I used to think that math was the perfect subject to teach via computer software (instead of lectures). My rationale was that computers are already good at math; and software-driven customization for each student is most useful for topics that require a solid knowledge of previous topics (e.g. algebra builds on multiplication and fractions).
This TED talk by Dan Meyer challenges those assumptions. He suggests that good math education starts with good discussions. It uses open-ended questions whose answers may be as unpredictable as responses to works of literature. It emphasizes how math relates to intuition and the real world, and deemphasizes arithmetic and equation solving. In other words, it humanizes math, a notion which makes a lot of sense in a world where computers not only compute sums but can easily solve, graph, and symbolically manipulate indefinite integrals. (On a cell phone. For free.)
Indeed, a lot (most?) of cutting-edge science today involves calculations so complicated that it would never even occur to the scientists to complete the math by hand.
So why bother teaching students in detail how to do the things that computers will always be better at? Meyer’s approach focuses on the human side — understanding when and why to apply mathematical tools. It’s not immediately clear how computers themselves will figure into this educational mission.