University of Wyoming Open Journals
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Bridging Worlds: Turning SoTL Principles into Global Learning
No full textMore 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
Blog: First-Year Student Success
No full textMy 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
On the rank of m×2×2 and m×3×2 tensors over arbitrary fields
No full textIn this paper, we provide exact rank computations for and 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
On dimensions of maximal faces of completely positive cones
No full textBecause of the lack of characterizations of exposed extreme rays of the copositive cone in general except for , by no means so far can we characterize all maximal faces of the completely positive cone for . 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
Integrating CT in Science Methods: Advancing Practice and Pedagogy
No full textDespite 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
The angular spectrum of the copositive cone
No full textGiven a vector and a closed convex cone in an -dimensional inner product space. If is not in the dual cone of , then the maximal angle between and is greater than . In this case, a formula regarding the maximal angle between and is given in terms of the metric projection of on . Critical angles between two convex cones that are greater than or equal to 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 positive semidefinite cone and the cone of all symmetric nonnegative matrices are presented. Since the copositive cone is the same as the sum of the positive semidefinite cone and the cone of all symmetric nonnegative matrices for , 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
Expressing matrices in as products of commutators of unipotent matrices
No full textThis paper aims to show that for two positive integers , every nonscalar matrix in the special linear group of degree over a field can be written as a product of a maximum of two commutators of unipotent matrices of index . This fact also holds for scalar matrices over a quadratically closed field. Using GAP, some examples are provided to highlight the significance of the field's cardinality and to show that the assumption of quadratically closed fields is essential
Transformations Throw Down: Extending Mathematics Knowledge with Assemblr
No full textThe 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.
Introduction: Computational Thinking and Computer Science Special Issue
No full textAs 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
The non-symmetric strong multiplicity property for sign patterns
No full textWe develop a non-symmetric strong multiplicity property for matrices that may or may not be symmetric. We say a sign pattern allows the non-symmetric strong multiplicity property if there is a matrix with the non-symmetric strong multiplicity property that has the given sign pattern. We show that this property of a matrix pattern preserves multiplicities of eigenvalues for superpatterns of the pattern. We also provide a bifurcation lemma, showing that a matrix pattern with the property also allows refinements of the multiplicity list of eigenvalues. We conclude by demonstrating how this property can help with the inverse eigenvalue problem of determining the number of distinct eigenvalues allowed by a sign pattern