Most people agree that the best old-fashioned kind of education taught people to think. Perhaps some people disagreed on what, exactly, that meant, or just how to do it, but on the whole, it was considered a good thing to be able to use your brain for something more than just providing a place to hold your hat. But that was old-fashioned education, and nowadays many (if not all) scientists, mathematicians, and even artists use computational aids to help them in their work. The best use of such computational aids (in my opinion) is not as a substitute for thought (Garbage In, Gospel Out) but rather as an aid to thought: I call this process ``Computer-Mediated Thinking". It has become widely recognized in the past twenty years that this change in how people think has both enabled and necessitated a change in how people are educated. In this talk I will try to expose some interesting subtleties of these changes, from the point of view of someone who routinely uses computers to mediate his thinking and who has, for the past fifteen years, participated in a large-scale experiment in attempting to use technology in education at the first year University level.