Elementary mathematics is much more than the mastery of routine computations. Talking about invented strategies, finding patterns, and making conjectures are central to doing mathematics. In a classroom culture based on inquiry, communicating mathematical ideas in a variety of ways is vital to both children and adults. The Talking Mathematics project, funded by the National Science Foundation, explored ways teachers support mathematical discourse in elementary classrooms. Here, the authors share their reflections as well as many recommendations of the project participants. The book is designed for experienced elementary teachers and education students who are interested in supporting talk and building a culture of mathematical inquiry in the classroom. It highlights the role of talk in children's mathematics and shows ways to challenge and support children as they work. Three problems are included for teachers to try with their students, along with a selection of helpful readings. The approach is solidly based on theory and provides a practical framework and examples for teachers to use as they reflect on their practice. Classroom teachers, university students in mathematics methods or research courses, and service providers or staff developers who are planning teacher development experiences will find this book of great interest and value.