The Reasoning Algebraically about Operations Casebook was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the generalizations underlying the study of the operations in the elementary and middle grades and teaching strategies that support students' efforts to make sense of the concepts. Reading and discussing the cases under the guidance of the facilitator actively engages participants in their own learning enterprise as they- learn to recognize the key mathematical ideas with which students are grappling; consider the types of classroom settings and teaching strategies that support the development of student understanding; become aware of how core mathematical ideas develop across the grades; work on mathematical concepts and gain better understanding of mathematical content; and discover how to continue learning about children and mathematics. The casebook is composed of eight chapters: the first seven consist of classroom cases from kindergarten through grade 7; chapter 8 is an essay providing an overview of the research related to the situations described in the first seven chapters.