Topics of Interest: Ungrading, Service Learning, and Ethics

The SoTL group has been a great educational, professional development and inspirational tool for my career. It has showed me how interdisciplinary SoTL is. Our small group covers a large breadth from agriculture, education to intercultural development all with direct applications to SoTL. I have grown and learned from this community as a “junior” faculty member working with senior faculty. The importance of prioritizing, valuing and implementing SoTL for UW and it’s success as a land grant university is essential. UW should continue to pursue and strengthen SoTL to grow the foundation of teaching as research while improving UW for both students and faculty

On dimensions of maximal faces of completely positive cones

Because of the lack of characterizations of exposed extreme rays of the $n\times n$ copositive cone in general except for $n\le 6$, by no means so far can we characterize all maximal faces of the $n\times n$ completely positive cone for $n\ge 7$. In this paper, we use the information of the maximal faces of lower order completely positive cones to study the dimensions of a class of maximal faces of higher order completely positive cones. Specifically, we establish a connection between the dimension of a maximal face of a lower order completely positive cone and the dimension of a maximal face of a higher order completely positive cone via a connection between exposed rays of a lower order copositive cone and a higher order copositive cone. Such a connection is used to find formulas for the dimensions of a certain class of maximal faces of higher order completely positive cones, which has not been studied in the related literature to the best of our knowledge

A note on products of finite-dimensional quadratic matrices

Let $F$ be a field, $n$ be a positive integer, and $q(x) = (x-\lambda_1)(x-\lambda_2)$, where $\lambda_1$ and $\lambda_2$ are two nonzero elements in $F$. Denote by $\mathbb{M}_n(F)$ the ring of all $n \times n$ matrices over $F$. A matrix $A \in \mathbb{M}_n(F)$ is called quadratic with respect to $q(x)$ if $q(A) = 0$. In this paper, we investigate the question of when a matrix in $\mathbb{M}_n(F)$ can be expressed as a product of quadratic matrices with respect to $q(x)$. First, we prove that if $F$ is a field with more than $n+1$ elements, $k \ge 0$ is an integer, and $A \in \mathbb{M}_n(F)$ has determinant $\lambda_1^{s+2n}\lambda_2^{t+2n}$, where $s, t \ge 0$ are integers such that $s + t = kn$, then $A$ can be expressed as a product of $k+4$ quadratic matrices with respect to $q(x)$. In particular, if $\lambda_1 = 1$, $\lambda_2^r = 1$ for some integer $r \geq 2$, and $A \in \mathbb{M}_n(F)$ has a determinant that is a power of $\lambda_2$, then $A$ can be expressed as a product of at most $2r$ quadratic matrices with respect to $q(x)$. As a corollary, we derive results on the factorization of matrices as products of certain special quadratic matrices

Bridging Worlds: Turning SoTL Principles into Global Learning

More than ever, now there is a demand to an increasing collaborative scholarly work to advance global learning and instruction in international education. There is a need to examine and explore way of learning in diverse contexts globally. For example, we see the need in designing innovative study abroad programs, partnerships, and international exchanges that focus on exploration of learning environments, inquiry into learning, and intentional and self-reflected learning that have been informed by theory and research findings. Such evidence-based approach to teaching and learning is vital because it focuses on enhancing what We are learning and what We are not learning and what We are teaching and what We are not teaching globally.   Previously published on Gateway International Group LLC: ADD DIRECT LIN

Scratch Day: Hands-On Computational Thinking Activites for Youth and Adults

This lesson engages K-12 students, educators, and parents in original Scratch Day activities developed for lower-level (K-5th grade), upper-level (6th-12th grade), and post-secondary (adult) audiences. These lessons targeted individuals with limited knowledge regarding computational thinking. Activities involved sequencing and algorithmic expressions using block-based coding on the ScratchJr and Scratch web apps. Participants engaged in collaborative conversation and problem-solving as they made creative design decisions and debugged when they encountered coding issues

Transformations Throw Down: Extending Mathematics Knowledge with Assemblr

The purpose of these 8th grade math lessons was to extend students’ knowledge of sequences of mathematical transformations by providing students with a digital experience of transformations in a three- dimensional environment. Assemblr, an augmented reality app was used to create these experiences for students after they learned these concepts in 2D. Past studies noted that augmented reality activities and gamification promote active learning and increase academic performance (Lampropoulus, et al., 2022; Sukriadi et al,. 2023; Kurniawan, et al., 2024). Students used Assemblr to extend their knowledge in a 3D environment. Their learning was expressed in a game where correct answers to Assemblr challenge questions related to transformations initiated a turn for a team to connect dots and create a square.

Scratch Encore: Creating and Sustaining Culturally Responsive Computer Science Education

Scratch Encore (Canon Lab, n.d.) is a culturally relevant, student-centered, 14 module, computer science curriculum for 4th to 8th-grade learners that introduces foundational computing topics using the Scratch environment. It employs three key design goals: (a) supporting teachers, (b) supporting learners, and (c) using culturally responsive practices to address long standing inequities in computing. The curriculum offers equitable and effective learning experiences for students who have historically not had equal opportunities to fully participate in computing while providing a wide array of supports for educators who may be inexperienced with Scratch and/or programming. This article features a high-level overview of Scratch Encore and the first 6 modules in greater detail to help teachers understand the content and pacing of the curriculum

Introduction: Computational Thinking and Computer Science Special Issue

As computers become more functional and ubiquitous, societies are placing greater emphasis on programming and development skills. Computer science credentials and degree programs have long existed in higher education. Many high schools have also offered computer science courses like coding, computer graphics, game development, and cybersecurity. However, the desire to push computer science training to younger audiences is increasing. Currently, a dozen states require computer science instruction as a prerequisite for high school graduation (Barack, 2025). Many others provide opportunities for computer science experiences within PK-12 curricula. However, computer science topics may intimidate educators and students. Coding languages like Python, C#, and Javascript feel cryptic and take time to learn. Block options like Scratch provide easier entries into coding but still require sustained effort and attention

Eigenvalues and component factors in graphs

For a set $\mathcal{H}$ of connected graphs, an $\mathcal{H}$-factor of $G$ is a spanning subgraph $F$ of $G$ if each component of $F$ is isomorphic to an element of $\mathcal{H}.$ Kano, Lu and Yu [Electron. J. Combin. 26 (2019) P4.33] provided a good characterization based on an isolated vertex condition for the existence of a $\{K_{1,1},K_{1,2},\ldots,K_{1,k},$ $\mathcal{T}(2k+1)\}$-factor in graphs. Motivated by the above elegant result, we in this paper focus on the existence of a $\{K_{1,1},K_{1,2},\ldots,K_{1,k},$ $\mathcal{T}(2k+1)\}$-factor in graphs from perspective of eigenvalues. By adopting a crucial technique due to Tait [J. Combin. Theory Ser. A 166 (2019) 42-58] and combining typical spectral methods and structural analysis, we present tight sufficient conditions in terms of the spectral radius and the distance spectral radius for a graph to contain a $\{K_{1,1},K_{1,2},\ldots,K_{1,k},$ $\mathcal{T}(2k+1)\}$-factor, respectively