For better or worse we are entering a time of human/machine symbiosis known as the Age of the Centaur. This term comes from the chess world which has always seen the computer as a challenge to human dominance of the chess board. In various tests, chess champions acknowledged that computers have grown so sophisticated that they regularly beat Grand Masters. The surprise they found is that when chess masters team up with computers they win the most games. Hence the Age of the Centaur. We have to view the current interaction of our students with their smartphones as the intense preoccupation of a Centaur learning how to use a new tool that will become part of them. Something may be lost in this transformation, but something else may be gained.