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

Relearning to Teach Arithmetic 
Relearning to Teach Arithmetic is designed to help teachers revisit the operations of addition, subtraction, multiplication, and division and to consider how students can develop meaningful approaches to these operations. The program consists of two packages—Addition &amp; Subtraction and Multiplication &amp; Division. Each package offers a videotape and study guide, and is designed for viewing in a professional development situation. Each session is 1 ½ hours, but most of the sessions can easily grown to 2 hours or more as teachers become immersed in the program.
The study guide included in each package is also available separately. This resource is great for in-service workshops or teacher study groups and can be used during school, after school, or during the summer – it’s adaptable to fit the schedule of your school. Teachers will come away better prepared to guide and support their students.

Relearning to Teach Arithmetic: Addition and Subtraction Package

Pearson Canada

Facilitator's Guide provides detailed agendas and teaching strategies.

Building A System of Tens, Facilitator's Guide; Number and Operations, Part 1 (Developing Mathematical Ideas)

Dale Seymour Pubn

Participants examine different attributes of size, develop facility in composing and decomposing shapes, and apply these skills to make sense of formulas for area and volume. They also explore conceptual issues of length, area, and volume, as well as their complex inter-relationships.

Developing Mathematical Ideas Measuring Space in One, Two, and Three Dimensions Facilitators Guide

Dale-Seymour Publications

Book by Russell, Susan Jo, Corwin, Rebecca, Mokros, Janice R., Kapisovsky, Peggy

Beyond Drill and Practice: Expanding the Computer Mainstream

Corwin, Rebecca

Mokros, Janice R.

Kapisovsky, Peggy

Council for Exceptional Children

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Books by Russell, Susan Jo