This article traces some of the influential ideas and motivations that have shaped a large part of the research on the use of new technologies in mathematics education over the past 40 years. Particular attention is focused on Papert's legacy, Celia's Hoyles' transformation of it, and how both relate to the current research landscape that features not only dramatic changes in hardware and software, but also new philosophical perspectives on the embodied nature of the learner and of mathematics.