Developing Essential Understanding Of Mathematical Reasoning Prek Gr 8

Author : John K. Lannin,Amy B. Ellis,Rebekah Elliott
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 44,9 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536665

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Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8 by John K. Lannin,Amy B. Ellis,Rebekah Elliott Pdf

How do your students determine whether a mathematical statement is true? Do they rely on a teacher, a textbook or various examples? How can you encourage them to connect examples, extend their ideas to new situations that they have not yet considered and reason more generally? How much do you know...and how much do you need to know? Helping your students develop a robust understanding of mathematical reasoning requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about mathematical reasoning. It is organised around one big idea, supported by multiple smaller, interconnected ideas - essential understandings.Taking you beyond a simple introduction to mathematical reasoning, 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.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 2024-06-11
Category : Electronic
ISBN : OCLC:1372385356

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Developing essential understanding of mathematical reasoning, PreK-gr. 8 by Anonim Pdf

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 51,7 Mb
Release : 2011
Category : Addition
ISBN : 0873536649

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Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2 by Janet H. Caldwell Pdf

What is the relationship between addition and subtraction? How do you know whether an algorithm will always work? Can you explain why order matters in subraction but not in addition or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organised around two big ideas and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining an understanding about addition and subtraction is essential as they are the foundation for students’ later learning of multiplication and division. Essential Understanding Series topics include: Number and Numeration for Grades Pre-K-2 Addition and Subtraction for Grades Pre-K-2 Geometry for Grades Pre-K-2 Reasoning and Proof for Grades Pre-K-8 Multiplication and Division for Grades 3-5 Rational Numbers for Grades 3-5 Algebraic Ideas and Readiness for Grades 3-5 Geometric Shapes and Solids for Grades 3-5 Ratio, Proportion and Proportionality for Grades 6-8 Expressions and Equations for Grades 6-8 Measurement for Grades 6-8 Data Analysis and Statistics for Grades 6-8 Function for Grades 9-12 Geometric Relationships for Grades 9-12 Reasoning and Proof for Grades 9-12 Statistics for Grades 9-12

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 45,9 Mb
Release : 2010
Category : Curriculum planning
ISBN : 0873536223

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Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 by Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles Pdf

"A series for teaching mathematics."--P. [1] of cover.

Author : Maria L. Blanton
Publisher : Unknown
Page : 102 pages
File Size : 43,9 Mb
Release : 2011
Category : Algebra
ISBN : 0873536681

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Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5 by Maria L. Blanton Pdf

Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Author : Michael T. Battista
Publisher : National Council of Teachers of English
Page : 151 pages
File Size : 53,8 Mb
Release : 2016
Category : Algebra
ISBN : 0873537025

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Reasoning and Sense Making in the Elementary Grades, Prekindergarten-Grade 2 by Michael T. Battista Pdf

Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.

Author : Amy B. Ellis,Kristen Bieda,Eric J. Knuth
Publisher : National
Page : 128 pages
File Size : 51,8 Mb
Release : 2012
Category : Education
ISBN : UIUC:30112127286570

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Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 by Amy B. Ellis,Kristen Bieda,Eric J. Knuth Pdf

Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.

Author : Monica Neagoy
Publisher : Corwin Press
Page : 210 pages
File Size : 54,6 Mb
Release : 2012-04-20
Category : Education
ISBN : 9781452283630

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Planting the Seeds of Algebra, PreK–2 by Monica Neagoy Pdf

Help young minds explore algebraic concepts Algebra is the gateway to higher education, and preparing students to grasp algebraic concepts increases their opportunities to succeed. This book shows teachers how to create a strong foundation in algebra for very young children. Using in-depth math "explorations," the author unpacks—step by step—the hidden connections to higher algebra. Each exploration contains an elegantly simple grade-banded lesson (on addition, subtraction, patterns, and odd and even numbers), followed by a discussion of the algebra connections in the lesson, as well as suggestions for additional problems to explore. Throughout, readers will find: Clear explanations of algebraic connections Specific strategies for teaching the key ideas of algebra Lesson modifications for older or younger students An array of age-appropriate problems, games, and lessons Planting the seeds of Algebra, PreK–2 helps teachers foster mathematical habits of mind in students such as critical thinking, problem solving, adaptability, agility, communication, curiosity, and imagination. Growth in these ways of thinking and doing will transfer to other areas of education and life—raising the bar and challenging students to aspire.

Author : Marian Small
Publisher : Teachers College Press
Page : 129 pages
File Size : 49,6 Mb
Release : 2015-04-10
Category : Education
ISBN : 9780807756607

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Building Proportional Reasoning Across Grades and Math Strands, K-8 by Marian Small Pdf

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.

Author : Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman
Publisher : Corwin Press
Page : 185 pages
File Size : 42,9 Mb
Release : 2017-09-21
Category : Education
ISBN : 9781506394237

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Mathematical Argumentation in Middle School-The What, Why, and How by Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman Pdf

This research-based book brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive - all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.

Author : Elham Kazemi,Allison Hintz
Publisher : Taylor & Francis
Page : 171 pages
File Size : 51,6 Mb
Release : 2023-10-10
Category : Education
ISBN : 9781003843948

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Intentional Talk by Elham Kazemi,Allison Hintz Pdf

Math teachers know the first step to meaningful mathematics discussions is to ask students to share how they solved a problem and make their thinking visible; however, knowing where to go next can be a daunting task. In Intentional Talk: How to Structure and Lead Productive Mathematical Discussions , authors Elham Kazemi and Allison Hintz provide teachers with a framework for planning and facilitating purposeful math talks that move group discussions to the next level while achieving a mathematical goal.Through detailed vignettes from both primary and upper elementary classrooms, the authors provide a window into how teachers lead discussions and make important pedagogical decisions along the way. By creating equitable opportunities to share ideas, teachers can orient students to one another while enforcing that all students are sense makers and their ideas are valued. They examine students' roles as both listeners and talkers, offering numerous strategies for improving student participation.Intentional Talk includes a collection of lesson planning templates in the appendix to help teachers apply the right structure to discussions in their own classrooms.

Author : Karen S. Karp,Barbara J. Dougherty,Sarah B. Bush
Publisher : Corwin
Page : 209 pages
File Size : 51,9 Mb
Release : 2020-09-19
Category : Education
ISBN : 9781544399508

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The Math Pact, Elementary by Karen S. Karp,Barbara J. Dougherty,Sarah B. Bush Pdf

A school-wide solution for students’ mathematics success! Do you sometimes start to teach a mathematics concept and feel like you’re staring at a sea of bewildered faces? What happens when you discover students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to school, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. Through this work, you will identify, streamline, and become passionate about using clear and consistent mathematical language, notations, representations, rules, and generalizations within and across classrooms and grades. Importantly, you’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features of this book include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · Practical templates and checklists · PLC prompts and discussion points When teachers unite across grades, students hit the ground running every year. Take the next step together as a team and help all your students build on existing understanding to find new success and most importantly, love learning and doing mathematics!

Author : Barbara J. Dougherty,Sarah B. Bush,Karen S. Karp
Publisher : Corwin Press
Page : 201 pages
File Size : 46,8 Mb
Release : 2020-09-19
Category : Education
ISBN : 9781544399638

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The Math Pact, High School by Barbara J. Dougherty,Sarah B. Bush,Karen S. Karp Pdf

A schoolwide solution for mathematics success! When "rules" seem to change from year to year, mathematics can seem like a disconnected mystery for students. Clear up the confusion with a Mathematics Whole-School Agreement! Expanded from the highly popular "Rules that Expire" series of NCTM articles, this essential guide leads educators through the collaborative step-by-step process of establishing a coherent and consistent learner-centered and equitable approach to mathematics instruction. You’ll learn to avoid "rules that expire"—tricks that may seem to help students in one grade but hurt in the long run. Features include · Abundant grade-specific examples · Effective working plans for sustainability · Barrier-busting tips, to-dos, and try-it-outs · PLC prompts and discussion points

Author : Roza Leikin
Publisher : Springer Nature
Page : 580 pages
File Size : 40,5 Mb
Release : 2023-03-17
Category : Education
ISBN : 9783031188688

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Mathematical Challenges For All by Roza Leikin Pdf

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristics of challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.

Author : Tracy Johnston Zager
Publisher : Taylor & Francis
Page : 393 pages
File Size : 44,9 Mb
Release : 2023-10-10
Category : Education
ISBN : 9781003839514

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Becoming the Math Teacher You Wish You'd Had by Tracy Johnston Zager Pdf

Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.