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In a clear, well-developed presentation this book provides the first systematic treatment of structure results for algebras which are graded by a goup. The fruitful method of constructing graded orders of special kind over a given order, culminating in applications of the construction of generalized Rees rings associated to divisors, is combined with the theory of orders over graded Krull domains. This yields the construction of generalized Rees rings corresponding to the central ramification divisor of the orders and the algebraic properties of the constructed orders. The graded methods allow the study of regularity conditions on order. The book also touches upon representation theoretic methods, including orders of finite representation type and other aspects of this theory applicable to the classification of orders. The final chapter describes the ring theoretical approach to the classification of orders of global dimension two, originally carried out by M. Artin using more geometrical methods. Since its subject is important in many research areas, this book will be valuable reading for all researchers and graduate students with an interest in non-commutative algebra.
The moment is right for critical reflection on what has been assumed to be a core part of schooling. In Ungrading, fifteen educators write about their diverse experiences going gradeless. Some contributors are new to the practice and some have been engaging in it for decades. Some are in humanities and social sciences, some in STEM fields. Some are in higher education, but some are the K-12 pioneers who led the way. Based on rigorous and replicated research, this is the first book to show why and how faculty who wish to focus on learning, rather than sorting or judging, might proceed. It includes honest reflection on what makes ungrading challenging, and testimonials about what makes it transformative. CONTRIBUTORS: Aaron Blackwelder Susan D. Blum Arthur Chiaravalli Gary Chu Cathy N. Davidson Laura Gibbs Christina Katopodis Joy Kirr Alfie Kohn Christopher Riesbeck Starr Sackstein Marcus Schultz-Bergin Clarissa Sorensen-Unruh Jesse Stommel John Warner
"Joe Feldman shows us how we can use grading to help students become the leaders of their own learning and lift the veil on how to succeed. . . . This must-have book will help teachers learn to implement improved, equity-focused grading for impact." —Zaretta Hammond, Author of Culturally Responsive Teaching & The Brain Crack open the grading conversation Here at last—and none too soon—is a resource that delivers the research base, tools, and courage to tackle one of the most challenging and emotionally charged conversations in today’s schools: our inconsistent grading practices and the ways they can inadvertently perpetuate the achievement and opportunity gaps among our students. With Grading for Equity, Joe Feldman cuts to the core of the conversation, revealing how grading practices that are accurate, bias-resistant, and motivational will improve learning, minimize grade inflation, reduce failure rates, and become a lever for creating stronger teacher-student relationships and more caring classrooms. Essential reading for schoolwide and individual book study or for student advocates, Grading for Equity provides A critical historical backdrop, describing how our inherited system of grading was originally set up as a sorting mechanism to provide or deny opportunity, control students, and endorse a "fixed mindset" about students’ academic potential—practices that are still in place a century later A summary of the research on motivation and equitable teaching and learning, establishing a rock-solid foundation and a "true north" orientation toward equitable grading practices Specific grading practices that are more equitable, along with teacher examples, strategies to solve common hiccups and concerns, and evidence of effectiveness Reflection tools for facilitating individual or group engagement and understanding As Joe writes, "Grading practices are a mirror not just for students, but for us as their teachers." Each one of us should start by asking, "What do my grading practices say about who I am and what I believe?" Then, let’s make the choice to do things differently . . . with Grading for Equity as a dog-eared reference.
This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.
Asao B. Inoue argues for the use of labor-based grading contracts along with compassionate practices to determine course grades as a way to do social justice work with students.
Implement standards-based grading practices that help students succeed! Classroom assessment methods should help students develop to their full potential, but meshing traditional grading practices with students’ achievement on standards has been difficult. Making lasting changes to grading practices requires both knowledge and willpower. Discover eight guidelines for good grading, recommendations for practical applications, and suggestions for implementing new grading practices as well as: ? The why’s and the how-to’s of implementing standards-based grading practices ? Tips from 48 nationally and internationally known authors and consultants ? Additional information on utilizing level scores rather than percentages ? Reflective exercises ? Techniques for managing grading more efficiently
The current grading system doesn't provide equal opportunity for low-income students and that leads to grade inflation, high dropout rates, productivity loss, and more. To help all students succeed, and promote equity in learning, vast changes in grading policies and scheduling are needed. In this research-based resource, the authors examine why current grading practices are ineffective for fostering a growth mindset, including the effect poverty has on student achievement. Beyond the Grade present an evidence-based case for switching to an equitable, standards-based grading system that improves student achievement for diverse student populations. Use this book as a schoolwide study guide to ensure all staff fully understand the school variables that can influence student motivation and enhance achievement for all learners. Benefits Ascertain the school variables that can influence student motivation and enhance achievement, including absenteeism, early literacy education, and more. Explore the disadvantages of traditional grading practices and the advantages that come from the equity of implementing standards-based grading practices. Receive guidance on providing students with the extra time and help they require to meet their learning needs and build a growth mindset. Access a list of questions that can help bring focus to your discussions about grading practices and overcome opposition to the implementation of standards-based grading. Gain resources, including sample schedules, for implementing standards-based grading practices in elementary, middle, and high schools to engage students, foster a growth mindset, and promote learning. Contents Introduction Part I: Assess Problems in Traditional Grading Practices Chapter 1: Why It's Time to Reassess Chapter 2: Flawed Grading Practices and Policies Chapter 3: Poverty Creates Variables That Affect Achievement Part II: Solutions to the Problems Chapter 4: Improved Grading Practices and Policies Chapter 5: Strategies That Effectively Address Poverty and Its Variables Chapter 6: Rethinking Scheduling Epilogue: The Power of a Teacher
Create and sustain a learning environment where students thrive and stakeholders are accurately informed of student progress. Clarify the purpose of grades, craft a vision statement aligned with this purpose, and discover research-based strategies to implement effective grading and reporting practices. Identify policies and practices that render grading inaccurate, and understand the role grades play in students’ future success and opportunities.
Research shows that the quality of feedback is one of the most important factors in improving student learning. Elements of Grading addresses problems with the primary source of feedback: grades. Learn several strategies for reforming grading policy, while examining the common arguments against reform. With this practical guide, you can improve grading to meet four essential criteria-accuracy, fairness, specificity, timeliness-and also make the grading process quicker and more efficient. The book does not offer an ultimate answer or perfect system but shows how to begin a constructive, evidence-based conversation about improving grading systems. Dr. Reeves analyzes the main features of the grading systems many schools use today (such as the 100-point system and the policy of giving points for missed work) and evaluates each of them by his four criteria. He challenges and inspires readers in this comprehensive reevaluation of what grades are, why we use them, and whom they benefit.