Search results for ""National Council of Teachers of Mathematics""

Focuses on themes surrounding evolving conceptions of learning and teaching. In the last three decades, research in mathematics education has undergone dramatic changes. The articles selected for this volume offer perspectives on the development of these themes, some of which include the process-product paradigm, gender and mathematics, problem solving, students' thinking and the role of cultural practises in the acquisition of mathematical concepts and procedures.

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No matter what the mathematics class, infusing reasoning and sense making into the daily mathematical experience of all high school students is crucial. ""All high school students"" includes low-performing students; gifted students; students of different racial, sociolinguistic and socioeconomic status; students with disabilites and students who are mathematically talented. The writers of this volume hope to further the dialogue about how to create for all students empowering mathematical experiences that incorporate reasoning and sense making.

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This book offers ways of presenting and developing three topics emphasised in Principles and Standards for School Mathematics: counting, vertex-edge graphs and iterative and recursive processes.

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How can you maximize your students learning as they engage in mathematics? What does the latest research reveal about developing mathematically strong and engrossing math instruction?Reimagining the Mathematics Classroom presents a comprehensive systems approach to examining mathematics teaching. It synthesizes and illustrates current research on the essential elements of mathematics teaching and learning, unpacking each component the classroom physical space; mathematical discourse, tasks, assessments; and families and communities and providing concrete practical strategies and tools teachers can apply directly to their work. In addition, tips on using technology to assess and enhance learning are embedded throughout the book.Reimagining the Mathematics Classroom delivers proven techniques and real classroom examples written or videotaped to address these and other important questions and concerns with which teachers grapple: How can I encourage collaborative problem solving during group work? How do I establish norms, routines, and ground rules for group and whole-class math discourse? How can I build on existing textbook problems to make them more rigorous, relevant, and accessible? What technologies help elicit and extend students mathematical thinking? How do I assess students in their development of knowledge of procedures, concepts, and mathematical practices? How can I transform parental involvement to collaborative partnerships and joint engagement? Reimagining the Mathematics Classroom is a resource to explore individually, to share with a colleague, or to discuss as part of a study group. Professional development tools, such as those described below, are woven throughout the text, with supplementary materials (math problem worksheets, conversational prompts, purposeful questions, videos, and so forth available on NCTM s More4U website.Classroom cases in each chapter provide real-life scenarios of the research-based practices and guiding principles articulated in the chapter. Math examples from a range of grade levels focus on concepts that students have traditionally struggled to understand conceptually. Cases include reflection questions to guide in the analysis and implementation of these ideas in your own teaching practice. Every chapter ends with a bulleted list of strategies to help you follow through on that chapter's main theme in your own classroom.Reimagining the Mathematics Classroom is as practical as it is inspirational. It is sure to be a valuable addition to your professional library.

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Why do some equations have one solution, others two or even more solutions and some no solutions? Why do we sometimes need to ""switch"" the direction of an inequality symbol in solving an inequality? What could you say if a student described a function as an equation?How much do you know...and how much do you need to know?Helping your students develop a robust understanding of expressions, equations and functions requires that you understand this mathematics deeply. But what does that mean?This book focuses on essential knowledge for teachers about expressions, equations and functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas - essential understandings. Taking you beyond a simple introduction to expressions, equations and functions, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students - and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students' understanding of the topic.Focus on the ideas that you need to understand thoroughly to teach confidently.

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Throughout history, the need for more sophisticated measurements has led to the discovery of more sophisticated mathematics. This book highlights this important idea in activities that help students explore an array of measurement strategies and techniques. Investigations probe ancient methods for performing such tasks as measuring the speed of ships at sea and estimating the distance of the sun from the earth. Students apply simple formulas to measure complex shapes, explore iterative processes that lead to measurement formulas and develop an original formula for measuring the size of a tree. They also discover how to use advanced technology to make measurements and mathematical models of complex real-world phenomena. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students and additional readings for teachers.

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On the Money: Mathematics Activities to Build Financial Literacy, K– Grade 5 provides elementary teachers with the opportunity to integrate lessons into their classroom that use mathematics to model financial literacy concepts and skills, while also using financial concepts and skills to appropriately model mathematics. Its seventeen chapters help students develop their mathematical and financial knowledge through activities such as sorting coins, saving money, sticking to a budget, and starting to earn money of your own. Each activity is aligned with the relevant Common Core Standards and the Jump$tart Financial Literacy Standards.

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Formative assessment is a powerful pedagogical tool whose purpose is to inform learning as it takes place, with the goal of moving learning forward on the basis of matching instruction to the edge of a student’s current understanding. A Fresh Look at Formative Assessment in Mathematics Teaching takes this frequently overlooked and often misunderstood methodology from a generic set of techniques to a potent, efficient, and effective course of action by explicating its role in effective mathematics teaching and learning, describing what it looks like in practice, and demonstrating how teachers can be supported in developing the knowledge and skills needed for its successful implementation.The book is specifically intended for educators who wish to improve mathematics teaching and learning. In particular, it is designed to provide mathematics teacher educators and professional development specialists with examples of where and how formative assessment can be integrated into a variety of professional learning efforts to support its effective use as a critical component of daily instructional decision-making. The chapters within A Fresh Look at Formative Assessment in Mathematics Teaching illustrate how formative assessment is deeply connected to many other instructional frameworks, tools, and approaches with which mathematics teachers and teacher educators are familiar, such as cognitively guided instructions (CGI) and the mathematical tasks framework, among others.

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Focus in Grade 2: Teaching with Curriculum Focal Points describes and illustrates learning paths for the mathematical concepts and skills of each grade 2 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about mathematical thinking and provide a foundation for fluency with the core ideas. This book also discusses common student errors and misconceptions, reasons the errors may arise and teaching methods or visual representations to address the errors.Because learning paths cut across grades, some discussion of related Focal Points at grades 1 and 3 have been included to describe and clarify prerequisite knowledge and show how the grade 2 understandings build on what went before.Focus in Grade 2, one in a series of grade-level publications, is designed to support teachers, supervisors and coordinators as they develop and refine the mathematics curriculum.

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Written for all teachers of young children, this book illustrates activities that promote early mathematics development for children ages three to five and "showcases" mathematics for the young child. The thirty-five activities in this book are distributed into five content areas: number and operations, geometry, algebra, measurement and data analysis. The content areas are connected by a continuing story, "Hanny the Honey Bear Discovers the World of Mathematics in the Big Zoo." Teachers can use this book to help themselves teach mathematics, learn mathematics and most important, "listen to children think!

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The same five practices teachers know and love for planning and managing powerful conversations in mathematics classrooms, updated with current research and new insights on anticipating, lesson planning, and lessons learned from teachers, coaches, and school leaders. This framework for orchestrating mathematically productive discussions is rooted in student thinking to launch meaningful discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated. Learn the 5 practices for facilitating effective inquiry-oriented classrooms: Anticipating what students will do and what strategies they will use in solving a problem Monitoring their work as they approach the problem in class Selecting students whose strategies are worth discussing in class Sequencing those students′ presentations to maximize their potential to increase students′ learning Connecting the strategies and ideas in a way that helps students understand the mathematics learned

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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.

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Mathematics education will never truly improve until it adequately addresses those students whom the system has most failed. The 2018 volume of Annual Perspectives in Mathematics Education (APME) series showcases the efforts of classroom teachers, school counselors and administrators, teacher educators, and education researchers to ensure mathematics teaching and learning is a humane, positive, and powerful experience for students who are Black, Indigenous, and/or Latinx. The book’s chapters are grouped into three sections: Attending to Students’ Identities through Learning Professional Development That Embraces Community Principles for Teaching and Teacher Identity To turn our schools into places where children who are Indigenous, Black, and Latinx can thrive, we need to rehumanize our teaching practices. The chapters in this volume describe a variety of initiatives that work to place these often marginalized students—and their identities, backgrounds, challenges, and aspirations—at the center of mathematics teaching and learning. We meet teachers who listen to and learn from their students as they work together to reverse those dehumanizing practices found in traditional mathematics education. With these examples as inspiration, this volume opens a conversation on what mathematics educators can do to enable Latinx, Black, and Indigenous students to build on their strengths and fulfill their promise.

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Do your students have the incorrect idea that addition “makes numbers bigger” and subtraction “makes numbers smaller”? Do they believe that subtraction is always “taking away”?What tasks can you offer - what questions can you ask - to determine what your students know or don’t know - and move them forward in their thinking?This book focuses on the specialized pedagogical content knowledge that you need to teach addition and subtraction effectively in prekindergarten–grade 2. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with these computations - not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts.Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of addition and subtraction. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.You have essential understanding. It’s time to put it into practice in your teaching.The Putting Essential Understanding into Practice Series moves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics - topics that are challenging to learn and teach but are critical to the development of mathematical understanding. Classroom vignettes and samples of student work bring each topic to life, and questions for reader reaction open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at nctm.org/more4U.

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This book explores the key concepts of middle school mathematics such as fractions, negative numbers, arithmetical operations, variables, the coordinate plane, and measurement formulas. It also highlights the rarely examined notions of the tree of mathematics and language of mathematics. The practical content knowledge is scaffolded using the history of the concepts in mathematics of various cultures around the world. The rich material for culturally responsive pedagogy is provided by relevant historical vignettes and alternative mathematical approaches.

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Throughout the working world, mathematical expertise and well-refined research skills are in great demand. Zoolutions creates a fun and interesting way for grade-school students to use research skills and math to solve problems. Featuring animals like mice, tigers and polar bears, Zoolutions provokes children's natural curiosity for problem-solving. Students must locate information on a given animal, read and analyze this information critically, and determine the solution using math and reasoning. In this way, students feel more confident in their ability to use information and ideas, and enjoy using math. Based on the National Council of Teachers of Mathematics Standards.

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Make learning count with activities and games that reflect early learning standards from the National Council of Teachers of Mathematics. Combining new activities and favorites from bestselling More Than Counting and Much More Than Counting by the same author team, this edition provides 124 math lessons for young children. Activities are organized by learning standard—number sense and operations, algebra, geometry, measurement and data analysis, and probability. A materials list, modifications for special needs, and a connection to early learning standards are provided for each activity.

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This text provides preservice prekindergarten through grade eight teachers with ideas, techniques, and approaches to teaching mathematics appropriate for the 21st century, and strongly integrates technology with hands-on experience. This is the only text to include practice Praxis II-style test questions to prepare teacher candidates to pass the high-stakes test used for teacher certification. The new sixth edition has been updated with the National Council of Teachers of Mathematics (NCTM) Curriculum Focal Points, which provide focus on significant concepts for each grade level.

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Number puzzles, spatial/visual puzzles, cryptograms, Sudoku, Kokuro, logic puzzles, and word games like Frame Games are all a great way to teach math and problem-solving skills to elementary and middle school students. In these two new collections, puzzle master Terry Stickels provides puzzles and brain games that range from simple to challenging and are organized by grade level and National Council of Teachers of Mathematics (NCTM) content areas. Each book offers over 300 brain games that will help students learn core math concepts and develop critical thinking skills. The books include a wide range of puzzle types and cover a variety of math topics, from fractions and geometry to probability and algebra.

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Everyday activities such as sharing a meal, sorting socks, and getting ready for school can be part of learning math. In the MathStart series, everyday life is the basis for each entertaining story. Simple math concepts are embedded in each story so that young children intuitively understand them. Adults can use the creative suggestions for activities in the back of each book to extend learning opportunities with children. Developmentally appropriate and correlated to school grade levels and the curriculum standards of the National Council of Teachers Of Mathematics, MathStart can give children a head start!

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Math Essentials, Middle School Level gives middle school math teachers the tools they need to help prepare all types of students (including gifted and learning disabled) for mathematics testing and the National Council of Teachers of Mathematics (NCTM) standards. Math Essentials highlights Dr. Thompson's proven approach by incorporating manipulatives, diagrams, and independent practice. This dynamic book covers thirty key objectives arranged in four sections. Each objective includes three activities (two developmental lessons and one independent practice) and a list of commonly made errors related to the objective. The book’s activities are designed to be flexible and can be used as a connected set or taught separately, depending on the learning needs of your students. Most activities and problems also include a worksheet and an answer key and each of the four sections contains a practice test with an answer key.

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Copublished with the National Council of Teachers of Mathematics (NCTM). With a focus on ways to best tailor instruction to captitalize upon the strengths each ELL brings to the classroom, The Common Core State Standards in Mathematics for English Language Learners, High School, explores some of the ways high school mathematics content can be made accessible to ELLs by building from their strengths and scaffolding their opportunities to learn more. The chapters included in this text describe specific lessons and instructional moves teachers may make that will not only support their students in learning the mathematical content, but also the associated English structures that accompany the content. Each chapter also provides Reflection Questions and Action Plans that are useful for practicing teachers, preservice teachers, graduate students, academics, researchers, and professional development providers.

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KenKen is the world's fastest growing puzzle since sudoku. It was developed in a Japanese Classroom in 2004 by renowned educator, Tetsuya Miyamoto, and was later introduced internationally as both an adult and educational math and logic puzzle in 2008. Originally intended to improve reasoning, creativity, concentration, and perseverance, this simple yet sophisticated puzzle has since expanded beyond the classroom into a global sensation. KenKen can be found daily in The New York Times and is now available in over 200 publications worldwide. Unlimited KenKen puzzles can be accessed on www.kenkenpuzzle.com and can also be played on mobile devices via the KenKen Classic app. It is supported by the National Council of Teachers of Mathematics (NCTM), the world's largest math education organization, and is used by over 30,000 educators worldwide.

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From bestselling authors Judith and Gary Muschla, The Math Teacher's Problem-a-Day is a hands-on resource containing 180 handy worksheets, one for each day of the school year, to help students in grades 4-8 acquire the skills needed to master mathematics. These reproducible worksheets are perfect for "sponge activities"—five-minute challenges to start or end a class period—that can also be used as supplemental lessons, homework, or extra credit. With problems based on the Standards and Focal Points of the National Council of Teachers of Mathematics, the book is designed to give students valuable practice in math skills, using specific activities to enhance critical thinking and boost test scores. The topics covered focus on the core math concepts and skills required for middle school students, including: Numbers and Operations Algebra Geometry Measurement Data Analysis Part of the 5-Minute Fundamentals series, The Math Teacher's Problem-a-Day is an important resource that will help today's students understand more concepts, make connections between branches of mathematics, and apply math skills to a variety of real-life problems.

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This second edition of the popular math teaching resource book Math Stories for Problem Solving Success offers updated true-to-life situations designed to motivate teenagers to use math skills for solving everyday problems. The book features intriguing short stories followed by sets of problems related to the stories that are correlated to the standards of the National Council of Teachers of Mathematics. Each of the easy-to-read stories is followed by three increasingly difficult groups of problem sets. This makes it simple for teachers to select the appropriate problem set for students of different abilities and at different grade levels. To further enhance student involvement, the stories feature recurring characters and can be used either sequentially or out of order. The problems in the book cover many basic math topics, including decimals, fractions, and percents; measurement; geometry; data, statistics, and probability; algebra; and problem solving. In addition to having all the answers, an Answer Key at the end of the book offers explanations and background information about the problems that can be helpful to both teachers and students. Math Stories for Problem Solving Success will help you show students that math is something they are already using every day.

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Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein’s Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid’s purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer’s Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane.

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Blue Ribbon Blueberry Pie. If the bear cubs gather enough nuts, seeds and blueberries, Mama Bear has agreed to make her special, lip-smacking-good pie. Each time they fill their baskets, the cubs count berries, seeds and nuts by putting them in groups of tens and ones to see if they have enough for pie. Everyday activities such as sharing a meal, sorting socks and getting ready for school can be part of learning math. In the MathStart Series, everyday life is the basis for each entertaining story. Simple math concepts are embedded in each story so that young children can intuitively understand them. Adults can use the creative suggestions for activities in the back of each book to extend learning opportunities with children. Developmentally appropriate and correlated to school grade levels and the curriculum standards of the National Council of Teachers of Mathematics, MathStart can give children a head start!Blue Ribbon Blueberry Pie is the best-but do these bear cubs have enough ingredients to bake one? Regrouping their berries, nuts, and seeds by tens and ones reveals that one cub has not done her fair bear share. John Speirs's irresistible bear cubs make this lesson in regrouping one children will enjoy. Blue Ribbon Blueberry Pie is the best-but do these bear cubs have enough ingredients to bake one? Regrouping their berries, nuts, and seeds by tens and ones reveals that one cub has not done her fair bear share. John Speirs's irresistible bear cubs make this lesson in regrouping one children will enjoy.

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"Seldom has a book been as timely or as necessary as Productive Math Struggle is today. . . One of the remarkable accomplishments of SanGiovanni, Katt, and Dykema’s work lies in how they seamlessly connect the research on high-quality tasks, high expectations, identity, and equity to productive math struggle. This is perhaps their greatest contribution. The authors see productive math struggle as a critical feature of mathematics classrooms that support access, equity, and empowerment, specifically arguing that every student is ‘worthy of struggle.’" From the Foreword by Matt Larson, Ph.D. Past President (2016-2018), National Council of Teachers of Mathematics Associate Superintendent for Instruction, Lincoln Public Schools, Nebraska Struggle is hard. Productive struggle is power. 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. Persevering through difficult challenges to reach new learning is the core of Productive Math Struggle. When left unsupported, struggle can become unproductive and demoralizing, negatively influencing students’ mathematical identities. The authors guide 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 and vignettes representative of each grade level Real-world examples showcasing classroom photos and student work samples A book study guide is available under the Free Resources tab that helps math educators to learn together on how to incorporate productive math struggle in their classrooms. Revolving around the idea that math is a way of thinking and understanding, and not just the pursuit of answers and procedures, this book empowers students to embrace productive struggle to build essential skills for learning and living—both inside and outside the classroom.

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