This book describes an approach to mathematics instruction that attempts to honor children's thinking and sense-making ability. The book aims to weave strands of mathematics (addition, subtraction, place value, and problem solving) together and offer a wide variety of contexts for genuine mathematical exploration. The book is intended as a practical resource, and throughout the book, classroom teachers reflect on their experiences and offer suggestions on a comprehensive range of issues, including how to get started, where to find good problems, when to provide help, when to step back, where manipulatives fit in, how to integrate problem solving into the curriculum, and how to assess students' learning. The book also shows how number sense and computation can be learned within a problem-centered framework. Classroom examples and teacher observations provide guidance in developing both invented and familiar computational approaches. (MM)