This book presents comprehensive results from case studies of three innovations in mathematics education that have much to offer toward understanding current reforms in this field. Each chapter tells the story of a case in rich detail, with extensi ve documentation, and in the voices of many of the participants-the innovators, the teachers, the students. Similarly, Volume 2 of Bold Ventures pre- sents the results from case studies of five innovations in science education. Volume 1 provides a cross-case analysis of all eight innovations. Many U.S. readers certainly will be very familiar with the name of at least if not all of the mathematics innovations discussed in this volume-for one example, the NCTM Standards-and probably with their general substance. Much of the education community's familiarity with these" arises from the pro- jects' own dissemination efforts. The research reported in this volume, however, is one of the few detailed studies of these innovations undertaken by researchers outside the projects themselves.