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In the second book in the Uncomplicating Mathematics Series, professional developer Marian Small shows teachers how to uncomplicate the teaching of algebra by focusing on the most important ideas that students need to grasp. Organized by grade level around the Common Core State Standards for Mathematics, Small shares approaches that will lead to a deeper and richer understanding of algebra for both teachers and students. The book opens with a clear discussion of algebraic thinking and current requirements for algebraic understanding within standards-based learning environments. The book then launches with Kindergarten, where the first relevant standard is found in the operations and algebraic thinking domain, and ends with Grade 8, where the focus is on working with linear equations and functions. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical "doers." This resource will be invaluable for pre- and inservice teachers as they prepare themselves to understand and teach algebra with a deep level of understanding.
In the second book in the Uncomplicating Mathematics Series, professional developer Marian Small shows teachers how to uncomplicate the teaching of algebra by focusing on the most important ideas that students need to grasp. Organized by grade level around the Common Core State Standards for Mathematics, Small shares approaches that will lead to a deeper and richer understanding of algebra for both teachers and students. The book opens with a clear discussion of algebraic thinking and current requirements for algebraic understanding within standards-based learning environments. The book then launches with Kindergarten, where the first relevant standard is found in the operations and algebraic thinking domain, and ends with Grade 8, where the focus is on working with linear equations and functions. In each section the relevant standard is presented, followed by a discussion of important underlying ideas associated with that standard, as well as thoughtful, concept-based questions that can be used for classroom instruction, practice, or assessment. Underlying ideas include: Background to the mathematics of each relevant standard. Suggestions for appropriate representations for specific mathematical ideas. Suggestions for explaining ideas to students. Cautions about misconceptions or situations to avoid. The Common Core State Standards for Mathematics challenges students to become mathematical thinkers, not just mathematical “doers.” This resource will be invaluable for pre- and inservice teachers as they prepare themselves to understand and teach algebra with a deep level of understanding. “Uncomplicating Algebra is an excellent resource for teachers responsible for the mathematical education of K–8 students. It is also a valuable tool for the training of preservice teachers of elementary and middle school mathematics.” —Carole Greenes, associate vice provost for STEM education, director of the Practice Research and Innovation in Mathematics Education (PRIME) Center, professor of mathematics education, Arizona State University “The current climate in North America places a major emphasis on standards, including the Common Core State Standards for Mathematics in the U.S. In many cases, teachers are being asked to teach content with which they themselves struggle. In this book, Dr. Small masterfully breaks down the big ideas of algebraic thinking to assist teachers, math coaches, and preservice teachers—helping them to deepen their own understanding of the mathematics they teach. She describes common error patterns and examines algebraic reasoning from a developmental viewpoint, connecting the dots from kindergarten through grade 8. The book is clearly written, loaded with specific examples, and very timely. I recommend it strongly as a ‘must-read’ for all who are seeking to broaden their understanding of algebra and how to effectively teach this important content area to children.” —Daniel J. Brahier, director, Science and Math Education in ACTION, professor of mathematics education, School of Teaching and Learning, Bowling Green State University
Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K-8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily.
Learn how to provide rich, online mathematics instruction that optimizes the limited time you have with students, while doing it in a way that does not overwhelm parents. This practical resource: highlights the value of open questions for differentiating instruction in the K–8 virtual environment; shows teachers how to adapt the materials that they are already using; illustrates how students can incorporate items from their home environment into math lessons; demonstrates how to build and maintain community with students online; explores the logistics of independent meetings with students and parents; provides samples and directions for creating tools like number lines and manipulatives at home; and much more. Featuring professional developer Marian Small’s special brand of lucid explanation of difficult concepts, engaging teaching examples, troubleshooting tips, and formative assessments, Teaching Math Online is a must-have for anyone teaching math either wholly online or in blended classrooms. Book Features: Provides immediate assistance for teachers with little or no experience teaching math online. Offers specific suggestions for supporting parents in their new role as the link between teacher and student. Addresses both logistical and pedagogical issues important to successful online learning. Provides online problem visuals for teachers to use with students. Includes reproducibles for creating math manipulatives and tools. Discusses distanced formative assessment. Includes access to exemplar videos for communicating with parents, and for providing students with spoken instruction that they can save and replay.
Now in its Fourth Edition—with more than 50 new questions and a new chapter on financial literacy—this bestselling resource helps experienced and novice teachers to effectively and efficiently differentiate mathematics instruction in grades K–8. Math education expert Marian Small shows teachers how to get started and become expert at using two powerful and universal strategies: Open Questions and Parallel Tasks. This edition is even easier for teachers to use in all quality state standards environments, including direct links to content standards and standards for mathematical practice. Parallel tasks and question examples are provided at each grade band: K–2, 3–5, and 6–8. Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners. “A must-read for every preservice and inservice teacher.” —Carole Greenes, professor emerita, Arizona State University “Small addresses the topic of open questions in a very accessible way. I look forward to using this book the next time I teach Elementary Math Methods to teacher candidates.” —Felicia Darling, math instructor at Santa Rosa Junior College
This new resource by math education expert Marian Small helps schools and districts to refine their teaching of standards-based mathematical practices. Small devotes a chapter to each of the eight standards of practice and includes a discussion of what each standard looks like in grades K–2, 3–5, and 6–8. Specific attention is given to helping students make sense of problems and persevere in solving them (Standard 1) and to encouraging students to create viable mathematical arguments and to effectively and respectfully critique the reasoning of others (Standard 3). The author also discusses how to formatively assess student performance for each practice standard. To provide additional support to U.S. teachers in their instructional planning, this resource includes attention to the Canadian math processes of visualization and mental math and estimation. Book Features: Addresses common misunderstandings and places where teachers and students struggle. Provides lucid explanations of difficult concepts. Presents fresh and engaging teaching examples. Offers helpful troubleshooting tips. Includes examples of student work. PROFESSIONAL DEVELOPMENT: Visit Marian Small’s website onetwoinfinity.ca for in-person and online professional development.
Educators of young children who don’t yet know the work of Marian Small are in for a gift—a treasure trove to enhance their teaching and thinking about math. This book focuses on the most important concepts and skills needed to provide early learners (preK–2) with a strong foundation in mathematics, in ways that are fun for both children and educators! For each mathematical concept, professional developer Marian Small provides sample activities and lessons, as well as guidance for using children’s books, games, manipulatives, and electronic devices. This resource also demonstrates how to differentiate instruction using tasks and questions designed to include all students. Like other Marian Small bestsellers, the text features her special brand of lucid explanation of difficult concepts, fresh and engaging teaching examples, troubleshooting tips, and formative assessments. Fun and Fundamental Math for Young Children is separated into special grade level sections for pre-K, kindergarten, first grade, and second grade. It can be used with any early childhood curriculum or as a stand-alone program in preschools. Marian Small is available for in-person and online professional development. “Within the first few pages it quickly became apparent that, whether you are a new or veteran teacher, your knowledge and appreciation of and for primary mathematics will grow page by page.” —From the Foreword by Graham Fletcher, math specialist, Atlanta, Georgia “Marian Small describes the development of major aspects of children’s mathematical thinking and connects them to many interesting and useful classroom activities.” —Herbert Ginsburg, professor emeritus, Teachers College, Columbia University “I love this book! The ideas are invaluable and the attention to detail is amazing.” —Nicki Newton, math consultant
In this insightful math resource for grades 3–8, popular professional developer Marian Small helps teachers understand and facilitate meaningful assessments to advance student understandings. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess; construct meaningful assessments—both formative and summative—to measure student understanding; and provide students with feedback that is clear, timely, and specific. Examples for each grade level are provided, along with details on how to pose questions, analyze errors, and help students understand and learn from their mistakes. The book provides specific guidance for when and how to offer feedback on both correct and incorrect answers in order to advance students’ mathematical thinking. Like other Marian Small bestsellers, Math That Matters combines her special brand of lucid explanation of difficult concepts with fresh and engaging activities. “Our understanding of the power of assessment to improve learning has deepened significantly in the past two decades. . . . Marian Small draws upon the critical research behind this understanding to explain what effective practice looks like. It is essential reading for all elementary educators and has the potential to profoundly affect the quality of mathematics assessment in our schools.” —From the Foreword by Damian Cooper, president, Plan Teach Assess “Teachers are often clamoring for concise classroom assessments that can capture students’ conceptual understanding. Clamor no more! Math That Matters is a timely response to that need. Marian Small removes the mystery of how to engage students in learning while collecting assessment data that drive next instructional plans.” —Karen Karp, Johns Hopkins University “The beauty of this book is that it is simple enough for brand new teachers and complex enough for experienced teachers. The author offers an amazing gift by linking assessment ideas directly to common state standards.” —Felicia Darling, Santa Rosa Junior College
If you're a librarian charged with collecting curriculum materials and children's literature to support the Common Core State Standards, then this book—the only one that offers explicit advice on collection development in curriculum collections—is for you. While there are many publications on the Common Core for school librarians and K–12 educators, no such literature exists for curriculum librarians at the post-secondary level. This book fills that gap, standing alone as a guide to collection development for curriculum librarians independent of the Common Core State Standards (CCSS). The book provides instruction and guidance to curriculum librarians who acquire and manage collections so you can develop a collection based on best practices. The book begins with a primer on the CCSS and how curriculum librarians can support them. Discussion of the Standards is then woven through chapters, arranged by content area, that share research-based practices in curriculum development and instruction to guide you in curriculum selection. Material types covered include games, textbooks, children's literature, primary sources, counseling, and nonfiction. Additional chapters cover the management of curriculum collections, testing collections, and instruction and reference, as well as how to support and collect for special needs learners. Current practices in collection development for curriculum materials librarians are also reviewed. The book closes with a discussion of the future of curriculum materials.
The pressure is on. Principals, expected to improve math performance at their schools, often don’t know where to begin—as they may be uncomfortable with math themselves or believe that their schools are already doing all that they can. How can K–12 school leaders recognize and ensure that their school or district is supporting good math instruction? Marian Small and Doug Duff provide the answer to that and other questions in The School Leader’s Guide to Building and Sustaining Math Success. Drawing on their vast experience working with administrators, Small and Duff provide practical advice and helpful tools for improving math instruction. They guide you through the initial steps of establishing a strong math culture, developing common tasks, and getting buy-in, and then offer specific suggestions for monitoring, supporting, and sustaining improvement. You’ll learn what sort of data to collect, what to look for in the classroom, what to listen for in conversations with teachers and students, and how to deal with reluctant staff or parents. With its real-world examples and insights, this book is essential reading for any principal who wants to bring about positive change and real growth in the teaching and learning of math in their school.