Teaching By Design In Elementary Mathematics Grades K 1

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Teaching by Design in Elementary Mathematics, Grades K–1

Author : Jennifer Stepanek
Publisher : Corwin Press
ISBN 13 : 1452238839
Total Pages : 257 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Teaching by Design in Elementary Mathematics, Grades K–1 by : Jennifer Stepanek

Download or read book Teaching by Design in Elementary Mathematics, Grades K–1 written by Jennifer Stepanek and published by Corwin Press. This book was released on 2010-11-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration.

Teaching by Design in Elementary Mathematics, Grades K1

Author : Jennifer Stepanek
Publisher : Corwin Press
ISBN 13 : 1412987040
Total Pages : 257 pages
Book Rating : 4.4/5 (129 download)

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Book Synopsis Teaching by Design in Elementary Mathematics, Grades K1 by : Jennifer Stepanek

Download or read book Teaching by Design in Elementary Mathematics, Grades K1 written by Jennifer Stepanek and published by Corwin Press. This book was released on 2010-11-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration.

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin Press
ISBN 13 : 1544374925
Total Pages : 189 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Strengths-Based Teaching and Learning in Mathematics by : Beth McCord Kobett

Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin Press. This book was released on 2020-02-27 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Building Thinking Classrooms in Mathematics, Grades K-12

Author : Peter Liljedahl
Publisher : Corwin Press
ISBN 13 : 1544374844
Total Pages : 454 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Building Thinking Classrooms in Mathematics, Grades K-12 by : Peter Liljedahl

Download or read book Building Thinking Classrooms in Mathematics, Grades K-12 written by Peter Liljedahl and published by Corwin Press. This book was released on 2020-09-28 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

Teaching Math at a Distance, Grades K-12

Author : Theresa Wills
Publisher : Corwin Press
ISBN 13 : 1071837125
Total Pages : 194 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Teaching Math at a Distance, Grades K-12 by : Theresa Wills

Download or read book Teaching Math at a Distance, Grades K-12 written by Theresa Wills and published by Corwin Press. This book was released on 2020-10-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Activating Math Talk

Author : Paola Sztajn
Publisher : Corwin Press
ISBN 13 : 1071821571
Total Pages : 225 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Activating Math Talk by : Paola Sztajn

Download or read book Activating Math Talk written by Paola Sztajn and published by Corwin Press. This book was released on 2020-09-24 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Answers to Your Biggest Questions About Teaching Elementary Math

Author : John J. SanGiovanni
Publisher : Corwin Press
ISBN 13 : 1071861220
Total Pages : 233 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Answers to Your Biggest Questions About Teaching Elementary Math by : John J. SanGiovanni

Download or read book Answers to Your Biggest Questions About Teaching Elementary Math written by John J. SanGiovanni and published by Corwin Press. This book was released on 2021-08-31 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your guide to grow and learn as a math teacher! Let’s face it, teaching elementary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Today, we recognize placing the student at the center of their learning increases engagement, motivation, and academic achievement soars. Teaching math in a student-centered way changes the role of the teacher from one who traditionally “delivers knowledge” to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching elementary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your elementary math classroom: 1. How do I build a positive math community? 2. How do I structure, organize, and manage my math class? 3. How do I engage my students in math? 4. How do I help my students talk about math? 5. How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey?

Teaching by Design in Elementary Mathematics, Grades 2–3

Author : Jennifer Stepanek
Publisher : Corwin Press
ISBN 13 : 1452238812
Total Pages : 257 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Teaching by Design in Elementary Mathematics, Grades 2–3 by : Jennifer Stepanek

Download or read book Teaching by Design in Elementary Mathematics, Grades 2–3 written by Jennifer Stepanek and published by Corwin Press. This book was released on 2010-11-19 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration.

Teaching by Design in Elementary Mathematics, Grades 4–5

Author : Melinda Leong
Publisher : Corwin Press
ISBN 13 : 1452238820
Total Pages : 273 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Teaching by Design in Elementary Mathematics, Grades 4–5 by : Melinda Leong

Download or read book Teaching by Design in Elementary Mathematics, Grades 4–5 written by Melinda Leong and published by Corwin Press. This book was released on 2010-12-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration.

Visible Learning for Mathematics, Grades K-12

Author : John Hattie
Publisher : Corwin Press
ISBN 13 : 1506362958
Total Pages : 209 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Visible Learning for Mathematics, Grades K-12 by : John Hattie

Download or read book Visible Learning for Mathematics, Grades K-12 written by John Hattie and published by Corwin Press. This book was released on 2016-09-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Author : Jennifer M. Bay-Williams
Publisher : Corwin
ISBN 13 : 1071818430
Total Pages : 265 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 by : Jennifer M. Bay-Williams

Download or read book Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 written by Jennifer M. Bay-Williams and published by Corwin. This book was released on 2021-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Teaching Numeracy

Author : Margie Pearse
Publisher : Corwin Press
ISBN 13 : 1452224404
Total Pages : 241 pages
Book Rating : 4.4/5 (522 download)

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Book Synopsis Teaching Numeracy by : Margie Pearse

Download or read book Teaching Numeracy written by Margie Pearse and published by Corwin Press. This book was released on 2011-03-23 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Understanding by Design

Author : Grant P. Wiggins
Publisher : ASCD
ISBN 13 : 1416600353
Total Pages : 383 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Understanding by Design by : Grant P. Wiggins

Download or read book Understanding by Design written by Grant P. Wiggins and published by ASCD. This book was released on 2005 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is understanding and how does it differ from knowledge? How can we determine the big ideas worth understanding? Why is understanding an important teaching goal, and how do we know when students have attained it? How can we create a rigorous and engaging curriculum that focuses on understanding and leads to improved student performance in today's high-stakes, standards-based environment? Authors Grant Wiggins and Jay McTighe answer these and many other questions in this second edition of Understanding by Design. Drawing on feedback from thousands of educators around the world who have used the UbD framework since its introduction in 1998, the authors have greatly revised and expanded their original work to guide educators across the K-16 spectrum in the design of curriculum, assessment, and instruction. With an improved UbD Template at its core, the book explains the rationale of backward design and explores in greater depth the meaning of such key ideas as essential questions and transfer tasks. Readers will learn why the familiar coverage- and activity-based approaches to curriculum design fall short, and how a focus on the six facets of understanding can enrich student learning. With an expanded array of practical strategies, tools, and examples from all subject areas, the book demonstrates how the research-based principles of Understanding by Design apply to district frameworks as well as to individual units of curriculum. Combining provocative ideas, thoughtful analysis, and tested approaches, this new edition of Understanding by Design offers teacher-designers a clear path to the creation of curriculum that ensures better learning and a more stimulating experience for students and teachers alike.

Teaching Student-centered Mathematics

Author : John A. Van de Walle
Publisher : Allyn & Bacon
ISBN 13 : 9780205408436
Total Pages : 0 pages
Book Rating : 4.4/5 (84 download)

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Book Synopsis Teaching Student-centered Mathematics by : John A. Van de Walle

Download or read book Teaching Student-centered Mathematics written by John A. Van de Walle and published by Allyn & Bacon. This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes activities with assessment tools necessary to teach basic math concepts for grades K-3.

Partnering With Parents in Elementary School Math

Author : Hilary Kreisberg
Publisher : Corwin Press
ISBN 13 : 1071810871
Total Pages : 175 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Partnering With Parents in Elementary School Math by : Hilary Kreisberg

Download or read book Partnering With Parents in Elementary School Math written by Hilary Kreisberg and published by Corwin Press. This book was released on 2021-02-15 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to build productive relationships in math education I wasn’t taught this way. I can’t help my child! These are common refrains from today’s parents and guardians, who are often overwhelmed, confused, worried, and frustrated about how to best support their children with what they see as the "new math." The problem has been compounded by the shift to more distance learning in response to a global pandemic. Partnering With Parents in Elementary School Math provides educators with long overdue guidance on how to productively partner and communicate with families about their children’s mathematics learning. It includes reproducible surveys, letters, and planning documents that can be used to improve the home-school relationship, which in turn helps students, parents, teachers, and education leaders alike. Readers will find guidance on how to: · Understand and empathize with what fuels parents’ anxieties and concerns · Align as a school and set parents’ expectations about what math instruction their children will experience and how it will help them · Communicate clearly and productively with parents about their students’ progress, strengths, and needs in math · Run informative and fun family events · support homework · Coach parents to portray a productive disposition about math in front of their children Educators, families, and students are best served when proactive, productive, and healthy relationships have been developed with each other and with the realities of today′s math education. This guide shows how these relationships can be built.

Every Math Learner, Grades K-5

Author : Nanci N. Smith
Publisher : Corwin Press
ISBN 13 : 1506390315
Total Pages : 305 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Every Math Learner, Grades K-5 by : Nanci N. Smith

Download or read book Every Math Learner, Grades K-5 written by Nanci N. Smith and published by Corwin Press. This book was released on 2017-02-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website.

Knowing and Teaching Elementary Mathematics

Author : Liping Ma
Publisher : Routledge
ISBN 13 : 1135149496
Total Pages : 290 pages
Book Rating : 4.1/5 (351 download)

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Book Synopsis Knowing and Teaching Elementary Mathematics by : Liping Ma

Download or read book Knowing and Teaching Elementary Mathematics written by Liping Ma and published by Routledge. This book was released on 2010-03-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.