This book presents ideas developed by Paul Cobb and his colleagues that have significantly influenced the field of mathematics education over the past three decades. In this volume, they are brought together for readers to present a clear view of how the field has changed during that time. During his career Cobb moved from looking at a single child's mathematical reasoning, to a class learning a particular mathematical topic, to a group of school teachers, and to a school district with all its teachers, teachers' teachers and principals. It was his wish to make a real difference and his constantly revised understanding of what it takes to do so that dictated this gradual broadening of the unit of analysis. This development is presented in this book with the help of chronologically organized previously published papers, each of which represents a distinct stage in this intellectual journey and is preceded by a new commentary that sheds additional light on the processes of reconceptualization and thus helps the reader to understand the reasons, mechanisms, and outcomes of researchers' constant pursuit of new insights. This book thus demonstrates how research develops and evolves when theory and practice are taken as mutually informing aspects of the researcher's work. In this sense, the volume is relevant to audiences primarily interested in practical aspects of mathematics education as well as to those whose primary interests lie in theoretical developments.

Zusammenfassung
Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb's own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb's contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb's work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have foundhis "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb's work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers' constant pursuit of new insights.

Inhalt
Radical Constructivism.- Social Constructivism.- Symbolizing and Instructional Design.- Mathematical Practices.- Equity and Identity.- Institutional Setting of Mathematics Teaching and Learning.