This book reports on an extensive research effort involving teaching teachers and their students about dynamic geometry in an online collaboration environment. Specifically, it documents the cognitive development of a team of three students learning in that online social setting. The extended case study shows how the team enacted the tools and adopted group practices within an educational research project, which was designed to extend and support their ability to collaborate, to engage in mathematical discourse and to explore or construct dynamic-geometric figures. As a whole, the book provides detailed empirical support for the theory and practice of group cognition.