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Digital Florilegium: A High-Tech Twist on an Ancient Reading Practice
No full textThis lesson explains an approach to engaging students in close reading of challenging texts. It introduces florilegium, an ancient reading practice utilized by copyists in medieval European monasteries. This lesson’s approach to florilegium took a digital twist: rather than hand-writing snippets of text into a copybook as medieval monks might, we used a Google form to capture the whole class’s snippets from a shared reading. These text snippets became a shared digital repository that students could use to engage the text in a variety of interactive, creative ways. In the instance described in this article, the students were graduate students taking an online Educational Technology course, but the practice is flexible and could be adapted for use in many different content areas and grade levels
Exploring Geometry and Art through Tessellations
No full textIn this lesson, elementary school students explore geometric shapes and tessellations using a Cricut Maker 3. During Part 1 of the activity, students review geometric concepts of regular versus irregular polygons and lines of symmetry. This includes using shapes cut by the Cricut machine to determine which regular polygons form a tessellation when put together. Then students answer reflection questions. During Part 2, there is a discussion about how the artist MC Escher used different types of symmetry (e.g., translations, rotations, and reflections) to modify irregular shapes to create tessellations. In Part 3, students are given materials to prototype their own tessellation using regular and irregular shapes and at least one type of symmetry transformation
Using Roblox to Explore Natural Selection
No full textThis is part of a series of biology lessons that teach 9th to 12th graders about natural selection and uses the Roblox game to engage students. This lesson begins with a reminder to students about expectations and rules regarding appropriate use of technology, which can provide opportunities to explore scientific concepts in the virtual environment of Roblox. Students are expected to explore the Darwin postulates of natural selection using the examples provided. Then they discuss their findings with fellow students. This discussion is followed by an activity where students model evolution using previously created Roblox games. Next, students create their own Roblox game. This lesson concludes with students exchanging their finished games for others to explore
Using Discussion Boards to Teach CSS and Improve Canvas Course Layouts
No full textIn this three-week lesson, situated in a five-week, shortened summer course, instructional design graduate students learn basic cascading stylesheet (CSS) skills to facilitate page layouts within learning management systems. During Week 1, basic HTML tags (e.g., heading levels, lists, paragraphs, images, divider, span, link tags) and tag attributes, including style (used for inline CSS in Canvas), are introduced. In Week 2, learners are introduced to CSS attributes: background color, font color, borders, margins, and padding. During Week 3, they learn about block position, float, clear, and z-index. Throughout the three weeks, learners leverage low-stakes discussion boards to share ideas and refine skills
Structured level-2 condition numbers of matrix functions
No full textMatrix functions play an increasingly important role in many areas of scientific computing and engineering disciplines. In such real-world applications, algorithms working in floating-point arithmetic are used for computing matrix functions and additionally input data might be unreliable, e.g., due to measurement errors. Therefore, it is crucial to understand the sensitivity of matrix functions to perturbations, which is measured by condition numbers. However, the condition number itself might not be computed exactly as well due to round-off and errors in the input. The sensitivity of the condition number is measured by the so-called level-2 condition number. For the usual (level-1) condition number, it is well known that structured condition numbers (i.e., where only perturbations are taken into account that preserve the structure of the input matrix) might be much smaller than unstructured ones, which, e.g., suggests that structure-preserving algorithms for matrix functions might yield much more accurate results than general-purpose algorithms. In this work, we present a novel upper bound on the structured level-2 condition number, focusing on perturbation matrices within an automorphism group, a Lie or Jordan algebra, or the space of quasi-triangular matrices. In numerical experiments, we then compare the unstructured level-2 condition number with the structured one for some specific matrix functions such as the matrix logarithm, matrix square root, and matrix exponential
Flag-shaped blockers of 123-avoiding permutation matrices
No full textA blocker of -avoiding permutation matrices refers to the set of zeros contained within an -forcing matrix. Recently, Brualdi and Cao provided a characterization of all minimal blockers, which are blockers with a cardinality of . Building upon their work, a new type of blocker, flag-shaped blockers, which can be seen as a generalization of the -shaped blockers defined by Brualdi and Cao, are introduced. It is demonstrated that all flag-shaped blockers are minimum blockers. The possible cardinalities of flag-shaped blockers are also determined, and the dimensions of subpolytopes that are defined by flag-shaped blockers are examined
The number of spanning trees of the bipartite complement of a semiregular bipartite graph
No full textFor a bipartite graph on parts of cardinality and , the bipartite complement of is defined as the graph obtained from the complete bipartite graph by removing the edges of an isomorph of . In this paper, based on the matrix-tree theorem and the Schur complement technique, we give a determinant expression for the number of spanning trees of the bipartite complement of a semiregular bipartite graph. As by-products, we show that the corresponding result can generalize some previous results on the problem of enumerating spanning trees and obtain an explicit formula for the number of spanning trees of the bipartite complement of the subdivison of a regular circulant graph
Concave function inequalities for sum of matrices
No full textIn this paper, we present some norm inequalities for concave functions, which generalize the main results in [Y. Zhang. Linear Algebra Appl., 574:60-66, 2019]
Gildea, R. (2023) Backbone of the Nation: Mining Communities and the Great Strike of 1984-85. Yale University Press
No full textWelcoming Newcomers to Makerspaces
No full textThis article provides several self-guided, simple, creative activities to help learners gain familiarity and create with maker tools. Activities center around four categories: low technology, paper circuitry, Sphero robotics, and Cricut cutting machines. Learners use maker resources to build animals, construct LED bracelets or lanterns, code sirens, design stickers, and more. Although the intended audience for this article was undergraduate preservice teachers, most activities have also been completed by students in grades 3-8. Because materials differ by activity, they are presented in each activity