This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in mathematics education. A heuristic taxonomy of seven functions that mathematics educational technologies can serve to promote the aims of mathematical thinking is proposed. Two types of functions are distinguished: (1) "purpose" functions, that may affect whether students choose to think mathematically and (2) "process" functions that may support the component mental activities of mathematical thinking. Definitions and examples of computer software are used throughout the document to illustrate the seven functions. (TW)