Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5

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Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5

Maria L. Blanton

Author : Maria L. Blanton
Publisher : Unknown
Page : 102 pages
File Size : 53,9 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.

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5

Carne Barnett-Clarke

Author : Carne Barnett-Clarke
Publisher : National Council of Teachers of English
Page : 83 pages
File Size : 40,5 Mb
Release : 2010
Category : Mathematics
ISBN : 0873536304

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Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades? How much do you know… and how much do you need to know? Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about rational numbers. It is organised around four big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to rational numbers, 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.

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5

Albert Dean Otto

Author : Albert Dean Otto
Publisher : National Council of Teachers of English
Page : 84 pages
File Size : 47,9 Mb
Release : 2011
Category : Division
ISBN : 0873536673

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Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 by Albert Dean Otto Pdf

Unpacking"" the ideas related to multiplication and division is a critical step in developing a deeper understanding. To those without specialised training, many of these ideas might appear to be easy to teach. But those who teach in grades 3-5 are aware of their subtleties and complexities. This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3–5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modelled by multiplication have an element that represents the scalar and an element that represents the quantity to which the scalar applies. Big Idea 2 relates to the algorithms that problem solvers have invented - some of which have become “standard” - for multiplying and dividing. The authors examine the ways in which counting, adding and subtracting lead to multiplication and division, as well as the role that these operations play in algebraic expressions and other advanced topics. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2

Barbara J. Dougherty

Author : Barbara J. Dougherty
Publisher : Unknown
Page : 60 pages
File Size : 40,9 Mb
Release : 2010
Category : Number concept
ISBN : 0873536290

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Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 by Barbara J. Dougherty Pdf

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world. 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

Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8

John K. Lannin,Amy B. Ellis,Rebekah Elliott

Author : John K. Lannin,Amy B. Ellis,Rebekah Elliott
Publisher : National Council of Teachers of English
Page : 95 pages
File Size : 46,9 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.

Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Prekindergarten-grade 2

Janet H. Caldwell

Author : Janet H. Caldwell
Publisher : National Council of Teachers of English
Page : 85 pages
File Size : 40,9 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

Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8

Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star

Author : Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star
Publisher : National Council of Teachers of English
Page : 116 pages
File Size : 47,7 Mb
Release : 2011
Category : Effective teaching
ISBN : 0873536703

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Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8 by Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star Pdf

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.

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Carolyn Kieran

Author : Carolyn Kieran
Publisher : Springer
Page : 443 pages
File Size : 49,6 Mb
Release : 2017-12-04
Category : Education
ISBN : 9783319683515

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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by Carolyn Kieran Pdf

This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5

Cheryl Rose Tobey,Emily R. Fagan

Author : Cheryl Rose Tobey,Emily R. Fagan
Publisher : Corwin Press
Page : 249 pages
File Size : 43,7 Mb
Release : 2013-11-27
Category : Education
ISBN : 9781483340203

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Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5 by Cheryl Rose Tobey,Emily R. Fagan Pdf

Take the guesswork out of grades 3-5 math assessment! Quickly pinpoint and reverse your students’ common math difficulties with this detailed and easy-to-follow resource from best-selling authors Cheryl Tobey and Carolyn Arline. Twenty research-based assessment probes help you ask the right questions to uncover just where your students get confused – while learning is already underway. These CCSM-aligned probes eliminate all guesswork and will help you: Systematically address conceptual and procedural mistakes Plan targeted instruction and remediation in multiplication and division, problem solving, the four operations, factorization, and beyond Master essential CCSM mathematical processes and proficiencies for Grades 3-5

Strengths-Based Teaching and Learning in Mathematics

Beth McCord Kobett,Karen S. Karp

Author : Beth McCord Kobett,Karen S. Karp
Publisher : Corwin
Page : 273 pages
File Size : 48,9 Mb
Release : 2020-02-27
Category : Education
ISBN : 9781544374901

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Strengths-Based Teaching and Learning in Mathematics by Beth McCord Kobett,Karen S. Karp Pdf

"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.

Connecting Arithmetic to Algebra

Susan Jo Russell,Deborah Schifter,Virginia Bastable

Author : Susan Jo Russell,Deborah Schifter,Virginia Bastable
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 52,9 Mb
Release : 2011
Category : Education
ISBN : 0325041911

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Connecting Arithmetic to Algebra by Susan Jo Russell,Deborah Schifter,Virginia Bastable Pdf

"To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.

Number and Operations

Deborah Schifter

Author : Deborah Schifter
Publisher : Unknown
Page : 164 pages
File Size : 53,9 Mb
Release : 1999
Category : Education
ISBN : UVA:X004622222

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Number and Operations by Deborah Schifter Pdf

Developing mathematical ideas : part 1, building a system of tens : DS21961.

Algebra in the Early Grades

James J. Kaput,David W. Carraher,Maria L. Blanton

Author : James J. Kaput,David W. Carraher,Maria L. Blanton
Publisher : Routledge
Page : 552 pages
File Size : 43,8 Mb
Release : 2017-09-25
Category : Education
ISBN : 9781351577090

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Algebra in the Early Grades by James J. Kaput,David W. Carraher,Maria L. Blanton Pdf

This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.

Early Algebraization

Jinfa Cai,Eric Knuth

Author : Jinfa Cai,Eric Knuth
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 44,7 Mb
Release : 2011-02-24
Category : Education
ISBN : 9783642177354

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Early Algebraization by Jinfa Cai,Eric Knuth Pdf

In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8

Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles

Author : Joanne Elizabeth Lobato,Amy B. Ellis,Randall Inners Charles
Publisher : National Council of Teachers of English
Page : 0 pages
File Size : 46,5 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.

Developing Essential Understanding Of Algebraic Thinking For Teaching Mathematics In Grades 3 5

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

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3/5 by Carne Barnett-Clarke Pdf

Developing Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 by Albert Dean Otto Pdf

Developing Essential Understanding of Number and Numeration for Teaching Mathematics in Prekindergarten--grade 2 by Barbara J. Dougherty Pdf

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

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

Developing Essential Understanding of Expressions, Equations, and Functions for Teaching Mathematics in Grades 6-8 by Gwendolyn M. Lloyd,Beth A. Herbel-Eisenmann,Jon R. Star Pdf

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by Carolyn Kieran Pdf

Uncovering Student Thinking About Mathematics in the Common Core, Grades 3-5 by Cheryl Rose Tobey,Emily R. Fagan Pdf

Strengths-Based Teaching and Learning in Mathematics by Beth McCord Kobett,Karen S. Karp Pdf

Connecting Arithmetic to Algebra by Susan Jo Russell,Deborah Schifter,Virginia Bastable Pdf

Number and Operations by Deborah Schifter Pdf

Algebra in the Early Grades by James J. Kaput,David W. Carraher,Maria L. Blanton Pdf

Early Algebraization by Jinfa Cai,Eric Knuth Pdf

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

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