eye and an arbitrary astigmatic heterocentric four-surface eye. Conclusion: Aperture-independent chromatic properties include chromatic difference in power and refractive compensation, both given as 2 × 2 matrices. Aperture-dependent chromatic properties are all dependent on longitudinal shifts in the plane of the limiting aperture. In addition, chromatic difference in position and inclination depend on both object and transverse aperture position. Chromatic difference in image size or angular spread depends on object position and is independent of transverse aperture position. These four aperture-dependent chromatic properties are given as 2 × 1 vectors. Chromatic magnifications are independent of object and transverse aperture position and are given as 2 × 2 matrices