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:

• noticing relationships across sets of problems, equations, or expressions
• articulating a claim about what they notice
• investigating their claim through representations such as manipulatives, diagrams, or story contexts
• using their representations to demonstrate why a claim must be true or not
• extending their thinking from one operation to another.

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.

Susan Jo Russell is a principal scientist at the Education Research Collaborative at TERC. Following ten years of classroom teaching and coaching in elementary schools, Dr. Russell directed projects focused on mathematics professional development, research on students' and teachers' understanding of mathematics, and mathematics curriculum. She co-directed the development of the NSF-funded elementary curriculum, Investigations in Number, Data, and Space and the professional development materials, Developing Mathematical Ideas. Her recent work is on supporting teachers to integrate a focus on generalizing about the operations into their core arithmetic instruction.

Deborah Schifter is Principal Research Scientist at the Education Development Center (EDC) where she leads a range of projects concerning professional development in mathematics and research into student learning. Working with a variety of colleagues, she is coauthor of Reconstructing Mathematics Education, Developing Mathematical Ideas, The Mathematical Education of Teachers, and the Second Edition of Investigations in Number, Data, and Space. She also edited What's Happening in Math Class? (an anthology of teacher writing) and is co-editor of A Research Companion to the NCTM Standards. Deborah loves learning from the teachers with whom she works.

Virginia Bastable has been the Director of the SummerMath for Teachers Program at Mount Holyoke College since 1993. She taught middle school and high school mathematics for more than twenty years. She is coauthor of the Developing Mathematical Ideas professional development curriculum and the Second Edition of Investigations in Number, Data, and Space. Dr. Bastable particularly enjoys helping others to discover their interest and abilities in mathematics, even if those interests and abilities have been blunted by past negative experiences with the subject.