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| focus on mathematical practices: Engage in the Mathematical Practices Kit Norris, Sarah Schuhl, 2016 Increase student learning with engaging lesson plans and high-level tasks. In this user-friendly guide, mathematics teachers will discover more than 40 strategies for ensuring students learn critical reasoning skills and retain understanding. Each chapter is devoted to a different Standard for Mathematical Practice and offers an in-depth look at why the standard is important for students' understanding of mathematics. |
| focus on mathematical practices: Routines for Reasoning Grace Kelemanik, Amy Lucenta, Susan Janssen Creighton, 2016 Routines can keep your classroom running smoothly. Now imagine having a set of routines focused not on classroom management, but on helping students develop their mathematical thinking skills. Routines for Reasoning provides expert guidance for weaving the Standards for Mathematical Practice into your teaching by harnessing the power of classroom-tested instructional routines. Grace Kelemanik, Amy Lucenta, and Susan Janssen Creighton have applied their extensive experience teaching mathematics and supporting teachers to crafting routines that are practical teaching and learning tools. -- Provided by publisher. |
| focus on mathematical practices: Putting the Practices Into Action Susan O'Connell, John SanGiovanni, 2013 The Standards for Mathematical Practice promise to elevate students' learning of math from knowledge to application and bring rigor to math classrooms. Here, the authors unpack each of the eight Practices and provide a wealth of practical ideas and activities to help teachers quickly integrate them into their existing math program. |
| focus on mathematical practices: Activating Math Talk Paola Sztajn, Daniel Heck, Kristen Malzahn, 2020-09-24 Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning. |
| focus on mathematical practices: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| focus on mathematical practices: The Five Practices in Practice [Elementary] Margaret (Peg) Smith, Victoria Bill, Miriam Gamoran Sherin, 2019-08-14 Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. |
| focus on mathematical practices: Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 Jennifer M. Bay-Williams, John J. SanGiovanni, 2021-03-02 Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: Seven Significant Strategies to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers. |
| focus on mathematical practices: Five Practices for Orchestrating Productive Mathematics Discussions Margaret Schwan Smith, Mary Kay Stein, 2011 Describes five practices for productive mathematics discussions, including anticipating, monitoring, selecting, sequencing, and connecting. |
| focus on mathematical practices: Common Core Sense Christine Moynihan, 2023-10-10 Since the introduction of Common Core State Standards, many elementary teachers struggled with unpacking these processes and figuring out how to implement them in the classroom. Author Christine Moynihan introduces Common Core Sense: Tapping the Power of Mathematical Practices with the goal of making the eight Standards for Mathematical Practice more accessible and explicit.The Standards for Mathematical Practice provide a solid foundation for encouraging students to think, reason, and persevere like mathematicians. In her book, Moynihan demonstrates what each practice might look, sound, and feel like in the classroom by using the four-part GOLD framework:G - Go for the Goals: What are the major purposes of this practice?O - Open Your Eyes & Observe: What should you see the students doing as they utilize the practice? What should you see yourself doing as the teacher?L - Listen: What should you hear students saying as they use the practice? What should you hear yourself saying?D - Decide What to Do: What actions as a teacher must you put in to place to mine- the gold of the practice?Each chapter is dedicated to one practice and includes student work samples, classroom vignettes, and teacher thoughts. The consistent framework of the book outlines an easy way to learn and deepen the understanding of each practice. It provides teachers the planning and support they need to mine the GOLD. |
| focus on mathematical practices: A Focus on Addition and Subtraction Caroline Ebby, Elizabeth Hulbert, Rachel Broadhead, 2020-11-23 This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades. Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding; A focus on the OGAP Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on... collection, designed to aid the professional development of pre-service and in-service mathematics teachers. Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions. |
| focus on mathematical practices: Math in Focus Sta , 2017-08-10 |
| focus on mathematical practices: Strengths-Based Teaching and Learning in Mathematics Beth McCord Kobett, Karen S. Karp, 2020-02-27 This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful. |
| focus on mathematical practices: Everything You Need for Mathematics Coaching Maggie B. McGatha, Jennifer M. Bay-Williams, Beth McCord Kobett, Jonathan A. Wray, 2018-04-02 Math coaches wear many hats. You think on your feet and have to invent, react, and respond—often without time to prepare—in a myriad of professional contexts. What’s your go-to resource for support? Plan, focus, and lead: Your toolkit for inspiring math teachers Meet Everything You Need For Mathematics Coaching: Tools, Plans, and a Process That Works for Any Instructional Leader. This one-stop, comprehensive toolkit for improving mathematics instruction and learning is designed for busy math coaches and teacher leaders who often have to rely on their own competencies. Using the Leading for Mathematical Proficiency Framework, the authors position student outcomes as the focus of all professional work and connect the Eight Mathematical Practices for students with NCTM’s Eight Effective Teaching Practices to help you guide teachers toward growing mathematics proficiency in their classrooms. This hands-on resource details critical coaching and teaching actions, and offers nearly a hundred tools for: Shifting classroom practice in a way that leads to student math proficiency and understanding of mathematical concepts. Honing in on key areas, including content knowledge and worthwhile tasks, student engagement, questioning and discourse, analysis of student work, formative assessment, support for emergent language learners and students with special needs, and more. Navigating a coaching conversation. Planning and facilitating professional learning communities. Finding a focus for professional development or a learning cycle. Making connections between professional learning activities, teaching, and student learning. Using the coaching cycle—plan, gather data, reflect—to build trust and rapport with teachers. With examples from the field, a comprehensive list of resources for effective coaching, and a plethora of tools you can download and share with teachers, this toolkit is your must-have guide to designing a professional learning plan and leading with clarity and purpose. |
| focus on mathematical practices: Teaching for Thinking Grace Kelemanik, Amy Lucenta, 2022-01-24 Teaching our children to think and reason mathematically is a challenge, not because students can't learn to think mathematically, but because we must change our own often deeply-rooted teaching habits. This is where instructional routines come in. Their predictable design and repeatable nature support both teachers and students to develop new habits. In Teaching for Thinking, Grace Kelemanik and Amy Lucenta pick up where their first book, Routines for Reasoning, left off. They draw on their years of experience in the classroom and as instructional coaches to examine how educators can make use of routines to make three fundamental shifts in teaching practice: Focus on thinking: Shift attention away from students' answers and toward their thinking and reasoning Step out of the middle: Shift the balance from teacher-student interactions toward student-student interactions Support productive struggle: Help students do the hard thinking work that leads to real learning With three complete new routines, support for designing your own routine, and ideas for using routines in your professional learning as well as in your classroom teaching, Teaching for Thinking will help you build new teaching habits that will support all your students to become and see themselves as capable mathematicians. |
| focus on mathematical practices: A Focus on Fractions Marjorie M. Petit, Robert E. Laird, Edwin L. Marsden, Caroline B. Ebby, 2015-07-24 A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with the knowledge and tools to reveal students’ thinking so that they can modify their teaching and improve student learning of fraction concepts. A Focus on Fractions 2nd edition includes sections on the Common Core State Standards for Mathematics and the Ongoing Assessment Project (OGAP) Fraction Framework integrated into each chapter as well as a new chapter on the OGAP Fraction Progression and how it can be used for formative assessment purposes. This updated edition assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings. Additional images and examples serve to flesh out and supplement the newly-introduced concepts in this updated and expanded edition. Special Features: Looking Back Questions at the end of each chapter provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. New sections devoted to the CCSSM and OGAP Fraction Progression are woven throughout the book as well as a new stand alone chapter on the OGAP Fraction Progression. The OGAP Fraction Framework is an all-new eResource, now available as a free download from the book’s website: www.routledge.com/9781138816442. |
| focus on mathematical practices: Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics National Council of Teachers of Mathematics, 2006 Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence provides a rationale for focal points for each grade level, prekindergarten - 8. |
| focus on mathematical practices: Powerful Problem Solving Max Ray, 2013 How can we break the cycle of frustrated students who drop out of math because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say problem solved, by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the big picture of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be over and done, but to realize the many different ways to approach problems. Read a sample chapter. |
| focus on mathematical practices: Core Focus on Linear Equations McCaw, 2014-08-01 |
| focus on mathematical practices: Common Core Sense Christine Moynihan, 2023-10-10 Since the introduction of Common Core State Standards, many elementary teachers struggled with unpacking these processes and figuring out how to implement them in the classroom. Author Christine Moynihan introduces Common Core Sense: Tapping the Power of Mathematical Practices with the goal of making the eight Standards for Mathematical Practice more accessible and explicit.The Standards for Mathematical Practice provide a solid foundation for encouraging students to think, reason, and persevere like mathematicians. In her book, Moynihan demonstrates what each practice might look, sound, and feel like in the classroom by using the four-part GOLD framework:G - Go for the Goals: What are the major purposes of this practice?O - Open Your Eyes & Observe: What should you see the students doing as they utilize the practice? What should you see yourself doing as the teacher?L - Listen: What should you hear students saying as they use the practice? What should you hear yourself saying?D - Decide What to Do: What actions as a teacher must you put in to place to mine- the gold of the practice?Each chapter is dedicated to one practice and includes student work samples, classroom vignettes, and teacher thoughts. The consistent framework of the book outlines an easy way to learn and deepen the understanding of each practice. It provides teachers the planning and support they need to mine the GOLD. |
| focus on mathematical practices: Teaching Numeracy Margie Pearse, K. M. Walton, 2011-03-23 Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts. |
| focus on mathematical practices: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| focus on mathematical practices: Math Expressions Karen C. Fuson, 2013 |
| focus on mathematical practices: Mathematics as the Science of Patterns Patrick M. Jenlink, 2022 Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Pólya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching. |
| focus on mathematical practices: Guided Math Workshop Laney Sammons, Donna Boucher, 2017-03-01 This must-have resource helps teachers successfully plan, organize, implement, and manage Guided Math Workshop. It provides practical strategies for structure and implementation to allow time for teachers to conduct small-group lessons and math conferences to target student needs. The tested resources and strategies for organization and management help to promote student independence and provide opportunities for ongoing practice of previously mastered concepts and skills. With sample workstations and mathematical tasks and problems for a variety of grade levels, this guide is sure to provide the information that teachers need to minimize preparation time and meet the needs of all students. |
| focus on mathematical practices: Connecting the NCTM Process Standards and the CCSSM Practices Courtney Koestler, Mathew D. Felton, Kristen Bieda, Samuel Otten, 2013 Since their release in 2010, the Common Core State Standards Initiative (CCSSI) has had a profound impact on educational reform. The adoption of these standards represents an opportunity to support teachers in the common goal of helping students achieve a high-quality education. The Common Core State Standards for Mathematics will affect almost every K-12 student and the majority of the US’s teachers over the next decade. Although the CCSSM was created through a top-down approach, spearheaded by the National Governors Association and the Council of Chief State School officers, the primary audience and the ultimate users of the standards are classroom teachers. The focus of this book is on the Standards of Mathematical Practice outlined in the CCSSM. Although the CCSSM features these standards prominently, they are not described in detail and are not integrated into CCSSM's Standards for Mathematical Content. As a result, they are easy to overlook or ignore. The ideas in the Standards for Mathematical Practice are not new but linked to previous practices and standards articulated by other groups, including the National Council of Teachers of Mathematics (NCTM). For example, problem solving and reasoning are at the core of all practices outlined in CCSSM, just as they have been at the core of NCTM's vision for mathematics education since the publication of An Agenda for Action in 1980. Subsequent NCTM curriculum recommendations, emphasized and elaborated the role and place of mathematical processes and practices. The Standards of Mathematical Process outlined in CCSSM, and explored in greater detail in this book, reaffirm the significance of habits of mind, mathematical processes, and proficiency as crucial aspects of learning mathematics. Although the terms and emphasis may be new to teachers, the main ideas have existed a long time and remain unchanged. Intended for classroom teachers, this book makes explicit connections between these related ideas and the CCSSM Standards for Mathematical Practice. By connecting the CCSSM to previous standards and practices, the book serves as a valuable guide for teachers and administrators in implementing the CCSSM to make mathematics education the best and most effective for all students. |
| focus on mathematical practices: Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education Deborah Loewenberg, 2003-04-15 A clear need exists for substantial improvement in mathematics proficiency in U.S. schools. The RAND Mathematics Study Panel was convened to inform the U.S. Department of Education's Office of Educational Research and Improvement on ways to improve the quality and usability of education research and development (R&D). The panel identified three areas for focused R&D: development of teachers' mathematical knowledge used in teaching; teaching and learning of skills needed for mathematical thinking and problem-solving; and teaching and learning of algebra from kindergarten through the 12th grade. |
| focus on mathematical practices: Mathematical Mindsets Jo Boaler, 2015-10-12 Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age. |
| focus on mathematical practices: Mastering the Basic Math Facts in Multiplication and Division Susan O'Connell, John SanGiovanni, 2011 Presents an approach to teaching basic math facts to young students, featuring instructional strategies, tips, and classroom activities. Includes a CD-ROM with customizable activities, templates, recording sheets, and teacher tools. |
| focus on mathematical practices: A Focus on Multiplication and Division Elizabeth T. Hulbert, Marjorie M. Petit, Caroline B. Ebby, Elizabeth P. Cunningham, Robert E. Laird, 2017-06-26 A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K–6 mathematics educators. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers. |
| focus on mathematical practices: Teaching Math at a Distance, Grades K-12 Theresa Wills, 2020-10-12 Make Rich Math Instruction Come to Life Online In an age when distance learning has become part of the new normal, educators know that rich remote math teaching involves more than direct instruction, online videos, and endless practice problems on virtual worksheets. Using both personal experience and those of teachers in real K-12 online classrooms, distance learning mathematics veteran Theresa Wills translates all we know about research-based, equitable, rigorous face-to-face mathematics instruction into an online venue. This powerful guide equips math teachers to: Build students’ agency, identity, and strong math communities Promote mathematical thinking, collaboration, and discourse Incorporate rich mathematics tasks and assign meaningful homework and practice Facilitate engaging online math instruction using virtual manipulatives and other concrete learning tools Recognize and address equity and inclusion challenges associated with distance learning Assess mathematics learning from a distance With examples across the grades, links to tutorials and templates, and space to reflect and plan, Teaching Math at a Distance offers the support, clarity, and inspiration needed to guide teachers through teaching math remotely without sacrificing deep learning and academic growth. |
| focus on mathematical practices: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| focus on mathematical practices: Where's the Math? Mary Hynes-Berry, Laura Grandau, 2019-09-10 Use the powerful strategies of play and storytelling to help young children develop their math brains. This easy-to-use resource includes fun activities, routines, and games inspired by children's books that challenge children to recognize and think more logically about the math all around them. |
| focus on mathematical practices: Making and Breaking Mathematical Sense Roi Wagner, 2017-01-10 In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike. |
| focus on mathematical practices: Mathematics Learning in Early Childhood National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Committee on Early Childhood Mathematics, 2009-11-13 Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children. |
| focus on mathematical practices: Productive Math Struggle John J. SanGiovanni, Susie Katt, Kevin J. Dykema, 2020-03-09 All students face struggle, and they should—it is how they learn and grow. The teacher’s job is not to remove struggle, but rather to value and harness it, helping students develop good habits of productive struggle. But what’s missing for many educators is an action plan for how to achieve this, especially when it comes to math. This book guides teachers through six specific actions—including valuing, fostering, building, planning, supporting, and reflecting on struggle—to create a game plan for overcoming obstacles by sharing · Actionable steps, activities, and tools for implementation · Instructional tasks representative of each grade level · Real-world examples showcasing classroom photos and student work |
| focus on mathematical practices: High Quality Teaching and Learning Linda Darling-Hammond, ANN LIEBERMAN, 2013-06-19 This book brings together and compares the teacher education policies and practices of eight high-achieving countries to consider what creates high-quality teachers in today's world. |
| focus on mathematical practices: Reggio-Inspired Mathematics Richmond School District, 2015-09-03 This booklet documents our school district's collaborative inquiry project looking at how Reggio-inspired practices can inform and enhance primary mathematics teaching and learning. |
| focus on mathematical practices: A Guide for Teachers Susan O'Connell, 2016 The Math in Practice series supports teachers, administrators, and entire school communities as they rethink the teaching of mathematics in grades K-5. The series contains a Teacher's Guide, Administrator's Guide, and grade level books for grades K-5 which provide lesson ideas, teaching tips, and practice activities. -- |
| focus on mathematical practices: Implementing Effective Mathematics Teaching Practices in Kindergarten-grade 5 DeAnn Huinker, 2017 |
| focus on mathematical practices: Math Workshop Essentials Rusty Bresser, Caren Holtzman, 2018-08 |
Standards for Mathematical practice- Quick Reference Guide …
The Standards for Mathematical Practice (SMP) support students’ development of the mathematical skills and knowledge necessary to build a robust and connected understanding …
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Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional …
Mathematical Practices
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Ensuring that students have the opportunity to reason mathematically is one of the most difficult challenges that teachers face. A key component is creating a classroom in which discourse is …
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Effective Mathematics Teaching Practices 1. Establish mathematics goals to focus learning. 2. Implement tasks that promote reasoning and problem solving. 3. Use and connect …
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Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional …
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Use estimation and other mathematical knowledge to detect possible errors. Identify relevant external mathematical resources to pose and solve problems. Use technological tools to …
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These Everyday Mathematics Goals for Mathematical Practice (GMPs) provide a framework for instruction in mathematical practices similar to the framework for mathematical skills and …
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Overall: The mathematics tasks focus on developing CONCEPTUAL UNDERSTANDING and encouraging ALL students to make sense of the mathematics and to persevere in solving …
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Effective Mathematics Teaching Practices 1. Establish mathematics goals to focus learning. (EMTP 1) 2. Implement tasks that promote reasoning and problem solving. (EMTP 2) 3. Use …
Effective Mathematics Teaching Practices - National Council …
Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional …
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In this condition, Teacher must examine effective mathematical teaching practices that support each and every student to develop a deep understanding of mathematics; and developing a …
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By highlighting how mathematics teachers at the middle and high school levels view the practices in relation to their classrooms, we were able to target areas to support high-quality teaching …
mathematics | Standards for mathematical Practice - TN.gov
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they …
Effective Mathematics Teaching Practices - National Council …
Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning …
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Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These …
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focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide …
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Standards for mathematical practice lesson planning tool This tool supports educators to plan for and elicit evidence of student progress towards learning goals of a lesson. Using a blend of the …
Using the 5 Practices in Mathematics Teaching
We open with a brief discussion of the meaning of the term active learning, and we discuss the five practices (Smith and Stein 2011) as a particularly illuminating model. The five practices …
Standards for Mathematical practice- Quick Reference G…
The Standards for Mathematical Practice (SMP) support students’ development of the mathematical skills and knowledge necessary to build a …
Establish mathematics goals to focus learning. Researc…
Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning …
Mathematical Practices
mathematical problem solving. Practices 2 and 3 focus on reasoning and justifying, both for oneself and for others, and are essential for …
Using the Mathematical Practices Effectively in the …
These strands outlined behaviors of mathematically proficient students including adaptive reasoning, strategic competence, conceptual …
Diving Deep into Five Practices for Facilitating P…
Ensuring that students have the opportunity to reason mathematically is one of the most difficult challenges that teachers face. A key component is …
