Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Innovation for Equity in Rural Education : Proceedings of the International Symposium for Innovation in Rural Education

PREFACE The concept of an international symposium on rural education arose from a meeting between members of the SiMERR National Centre, Australia and the NURI Teacher Education Innovation Centre (NURI-TEIC) at Kongju National University, Korea in 2007. Despite the very different national contexts, the teams were struck by the similarities of the challenges facing rural schools in the two countries, and curious about the degree to which these challenges were shared by other countries. At a subsequent meeting in Australia in December 2007, the two centre Directors - Professor John Pegg (SiMERR) and Professor Youn-Kee Im (NURI-TEIC) - agreed on a framework for the first International Symposium for Innovation in Rural Education (ISFIRE). This volume consists of the keynotes and refereed papers presented at ISFIRE 2009. The papers provide insights into rural education in Australia, Bhutan, Canada, Korea, Norway, South Africa and the United States along the following themes: 1. Promoting rural policy initiatives; 2. Nurturing the rural teacher experience; 3. Enhancing rural student experience and growth; 4. Optimising the curriculum; 5. Improving resources in rural schools; and 6. Addressing special issues in rural education. The authors and titles of a further 23 presentations based on refereed abstracts only are listed at the end of this volume. The abstracts for these presentations can be found in the symposium Program. The academics and practitioners who came together for this symposium are passionate about rural education and have dedicated their time and capacities to working for the benefit of rural teachers, students and communities. The papers in this volume offer direction not only for Australia and South Korea, who jointly hosted this symposium, but for all countries in which rural education is contested ground. The keynotes in particular contribute rich perspectives on rural education trends, policies and practices. We hope that this volume generates a greater appreciation of the advantages of rural education and the many innovative approaches being implemented to meet its challenges.

Women in leadership: An analysis of the gender pay gap in ASX-listed firms

This study provides evidence that after several decades of fighting for equal pay for equal work, an unexplained gender pay gap remains amongst senior executives in ASX-listed firms. After controlling for a large suite of personal, occupational and firm observables, we find female senior executives receive, on average, 22.58 percent less in base salary for the period 2002–2013. When executives are awarded performance-based pay, females receive on average 16.47 percent less in cash bonus and 18.21 percent less in long-term incentives than males. The results are robust to using firm fixed effects and propensity-score matching. Blinder–Oaxaca decomposition results show that the mean pay gap cannot be attributed to gender differences in attributes, including job titles. Instead, the results point to differences in returns on firm-specific variables, in particular firm risk.

Systematic review of the psychological consequences of false-positive screening mammograms

- Background In the UK, women aged 50–73 years are invited for screening by mammography every 3 years. In 2009–10, more than 2.24 million women in this age group in England were invited to take part in the programme, of whom 73% attended a screening clinic. Of these, 64,104 women were recalled for assessment. Of those recalled, 81% did not have breast cancer; these women are described as having a false-positive mammogram. - Objective The aim of this systematic review was to identify the psychological impact on women of false-positive screening mammograms and any evidence for the effectiveness of interventions designed to reduce this impact. We were also looking for evidence of effects in subgroups of women. - Data sources MEDLINE, MEDLINE In-Process & Other Non-Indexed Citations, EMBASE, Health Management Information Consortium, Cochrane Central Register for Controlled Trials, Cochrane Database of Systematic Reviews, Centre for Reviews and Dissemination (CRD) Database of Abstracts of Reviews of Effects, CRD Health Technology Assessment (HTA), Cochrane Methodology, Web of Science, Science Citation Index, Social Sciences Citation Index, Conference Proceedings Citation Index-Science, Conference Proceeding Citation Index-Social Science and Humanities, PsycINFO, Cumulative Index to Nursing and Allied Health Literature, Sociological Abstracts, the International Bibliography of the Social Sciences, the British Library's Electronic Table of Contents and others. Initial searches were carried out between 8 October 2010 and 25 January 2011. Update searches were carried out on 26 October 2011 and 23 March 2012. - Review methods Based on the inclusion criteria, titles and abstracts were screened independently by two reviewers. Retrieved papers were reviewed and selected using the same independent process. Data were extracted by one reviewer and checked by another. Each included study was assessed for risk of bias. - Results Eleven studies were found from 4423 titles and abstracts. Studies that used disease-specific measures found a negative psychological impact lasting up to 3 years. Distress increased with the level of invasiveness of the assessment procedure. Studies using instruments designed to detect clinical levels of morbidity did not find this effect. Women with false-positive mammograms were less likely to return for the next round of screening [relative risk (RR) 0.97; 95% confidence interval (CI) 0.96 to 0.98] than those with normal mammograms, were more likely to have interval cancer [odds ratio (OR) 3.19 (95% CI 2.34 to 4.35)] and were more likely to have cancer detected at the next screening round [OR 2.15 (95% CI 1.55 to 2.98)]. - Limitations This study was limited to UK research and by the robustness of the included studies, which frequently failed to report quality indicators, for example failure to consider the risk of bias or confounding, or failure to report participants' demographic characteristics. - Conclusions We conclude that the experience of having a false-positive screening mammogram can cause breast cancer-specific psychological distress that may endure for up to 3 years, and reduce the likelihood that women will return for their next round of mammography screening. These results should be treated cautiously owing to inherent weakness of observational designs and weaknesses in reporting. Future research should include a qualitative interview study and observational studies that compare generic and disease-specific measures, collect demographic data and include women from different social and ethnic groups.

In Situ Observation of the Thermal Decomposition of Weddelite by Heating Stage Environmental Scanning Electron Microscopy

The morphological and chemical changes occurring during the thermal decomposition of weddelite, CaC2O4·2H2O, have been followed in real time in a heating stage attached to an Environmental Scanning Electron Microscope operating at a pressure of 2 Torr, with a heating rate of 10 °C/min and an equilibration time of approximately 10 min. The dehydration step around 120 °C and the loss of CO around 425 °C do not involve changes in morphology, but changes in the composition were observed. The final reaction of CaCO3 to CaO while evolving CO2 around 600 °C involved the formation of chains of very small oxide particles pseudomorphic to the original oxalate crystals. The change in chemical composition could only be observed after cooling the sample to 350 °C because of the effects of thermal radiation.

Thermal decomposition of the synthetic hydrotalcite iowaite

The thermal stability and thermal decomposition pathways for synthetic iowaite have been determined using thermogravimetry in conjunction with evolved gas mass spectrometry. Chemical analysis showed the formula of the synthesised iowaite to be Mg6.27Fe1.73(Cl)1.07(OH)16(CO3)0.336.1H2O and X-ray diffraction confirms the layered structure. Dehydration of the iowaite occurred at 35 and 79°C. Dehydroxylation occurred at 254 and 291°C. Both steps were associated with the loss of CO2. Hydrogen chloride gas was evolved in two steps at 368 and 434°C. The products of the thermal decomposition were MgO and a spinel MgFe2O4. Experimentally it was found to be difficult to eliminate CO2 from inclusion in the interlayer during the synthesis of the iowaite compound and in this way the synthesised iowaite resembled the natural mineral.

Raman spectroscopy of the molybdate minerals chillagite (tungsteinian wulfenite-I4), stolzite, scheelite, wolframite and wulfenite

Raman spectra of chillagite, wulfenite, stolzite, scheelite and wolframite were obtained at 298 and 77 K using a Raman microprobe in combination with a thermal stage. Chillagite is a solid solution of wulfenite and stolzite. The spectra of these molybdate minerals are orientation dependent. The band at 695 cm-1 is interpreted as an antisymmetric bridging mode associated with the tungstate chain. The bands at 790 and 881 cm-1 are associated with the antisymmetric and symmetric Ag modes of terminal WO2 whereas the origin of the 806 cm-1 band remains unclear. The 4(Eg) band was absent for scheelite. The bands at 353 and 401 cm-1 are assigned as either deformation modes or as r(Bg) and (Ag) modes of terminal WO2. The band at 462 cm-1 has an equivalent band in the infrared at 455 cm-1 assigned as as(Au) of the (W2O4)n chain. The band at 508 cm-1 is assigned as sym(Bg) of the (W2O4)n chain.