Participants explore the base-ten structure of the number system, consider how that structure is exploited in multi-digit computational procedures, and examine how basic concepts of whole numbers reappear when working with decimals.

Building a Systems of Tens: Calculating With Whole Numbers and Decimals, Casebook (Developing Mathematical Ideas: Numbers and Operations)

Science & Math

Schifter, Deborah

Bastable, Virginia

Russell, Susan Jo

Mathematics

Modern Curriculum Pr

Participants examine the actions and situations modeled by the four basic operations. The seminar begins with a view of young children's counting strategies as they encounter word problems, moves to an examination of the four basic operations on whole numbers, and revisits the operations in the context of rational numbers.

Making Meaning of Operations: In the Domains of Whole Numbers and Fractions, Casebook (Developing Mathematical Ideas: Numbers and Operations)

Participants examine the actions and situations modeled by the four basic operations. The seminar begins with a view of young children's counting strategies as they encounter word problems, moves to an examination of the four basic operations on whole numbers, and revisits the operations in the context of rational numbers.

Making Meaning of Operations: In the Domains of Whole Numbers and Fractions (Developing Mathematical Ideas: Number and Operations)

Pearson Learning

"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.

Connecting Arithmetic to Algebra (Professional Book): Strategies for Building Algebraic Thinking in the Elementary Grades

Education & Teaching

Schools & Teaching

Heinemann

Connecting Arithmetic to Algebra Book Study Bundle Pack

If you ask students, "Why does that work?" do they know what you're asking and do you know what to listen for in their responses? Do you have images of what mathematical argument looks like in the elementary grades and how to help students learn to engage in this important practice? Do you have so much content to cover that finding time for this kind of work is difficult? But Why Does It Work? offers a simple, efficient teaching model focused on mathematical argument for developing the ability of students to justify their thinking and engage with the reasoning of others. Designed for individuals as well as study groups, this book includes access to classroom-ready instructional sequences, each built on a model supporting students in: <ul>
<li>noticing relationships across sets of problems, equations, or expressions</li> <li>articulating a claim about what they notice</li> <li>investigating their claim through representations such as manipulatives, diagrams, or story contexts</li> <li>using their representations to demonstrate why a claim must be true or not</li> <li>extending their thinking from one operation to another.</li> </ul>
Establishing a classroom culture where students gain confidence in their own mathematical voice and learn to value the contributions of their peers is a critical part of this work. The authors tell us, "If the idea underlying a student's reasoning is not made explicit, the opportunity for all students to engage in such thinking is lost." As students become a true community of mathematicians, they heighten each other's understanding by investigating questions, conjectures, and examples together. Enhanced with extensive video showing the instructional sequences in action-along with guiding focus questions and math investigations-But Why Does It Work? is a flexible approach that will help students confidently articulate and defend their reasoning, and share their deep thinking with others.

But Why Does It Work?: Mathematical Argument in the Elementary Classroom

Higgins, Traci

Kasman, Reva

Measuring Space in One, Two and Three Dimensions: Facilitator's Package

Pearson/Education

In recent years, a consensus has emerged around a constructivist vision for mathematics education, but few have seriously considered how to realise this vision. Employing case studies, the authors provide images of what is possible with this new mathematics pedagogy. "Reconstructing Mathematics Education" contains the experiences of teachers who, guided by evolving constructivist understandings of mathematics learning, work to bring the vision to life in their day-to-day practice. The reader is frequently brought into classrooms to observe students engaged in mathematical activity: second graders hypothesising about even and odd numbers; third graders demonstrating the commutative property of multiplication; sixth graders puzzling over the mysteries of fractions. In each situation, the authors consider the teacher's intentions in designing the activity, the instructional decisions she makes as the children engage in it, and her reflections afterwards.

Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform

Fosnot, Catherine Twomey

Teachers College Pr

first assignment of quantity to symbol

Creating mathematical community in elementary classrooms to support equitable engagement in deep mathematical content What does a mathematical community look like in an elementary classroom? How do teachers engage young mathematicians in deep and challenging mathematical content? How do we ensure that every student contributes their voice to this community? Interweaving Equitable Participation and Deep Mathematics: Building Community in the Elementary Classroom focuses on a dual commitment: to teaching deep and challenging mathematics and to equitable participation for all students in the classroom community. With practical strategies and real-life examples, Susan Jo Russell and Deborah Schifter offer a design for building community organized around four key aspects: every voice matters; collaboration supports student agency; student-created representations offer anchors, openings, and depth; and students become initiators and advocates for their own learning. Each chapter examines how teachers implement these ideas through video examples from six public elementary-school classrooms. A powerful resource for any educator interested in a mathematics education that fosters a true sense of community, this book <ul> <li>Provides a window into a learning community of educators applying their understanding of mathematics to develop a teaching practice that fosters students' curiosity, meaning-making, and mathematical agency</li> <li>Presents vivid examples of teachers and students in diverse classrooms engaged in rich mathematical tasks and deep collaborative conversations, inviting readers to reflect on their practices and students&#8242; learning</li> <li>Engages readers in math investigations to help them understand student thinking, provides reflection questions about the classroom video, and offers suggestions for taking next steps in one&#8242;s own practice</li> <li>Includes commentaries on the videos by a group of "critical friends"--educators with deep experience in mathematics and equity--and by the teachers of the classrooms in the videos</li> <li>Offers free online tools for professional development and book study groups, including a Facilitator's Guide and a Notes Organizer, and suggests resources for continued learning.</li> </ul> This book is a must-read for anyone passionate about creating positive change in the mathematics education system and ensuring that every student has the opportunity to thrive in their mathematical journey.

Interweaving Equitable Participation and Deep Mathematics: Building Community in the Elementary Classroom (Corwin Mathematics Series)

Corwin

See the best price to sell, buy, or rent books by Schifter, Deborah. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Schifter, Deborah

See the best price to sell, buy, or rent books by Schifter, Deborah. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Building a Systems of Tens: Calculating With Whole Numbers and Decimals, Casebook (Developing Mathematical Ideas: Numbers and Operations)

Making Meaning of Operations: In the Domains of Whole Numbers and Fractions, Casebook (Developing Mathematical Ideas: Numbers and Operations)

Making Meaning of Operations: In the Domains of Whole Numbers and Fractions (Developing Mathematical Ideas: Number and Operations)

Connecting Arithmetic to Algebra (Professional Book): Strategies for Building Algebraic Thinking in the Elementary Grades

Connecting Arithmetic to Algebra Book Study Bundle Pack

But Why Does It Work?: Mathematical Argument in the Elementary Classroom

Measuring Space in One, Two and Three Dimensions: Facilitator's Package

Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform

Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform

Interweaving Equitable Participation and Deep Mathematics: Building Community in the Elementary Classroom (Corwin Mathematics Series)