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.

“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.

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

All the talk of closing the achievement gap in schools obscures a more fundamental issue: do the grades we assign to students truly reflect the extent of their learning? In this lively and eye-opening book, educator Myron Dueck reveals how many of the assessment policies that teachers adopt can actually prove detrimental to student motivation and achievement and shows how we can tailor policies to address what really matters: student understanding of content. In sharing lessons, anecdotes, and cautionary tales from his own experiences revamping assessment procedures in the classroom, Dueck offers a variety of practical strategies for ensuring that grades measure what students know without punishing them for factors outside their control; critically examining the fairness and effectiveness of grading homework assignments; designing and distributing unit plans that make assessment criteria crystal-clear to students; creating a flexible and modular retesting system so that students can improve their scores on individual sections of important tests. Grading Smarter, Not Harder is brimming with reproducible forms, templates, and real-life examples of grading solutions developed to allow students every opportunity to demonstrate their learning. Written with abundant humor and heart, this book is a must-read for all teachers who want their grades to contribute to, rather than hinder, their students' success.

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

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.

Developed for grades K-2, this resource provides teachers with strategies to build every student's mastery of high-level thinking skills, promote active learning, and encourage students to analyze, evaluate, and create. Model lessons are provided as they integrate strategy methods including questioning, decision-making, creative thinking, problem solving, and idea generating.