This book is about mathematics, teaching and learning and how these are affected by a constructivist philosophy. Chapter 1 presents background to the study of an investigative approach to mathematics teaching. Chapter 2 provides an account of constructivism as a philosophy of knowledge and learning and includes a rationale for both radical and social constructivism and relationships between constructivism and knowledge, communication, and the classroom. Chapter 3 presents the author's early thinking about an investigative approach to mathematics teaching. Chapter 4 examines the choice of an ethnographic approach to research through participant observation and informal interviewing and also examines issues that arise from an interpretivist analysis. Chapters 6, 7, and 9 are case studies detailing a characterization of the teaching and thinking of three teachers and the development of theory through analysis of observations. Included is a descriptive model, the Teaching Triad, which arose from the categorization of data. Chapters 5 and 8 offer interludes of research reflections. Chapter 10 presents a synthesis of general concepts in terms of characteristics of an investigative approach and tensions that it raises for teachers in its classroom implementation. Chapter 11 offers a characterization of the teacher-researcher relationship which includes a descriptive model for reflective practice. Finally, Chapter 12 reexamines the relevance of constructivism to research outcomes in light of questions about the adequacy of radical constructivism to explain the complexities of classroom interaction. Each chapter contains notes. (Contains 221 references.) (MKR)