Intercultural Competencies in Scholarship of Teaching and Learning

In an increasingly interconnected world, fostering intercultural competence is essential for both personal growth and professional effectiveness. The Fulbright-Hays Spanish Language Program, with its immersive approach, aims to transform participants into interculturally competent individuals. This blog delves into a Scholarship of Teaching and Learning (SoTL) group study with a specific focus on intentional pedagogical practices in an intensive language and culture project in Costa Rica. By examining the experiences and reflections of participants, this study seeks to understand how such immersive programs enhance interactions across cultures and disciplines

On the rank of m×2×2 and m×3×2 tensors over arbitrary fields

In this paper, we provide exact rank computations for $m\times 2\times 2$ and $m\times 3\times 2$ tensors over arbitrary fields. By analyzing the structural properties of slice matrices, we reduce the tensor rank problem to computations involving matrix ranks and diagonalizations. This yields a complete and explicit rank classification for these families of tensors and provides a clearer structural understanding on rank of small tensors

Blog: First-Year Student Success

My Spring 2024 participation in the University of Wyoming Scholarship of Teaching and Learning (SoTL) group, facilitated by Dr. Dilnoza Khasilova, introduced me to other faculty and staff on campus who share an interest in the science of pedagogy. Dr. Khasilova’s guidance was invaluable, as she not only led the group but also invited guest speakers who helped us deepen our understanding of the IRB process and other critical aspects of our research. Through this experience, I learned how to narrow down my research questions, collaborate effectively with a team of like-minded faculty and staff, and create an impactful SoTL poster. With IRB approval now complete, I’m ready to begin a project researching best practices for the First Year Experience (FYE) course for Fall 2024. The project will incorporate qualitative and quantitative methods to understand the most beneficial aspects and perceived deficiencies of our FYE course

Integrating CT in Science Methods: Advancing Practice and Pedagogy

Despite the importance of computational thinking (CT) as a problem-solving process (Wing, 2008) and the growing spread in teacher education (Yadav et al., 2017), existing initiatives for preservice teachers (PSTs) tend to focus on the computer science domain without making explicit connections to disciplinary classroom settings and promoting critical perspectives. As a cohesive unit, this learning representation aims to assist PSTs in integrating CT into their work as they design and implement science-focused lessons. Centered around a contextual issue: accessing, growing, and sustaining food, this learning representation employs 2D and 3D block-based programming languages coupled with unplugged activities that demonstrate CT practices, processes, and concepts. PSTs’ group designs, lesson modifications, and full lesson plans provide opportunities for assessment

Derivations on rank kk triangular matrices

Let $n\geqslant 2$ be an integer and let $T_n(\mathcal{R})$ be the algebra of $n\times n$ upper triangular matrices over a unital ring $\mathcal{R}$. In this paper, we characterize derivations $\psi:T_n(\mathcal{R})\rightarrow T_n(\mathcal{R})$ on strictly upper triangular matrices, i.e., additive maps $\psi$ satisfying $\psi(AB)=A\psi(B)+\psi(A)B$ for all strictly upper triangular matrices $A,B\in T_n(\mathcal{R})$. We then deduce this result a complete structural characterization of derivations $\psi:T_n(\mathcal{R})\rightarrow T_n(\mathcal{R})$ on rank $k$ upper triangular matrices, where $1\leqslant k\leqslant n$ is a fixed integer and $\mathcal{R}$ is a division ring

New sufficient conditions for subdirect sums of Nekrasov matrices

Some new sufficient conditions ensuring that the $k$-subdirect sum of strictly diagonally dominant matrices and Nekrasov matrices is in the class of Nekrasov matrices are given. These sufficient conditions are different from those in [Electron. J. Linear Algebra, 38:339-346, 2022] and [Linear Multilinear Algebra, 64:208-218, 2016; 72:1044-1055, 2023]. In addition, some examples are given to illustrate the conditions presented

‘Sure why would they need Irish?’: Scoil an tSeachtar Laoch, Ballymun, and working-class decolonisation, c.1970-73

This article examines the struggle carried out by working-class Irish-language activists in Ballymun to found a gaelscoil (Irish-medium school) in the early 1970s. The article is based on archival research and interviews with two key participants involved in the campaign for Scoil an tSeachtar Laoch, Éilís Uí Langáin and Colm Ó Torna. The campaign to establish the school is viewed through the lenses of class and decolonisation. Firstly, the long-term socio-economic and political contexts to the campaign are outlined. Secondly, the social base and the pre-existing networks and ideology which allowed the campaign to develop are explored. Following this, the emergence of the campaign and its politics are examined. Finally, the lasting impact of the struggle for the school both locally and nationally is discussed. The conclusion reached is one that is of the utmost importance for Irish language, gaelscoil and decolonial activists, namely that it will be difficult to replicate the success of Ballymun again today in the neoliberal context because the material basis in terms of secure housing and a tight-knit urban community does not exist. At a time when there has been much talk in Irish revivalist circles about promoting Irish in Dublin with the launch of the Baile Átha Cliath le Gaeilge (Dublin For Irish) scheme, the history of Ballymun and Scoil an tSeachtar Laoch demonstrates how a secure home is the lynchpin on which real communal progress with regard the Irish language must be based. It is therefore necessary for those who wish to see the Irish language flourish in the city to learn the lessons of history and improve, first and foremost, the day-to-day lives of ordinary Dubliners by becoming active on the burning question of housing

On solutions of matrix equation AX=B{AX=B} over a Bezout domain

Let ${\mathrm R_{m,n}}$ be the set of $m\times n$ matrices over a Bezout domain $\mathrm R$ with identity $e\not= 0$ and let $0_{m,k}$ be the zero $m\times k$ matrix. Further, let $d_i(A)\in \mathrm{R}$ be an ideal generated by the $i$-th order minors of the matrix $A\in \mathrm{R}_{m,n},$ $i = 1, 2, \dots, \min\{m, n\}.$ In this article, we investigate a structure of solutions of a matrix equation $AX=B$, where $A\in {\mathrm R}_{m,n}$ and $B \in {\mathrm R}_{m,k}$ are known matrices and $X$ is unknown matrix over ${\mathrm R}$. It is known that matrix equation $AX=B$ is solvable over a Bezout domain $\mathrm{R}$ if and only if ${\rm rank } A = {\rm rank }A_B=r$ and $d_i(A) = d_i(A_B)$ for all $i = 1, 2, \dots , r,$ where $A_B= \begin{bmatrix} A & B \end{bmatrix}.$ On the other hand, $AX=B$ is solvable over $\mathrm{R}$ if and only if matrices $\begin{bmatrix} A & 0_{m,k} \end{bmatrix}$ and $A_B$ are right-equivalent, that is, the Hermitian normal forms of these matrices coincide. In this article, we give alternative necessary and sufficient conditions for the solvability of equation $AX=B$ over a Bezout domain $\mathrm R .$ If a solution of this equation exists, we also give an algorithm for its construction. We prove also that the matrix equation $AX=B$ over $\mathrm{R}$ has a symmetric solution if and only if $AX=B$ has a solution over $\mathrm{R}$ and the matrix $AB^T$ is symmetric. If symmetric solution exists, we propose the method for its construction

The angular spectrum of the 3×3\boldsymbol{3\times 3} copositive cone

Given a vector $x$ and a closed convex cone $\mathcal{C}$ in an $n$-dimensional inner product space. If $x$ is not in the dual cone of $\mathcal{C}$, then the maximal angle between $x$ and $\mathcal{C}$ is greater than $\frac{\pi}{2}$. In this case, a formula regarding the maximal angle between $x$ and $\mathcal{C}$ is given in terms of the metric projection of $-x$ on $\mathcal{C}$. Critical angles between two convex cones that are greater than or equal to $\frac{\pi}{2}$ are shown to be Nash angles by using this formula. Furthermore, some properties of critical pairs of the cone that is the sum of the $n\times n$ positive semidefinite cone and the cone of all $n\times n$ symmetric nonnegative matrices are presented. Since the $n\times n$ copositive cone is the same as the sum of the $n\times n$ positive semidefinite cone and the cone of all $n\times n$ symmetric nonnegative matrices for $n\le 4$, a detailed discussion on how to obtain the angular spectrum of the copositive cone of order 3 is given using the results proved in this paper

Lyapunov-like transformations on the tensor product of nuclear pairs of proper cones

Lyapunov-like transformation/matrix on a cone appears in the theory of dynamical systems and linear complementarity problems. The set of all Lyapunov-like transformations on a proper cone in a finite dimensional inner product space is the Lie algebra of the automorphism group of that cone. The dimension of this Lie algebra is called the Lyapunov rank. A pair of proper cones is said to be a nuclear pair if one of them is simplicial. In this paper, we find the Lyapunov rank and Lyapunov-like transformations on the tensor product of nuclear pairs of cones. Further, we prove that the space of Lyapunov-like transformations on the tensor product of a nuclear pair is the tensor product of the spaces of Lyapunov-like transformations on the individual cones. As a consequence, given a nuclear pair $(K_1,K_2)$, we describe the space of Lyapunov-like transformations on the cone of positive operators between $K_1$ and $K_2$