Are you guys talking about reform math? Hasn't that been around conceptually since the late 60's or something like that?
This is oversimplifying it, but it's about taking numbers apart and putting them back together. Playing with the numbers as opposed to straight memorization, if you will. I warned you, oversimplification! I've seen that instead of memorization they teach the itty bitty's to add/subtract using manipulatives, number lines, hundred's graph etc.

Even peeking over my shoulder at DD8 doing aleks, they teach quotient and remainder totally different then I remember.
I never remember doing estimating a sum. Doing a larger calculation in your head by rounding up to the larger numbers, adding/subtracting, etc. than subtracting away the number you added by rounding up to get the answer.

I kind of wish they taught math like that when I was younger, it seems more fun.

I think DD's favorite part of the day is the mental math test they have everyday. I agree with Kriston, drills have their use but mix it up, people, please!