Numerical Computing and Graphics for the Power Method Transformation Using Mathematica

This paper provides the requisite information and description of software that perform numerical computations and graphics for the power method polynomial transformation. The software developed is written in the Mathematica 5.2 package PowerMethod.m and is associated with fifth-order polynomials that are used for simulating univariate and multivariate non-normal distributions. The package is flexible enough to allow a user the choice to model theoretical pdfs, empirical data, or a user's own selected distribution(s). The primary functions perform the following (a) compute standardized cumulants and polynomial coefficients, (b) ensure that polynomial transformations yield valid pdfs, and (c) graph power method pdfs and cdfs. Other functions compute cumulative probabilities, modes, trimmed means, intermediate correlations, or perform the graphics associated with fitting power method pdfs to either empirical or theoretical distributions. Numerical examples and Monte Carlo results are provided to demonstrate and validate the use of the software package. The notebook Demo.nb is also provided as a guide for user of the power method.

Numerical Computing and Graphics for the Power Method Transformation Using Mathematica

This paper provides the requisite information and description of software that perform numerical computations and graphics for the power method polynomial transformation. The software developed is written in the Mathematica 5.2 package PowerMethod.m and is associated with fifth-order polynomials that are used for simulating univariate and multivariate non-normal distributions. The package is flexible enough to allow a user the choice to model theoretical pdfs, empirical data, or a user’s own selected distribution(s). The primary functions perform the following (a) compute standardized cumulants and polynomial coefficients, (b) ensure that polynomial transformations yield valid pdfs, and (c) graph power method pdfs and cdfs. Other functions compute cumulative probabilities, modes, trimmed means, intermediate correlations, or perform the graphics associated with fitting power method pdfs to either empirical or theoretical distributions. Numerical examples and Monte Carlo results are provided to demonstrate and validate the use of the software package. The notebook Demo.nb is also provided as a guide for user of the power method

Exploring the Interplay Between Equity Groups, Mental Health and Perceived Employability Amongst Students at a Public Australian University

This article explores the interplay between perceived employability (PE), mental health, and equity group membership amongst students at a large public urban university in Australia. The article reports from a study conducted between 2017 and 2022, during which students self-assessed their PE. Differences in PE by equity group membership were assessed using responses to structured fields in the questionnaire (n = 24,329). Custom measures were constructed using student responses to open-ended fields to proxy student wellbeing based on sentiment analysis and mention of mental health or synonymous terms (n = 12,819). Analyses included two-way tests of differences between groups and multivariate analyses considering the effect of equity group membership and mental health concerns on employability beliefs. Results indicate that students with a disability, with English as a second language, or with wellbeing concerns report lower perceived employability. Of all the PE dimensions, academic self-efficacy is most consistently affected by equity group membership and wellbeing concerns. Further, wellbeing concerns are more prevalent for students with disabilities. The findings strengthen support for policy and institutional initiatives focusing on student wellbeing in general but also specifically for equity groups that are already associated with poorer employability beliefs. In particular, students with disabilities appear to have poorer self-esteem and academic self-efficacy and are more likely to have mental health concerns.</p

Developing research-informed practice in initial teacher education through school-university partnering

There is limited research investigating models of partnering between University and Schools in initial teacher education (ITE). This project investigated, over a ten year period, how student teachers in an English University on a one year course, draw on theoretical models, introduced in university sessions, when planning for a ‘creative week’ placement in schools. Working within an interpretivist paradigm drawing on data from 52 student teachers, 10 teachers and 50 children this case study explored a model of teacher education provision. Findings illuminated factors which inhibited student teachers from planning engaging lessons which challenged their learners, including poor relationships between stakeholders, misunderstandings of the purpose of the placement and under developed knowledge and understandings of how to successfully draw on theoretical models to enhance learning, together with the challenges of limited time during a one year course. Findings also uncovered the extent to which student teachers were ‘allowed’ by some teachers, but not by others, to take risks in their practice, and the impact this has on student teachers’ sense of autonomy and confidence. Implications of the research demonstrate how findings can impact on initial teacher education course design and partnering models between University and schools