This book offers a new conceptual framework to reflect on the role of information and communication technology in mathematics education. Borba and Villarreal gave examples of research conducted in university-level education and a basic level, developed by their research group based in Brazil, and discuss their findings in the light of the relevant literature. Examples of research on education courses on-line mathematics, and the Internet are used in regular mathematics courses, are presented and discussed at the theoretical level. discussion of the theory developed in this book, along with examples of new, shed new light on discussions about visualization, experimentation, and multiple representations in mathematics education.