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For those who devour Comprehending Math as I did, their teaching will be clearer, bolder, more connected. And for the ultimate beneficiaries, they will have a chance to understand just how integrally our world is connected. Ellin Oliver Keene, author of Mosaic of Thought No matter the content area, students need to develop clear ways of thinking about and understanding what they learn. But this kind of conceptual thinking seems more difficult in math than in language arts and social studies. Fortunately we now know how to help kids understand more about mathematics than ever before, and in Comprehending Math you'll find out that much of math's conceptual difficulty can be alleviated by adapting what we have learned from research on language and cognition. In Comprehending Math Arthur Hyde (coauthor of the popular Best Practice) shows you how to adapt some of your favorite and most effective reading comprehension strategies to help your students with important mathematical concepts. Emphasizing problem solving, Hyde and his colleagues demonstrate how to build into your practice math-based variations of: K - W - L visualizing asking questions inferring predicting making connections determining importance synthesizing He then presents a practical way to "braid" together reading comprehension, math problemsolving, and thinking to improve math teaching and learning. Elaborating on this braided model of approach to problem solving, he shows how it can support planning as well as instruction. Comprehending Math is based on current cognitive research and features more than three dozen examples that range from traditional story problems to open-ended or extended-response problems and mathematical tasks. It gives you step-by-step ideas for instruction and smart, specific advice on planning strategy-based teaching. Help students do math and get it at the same time. Read Comprehending Math, use its adaptations of familiar language arts strategies, and discover how deeply students can understand math concepts and how well they can use that knowledge to solve problems.

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

A collection of formal and informal English and Spanish reading assessments for students in grades K-12. Includes assessment instructions, assessments and teacher scoring forms.

In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text.The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m

Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.

This is an excellent reference book for curriculum planning and enhancement.