Here's a good example of the total blindness that focus can cause. [Ed: shasta beat me to it] http://www.youtube.com/watch?v=2pK0BQ9CUHk; pretend there's money on it (like this guys presentation had) and focus on it hard.
Remember, magicians rely on misleading your focus for their entire acts. Watch the coin hidden in my right hand, when I really slipped it into my left hand and dropped it into my pocket and oh look the coin is gone. Is it behind your right ear? Oh no I took it out of my pocket and look it's behind your left ear!
For example, the methods of analytic geometry and calculus let you solve problems mechanically that would be difficult or even impossible by other means. That's great if you're just trying to get an answer. It's not so great when you realize after executing a rigorous calculus proof of Snell's Law that you are not an inch closer to understanding why Snell's Law is really true. You turned yourself into an unthinking piece of machinery.
This applies not only to calculus. Most people who can execute the algorithms for calculating with fractions or solving linear equations don't actually understand what they're doing. They want an answer and they get it.