CHAPTER 29 A Low Floor + High Ceiling for Mathematics Education George Gadanidis “The Fields Institute has been an integral part of math education knowledge development—facilitating access to deep thinkers, and fostering opportunities to ‘think-with-them’.” The first Fields Institute Symposium that I helped organize was on the topic of Online Mathematics Education, but it quickly expanded to address the broader subject of how computers can change mathematical learning. In planning the event, which ran in February 2003, I recall talking on the phone with the roving computer scientist and visionary Alan Kay, co-developer of what we now refer to as the computer “desktop.” I invited him to be a keynote speaker and he agreed, adding: “Seymour Papert is here with me. Would you like him to come, too?” Papert, a mathematician at MIT and one of the early pioneers of artificial intelligence, was internationally recognized as the seminal thinker about