Sid Chaplin: A Writer with a Cause

The aim of this article is to recover the radical subtext of both the life and work of Sid Chaplin by reasserting the essentially political dimensions of his writing. Chaplin devoted the whole of his career as a writer to documenting not only the decline of the coal mining industry in the north-east of Britain where he lived, but he also traced the impact this process had on the working-class communities that were dependent on the pits. In his two later novels set in the city of Newcastle, The Day of the Sardine (1961) and The Watchers and the Watched (1962), Chaplin went on to dramatize similarly troubled changes in urban working-class life in the 1950s and 60s. The article not only argues that it is this nexus of class, politics and literature that translates so convincingly into his Newcastle novels, it also claims that it is the fundamental radicalism of his own literary project that explains the problematic neglect of his work by both critics and readers

College Major Selection, Social Class, and the Gender Pay Gap in the United States

Although 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

Fortune-Telling Finches: Linear Functions as Predictors

This lesson gives students experience with block coding Finch robots to move across plexiglass surfaces. It builds student computational thinking skills, mathematical self-efficacy, and interest in technology careers (McLurkin, et al., 2013; Martin, 2019; Kazi, 2023). Finch robots are small, physical robots that can be coded to move in a space. In this 8th grade math unit, conducted in the library, students identify relationships between variables while using block coding to make predictions and test hypotheses. This lesson extends students' knowledge of linear functions through observing patterns and using the guess and check strategy to complete a variety of challenges

Unraveling Author’s Purpose: 5th Graders Step into the Role of Creator!

In this lesson, students demonstrate an understanding of author’s purpose by developing their own narrative and bringing it to life with Bloxels, a platform/app and physical kit for people to build their own video games. This lesson is a progressive activity where students apply what they learned about the authors' purpose, according to TEKs Guide (n.d.) ELA.5.10, and create a narrative. Students are divided into groups and given a base “setting.” They can expand this setting to fit their narrative using the included Bloxels Planning Materials. Groups plan their narrative, design key scenes using Bloxels, and narrate them using a consistent viewpoint. Students are expected to include: text (script, setting description, character descriptions), graphics/images, point of view, anecdote or hyperbole, figurative language

Near-bipartite Leonard pairs

Let $\mathbb{F}$ denote a field, and let $V$ denote a vector space over $\mathbb{F}$ with finite positive dimension. A Leonard pair on $V$ is an ordered pair of diagonalizable $\mathbb{F}$-linear maps $A: V \to V$ and $A^* : V \to V$ that each act on an eigenbasis for the other in an irreducible tridiagonal fashion. Let $A,A^*$ denote a Leonard pair on $V$. Let $\{v_i\}_{i=0}^d$ denote an eigenbasis for $A^*$ on which $A$ acts in an irreducible tridiagonal fashion. For $0 \leq i \leq d$, define an $\mathbb{F}$-linear map $E^*_i : V \to V$ such that $E^*_i v_i = v_i$ and $E^*_i v_j = 0$ if $j \neq i$ $(0 \leq j \leq d)$. The map $F = \sum_{i=0}^d E^*_i A E^*_i$ is called the flat part of $A$. The Leonard pair $A,A^*$ is bipartite whenever $F=0$. The Leonard pair $A,A^*$ is said to be near-bipartite whenever the pair $A-F, A^*$ is a Leonard pair on $V$. In this case, the Leonard pair $A-F, A^*$ is bipartite and called the bipartite contraction of $A,A^*$. Let $B,B^*$ denote a bipartite Leonard pair on $V$. By a near-bipartite expansion of $B,B^*$, we mean a near-bipartite Leonard pair on $V$ with bipartite contraction $B,B^*$. In the present paper, we have three goals. Assuming $\mathbb{F}$ is algebraically closed, (i) we classify up to isomorphism the near-bipartite Leonard pairs over $\mathbb{F}$; (ii) for each near-bipartite Leonard pair over $\mathbb{F}$ we describe its bipartite contraction; (iii) for each bipartite Leonard pair over $\mathbb{F}$ we describe its near-bipartite expansions. Our classification (i) is summarized as follows. We identify two families of Leonard pairs, said to have Krawtchouk type and dual $q$-Krawtchouk type. A Leonard pair of dual $q$-Krawtchouk type is said to be reinforced whenever $q^{2i} \neq -1$ for $1 \leq i \leq d-1$. A Leonard pair $A,A^*$ is said to be essentially bipartite whenever the flat part of $A$ is a scalar multiple of the identity. Assuming $\mathbb{F}$ is algebraically closed, we show that a Leonard pair $A,A^*$ over $\mathbb{F}$ with $d \geq 3$ is near-bipartite if and only if at least one of the following holds: (i) $A,A^*$ is essentially bipartite; (ii) $A,A^*$ has reinforced dual $q$-Krawtchouk type; and (iii) $A,A^*$ has Krawtchouk type

The numerical range of matrix products

We discuss what can be said about the numerical range of the matrix product $A_1A_2$ when the numerical ranges of $A_1$ and $A_2$ are known. If two compact convex subsets $K_1, K_2$ of the complex plane are given, we discuss the issue of finding a compact convex subset $K$ such that whenever $A_j$ ($j=1,2$) are either unrestricted matrices or normal matrices of the same shape with $W(A_j) \subseteq K_j$, it follows that $W(A_1A_2) \subseteq K$. We do this by defining specific deviation quantities for both the unrestricted case and the normal case

PK-12 Lesson Design Competition Awards Introduction

Hundreds of tiny, colorful, plastic cubes lay strewn across tables; dozens of ideas are being tossed about; and a crowd of people gather with a common goal of effectively integrating technology to improve teaching and learning. This was the PK-12 Lesson Design Competition at the 2024 Association for Educational Communications and Technology (AECT) International Convention. The Teacher Education Division (TED) of AECT sponsors this annual design competition. The professional community of TED members promote theory, research, and practice that supports teachers and teacher educators to design effective learning experiences for diverse learners

Connections between points of convexity of functions and centrality of elements in C∗C^*-algebras

In this paper, we give a characterization of central elements in a $C^*$-algebra $\mathcal{A}$ in terms of points of convexity of scalar functions. We prove that if $D$ is an open interval and $f\in\mathcal{C}^2(D)$ is a convex function satisfying a certain inequality, then a self-adjoint element $a\in\mathcal{A}$ with spectrum in $D$ is central if and only if it is a point of convexity of $f$. The class of functions with these properties contains the nontrivial real exponential ones and the power ones with exponent outside $[-1,2]$

Minimal rank weighted weak Drazin inverses

The concept of a minimal rank weak Drazin inverse for square matrices is extended to rectangular matrices. Precisely, a minimal rank weighted weak Drazin inverse is introduced and its properties are investigated. Some known generalized inverses such as the weighted Drazin inverse, the weighted core-EP inverse, and the weighted $p$-WGI are particular cases of a minimal rank weighted weak Drazin inverse. Thus, a wider class of generalized inverses is proposed. General representation forms of a minimal rank weighted weak Drazin inverse are presented as well as its canonical form. Applying the minimal rank weighted weak Drazin inverse, corresponding systems of linear matrix equations are solved and their solutions are expressed. As consequences of our results, new properties of minimal rank weak Drazin inverse are obtained

The nonnegative inverse eigenvalue problem with prescribed zero patterns in dimension three

The nonnegative inverse eigenvalue problem is considered in this paper with the additional restriction of fixed zero patterns in the matrix. A full analysis of the $3\times 3$ case is given. Some remarks on the four-dimensional case are made