Developing Mathematical Reasoning in Grades K-12 PDF Download
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Author: Lee Stiff
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 304
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Book Description
This book sharpens your view of mathematical reasoning and its development at all grade levels. It reveals the various perspectives about the nature of reasoning. Also, it addresses the many issues and concerns involving mathematical reasoning - how learners reason in mathematics, how communication promotes reasoning, how teachers gather evidence of student reasoning, what curricular approaches can be profitably explored, what can be done to ensure success in developing reasoning, and more. This useful resource lets you dig deep into the topic and offers many ideas useful in your classroom.
Author: Lee Stiff
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 304
Get Book
Book Description
This book sharpens your view of mathematical reasoning and its development at all grade levels. It reveals the various perspectives about the nature of reasoning. Also, it addresses the many issues and concerns involving mathematical reasoning - how learners reason in mathematics, how communication promotes reasoning, how teachers gather evidence of student reasoning, what curricular approaches can be profitably explored, what can be done to ensure success in developing reasoning, and more. This useful resource lets you dig deep into the topic and offers many ideas useful in your classroom.
Author: John K. Lannin
Publisher: National Council of Teachers of English
ISBN: 9780873536660
Category : Effective teaching
Languages : en
Pages : 95
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Book Description
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: Jennifer M. Bay-Williams
Publisher: Corwin
ISBN: 1071818430
Category : Education
Languages : en
Pages : 265
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Book Description
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.
Author: Grace Kelemanik
Publisher: Heinemann Educational Books
ISBN: 9780325078151
Category : Education
Languages : en
Pages : 0
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Book Description
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.
Author: Matthew Oldridge
Publisher: Rowman & Littlefield
ISBN: 1475843348
Category : Education
Languages : en
Pages : 135
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Book Description
“Teaching through problem-solving” is a commonly used phrase for mathematics educators. This book shows how to use worthwhile and interesting mathematics tasks and problems to build a classroom culture based on students’ reasoning and thinking. It develops a set of axioms about problem-solving classrooms to show teachers that mathematics is playful and engaging. It presents an aspirational vision for school mathematics, one which all teachers can bring into being in their classrooms.
Author: Grace Kelemanik
Publisher:
ISBN: 9780325120072
Category :
Languages : en
Pages : 184
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Book Description
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.
Author: Michael T. Battista
Publisher: National Council of Teachers of English
ISBN: 9780873537025
Category : Algebra
Languages : en
Pages : 151
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Book Description
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: Theresa Wills
Publisher: Corwin Press
ISBN: 1071837125
Category : Education
Languages : en
Pages : 194
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Book Description
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.
Author: 06907bbp
Publisher: Critical Thinking Books & Software
ISBN: 9780894558856
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Mathematical Reasoning helps your child devise strategies to solve a wide variety of math problems. These books emphasize problem solving and computation to build the math reasoning skills necessary for success in higher level math and math assessments. All books are written to the standards of the National Council of Teachers of Mathematics. These highly effective activities take students far beyond drill-and-practice by using step-by-step, discussion-based problem solving to develop a conceptual bridge between computation and the reasoning required for upper-level math. Activities and units spiral slowly, allowing students to become comfortable with concepts but also challenging them to continue building their math skills.
Author: Maggie B. McGatha
Publisher: Corwin Press
ISBN: 1544316992
Category : Education
Languages : en
Pages : 360
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Book Description
Plan, focus, and lead: Your toolkit for inspiring math teachers What’s your go-to resource for guiding teachers to grow mathematics proficiency in their classrooms? This comprehensive toolkit for busy math coaches positions student learning as the focus of all work, and connects the Eight Mathematical Practices for students with NCTM’s Eight Effective Teaching Practices to deliver coaching strategies that work. Use the coaching cycle—plan, gather data, reflect—to build trust and rapport with teachers. Navigate coaching conversations. Plan, focus, and facilitate professional learning communities. Includes examples from the field, resources, and a plethora of tools to download and share. Create a professional learning plan that empowers you to lead with clarity and purpose.
