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Connections between points of convexity of functions and centrality of elements in -algebras
No full textIn this paper, we give a characterization of central elements in a -algebra in terms of points of convexity of scalar functions. We prove that if is an open interval and is a convex function satisfying a certain inequality, then a self-adjoint element with spectrum in is central if and only if it is a point of convexity of . The class of functions with these properties contains the nontrivial real exponential ones and the power ones with exponent outside
A study of the validity of Oppenheim's inequality for Hurwitz matrices associated with Hurwitz polynomials
No full textIn this paper, Hurwitz polynomials, i.e., real polynomials whose roots are located in the open left half of the complex plane, and their associated Hurwitz matrices are considered. New formulae for the principal minors of Hurwitz matrices are presented which lead to () a new criteria for deciding whether a polynomial is Hurwitz, () an inequality of a type of Oppenheim's inequality for the Hurwitz matrices up to order , and () a necessary and sufficient condition for the Hadamard square root of Hurwitz polynomials of degree five to be Hurwitz
Order relations of the Wasserstein mean and the spectral geometric mean
No full textOn the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order relations on the curves defined by the Wasserstein mean and the spectral geometric mean. We show that the near order is stronger than the eigenvalue entrywise order and that for . We prove the monotonicity properties of the curves originated from the Wasserstein mean and the spectral geometric mean in terms of the near order. The Löwner order properties of the Wasserstein mean and the spectral geometric mean are also explored
“I would love to have these conversations with family”: A Listening Guide exploration of the relational experiences of first-generation students in helping professions
No full textFirst-generation students are, by and large, working-class students. While many have focused on their experiences of academic and social integration into college, first-generation students are often just as concerned with remaining integrated in their home communities, reflecting their tendency to value interdependence. This qualitative study explored the relational experiences of first-generation students attempting to share their learning in family conversations. I conducted focus groups with 19 first-generation students enrolled in programs preparing them for the helping professions, particularly social work and teaching. Transcripts were analyzed using the Listening Guide (Brown & Gilligan, 1992; Gilligan, 2015). Findings highlighted participants’ struggles to share their learning within their home communities, and varied responses, including self-silencing, being silenced by family, and an emerging sense of relational loss
College Major Selection, Social Class, and the Gender Pay Gap in the United States
No full textAlthough researchers have made plausible arguments about the contributions of several factors, occupational segregation and the “motherhood penalty” are widely considered to be two of the most important causes of the gender pay gap in the United States today. In this article we discuss some of the most important findings in the gender pay gap research in the U.S. We then summarize an exploratory study we conducted in spring 2024 into one particular stage in the process of occupational segregation: the choice of college major. We hypothesized that (a) female students would be overrepresented in lower-paying majors and (b) working-class females, while still overrepresented in these majors, would be more likely to choose higher-paying majors, given their backgrounds and the greater salience of economic security for them compared with their non-working-class female peers. Using enrollment data from a university in the Mid-Atlantic region of the U.S., our first hypothesis was supported: females were overrepresented, to a significant degree, in majors with the lowest starting salaries. Our second hypothesis was not supported: the distribution of working-class females in lower-paying majors was virtually identical to that of non-working-class females. We discuss these results as well as survey responses from a convenience sample of 38 students at that university, responses which further illuminate our quantitative findings. We plan to develop this study into a full empirical investigation in fall 2024
Three Poems: A Ship in Distress, A Christmas Carol for the Carers, The Service of my Baba’s Windows
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Designing Collaborative Tech-Rich Learning: Building a Multi-Player Game Controller with Makey Makeys
No full textThis lesson challenges learners to consider the educational benefits of using games to support teaching and learning practices through a Makey Makey design challenge. A Makey Makey is a digital toolkit that creates a closed-loop circuit by connecting alligator clips to conductive materials. I introduce the Makey Makey during a unit exploring the use of gaming technologies in PK-12 classrooms. During this lesson, groups of learners use a Makey Makey to build a multi-player game controller. This article describes a lesson that has been successfully integrated with undergraduate students in an Introduction to Technology in Education course and with middle and high school students
Acknowledgements
No full textThe Journal of Technology-Integrated Lessons and Teaching (JTILT) is an online, peer-reviewed, open-access journal that is published semi-annually by the University of Wyoming in partnership with the Teacher Education Division of the Association for Educational Communications and Technology (AECT). The journal publishes original, technology-rich lessons, activities, professional development, and micro-credentials for PK-16+ professionals and their international equivalents.
The views expressed in JTILT are not necessarily those of the publisher nor the partnering association
Robotic Badges for Girl Scouts: Coding Exploration Integrated with Multimodal Literacy
No full textThis three-day computer science (CS) robotics coding exploration targets three Girl Scouts (n.d.) Brownie (2nd/3rd grades) badges. For each badge, a 60-minute session follows the 5E instructional model, which incorporates various robots to provide learners with diverse coding experiences. Throughout the coding exploration, learners engaged with real-life robot applications and used different robots to complete coding challenges. This learning exploration concluded by having learners complete at least one robot coding challenge per session, tailored to their capability, and utilize their expressive language skills to describe and explain their designed artifacts, algorithms, and block-based codes. This coding exploration can be extended to support broader elementary-level CS instruction.