This reminds me of a conversation I recently had with a retired engineer who went to talk to the head of elementary mathematics for the county in which he lives. He wanted to know if long division is still taught in the elementary schools and how long was typically spent on it. (i.e. do they do division of a 5 digit number by a 4 digit number or only 3 by 2, for example.) His thought was to drastically decrease the amount of time spent practicing an algorithm and use that time to practice estimating what the result of the division *should* be and then confirming that with the calculator. This is similar to the idea that students can do integrals while having little idea of what they mean.
What are your thoughts on cutting instruction on long division in favor of estimation/prediction?