Personally, I think it sounds pretty cool.
From what I've read, the basic idea is that, when a new math operation (for instance, adding 3-digit numbers) is to be introduced, what happens is this process:
- The kids work to develop an algorithm to accomplish the task (e.g., they are told to add two 3-digit numbers without being taught how to do that).
- Once the kids have had a chance to develop their own methods, several different algorithms are taught.
- One specific algorithm, out of those taught, is considered the basic one, and kids are required to learn and demonstrate that they can carry it out.
I think that, had I been taught with this type of approach in elementary school, I would have enjoyed math more and developed much greater math skills and understanding.
Of course, I turned out just fine in math anyway, and presumably math curricula to turn me into, say, Ed, are not nearly as much in demand as those to raise the performance of average or below-average kids. There is also the question of whether this system is too difficult for elementary school teachers to carry out properly, since many seem math-phobic and have poor math skills. (We can wish that weren't the case, but there's no magic way to change it.)
Something that annoys me about both Ed's mom's (hypothetical) rejection of this system and my own delight in it is that the effectiveness of the curriculum is an empirical question. The U of C website lists some empirical studies that (of course) support their program. In my alternate life I'd like to study these issues in more depth.