deduce, induce, reduce, produce

In general, it seems more expedient to tell a thing, or even to show it, rather than relying on students' powers of logic. The free-thinking thing is not exactly comfortable for them-- ask them to copy, however, and it's like flicking a switch-- it's been programmed in. It's good to know there's that option-- they'll copy poetry and notes, etc., like there's no tommorrow. You'd think they'd complain about that. But what they really dislike isn't mindless monkeywork, its being asked to think for themselves.
This is not to imply that they're dumb or incapable, simply that its unfamiliar to them. In certain contexts, however, they can think for themselves without realizing they did. Sadly, many have to be tricked into it. There is the whole idea of having steps...guiding their free thought. Which makes sense, and is easy, but feels impure-- cheating, in a sense, on my part. To what extent is discovery discovery if there's no room for error?
I fully agree with the whole 'teach a man to fish' idea, though. Ownership, really. I can be told something a million times, but I only learn through experience, through trial and error, through reinventing the wheel. I beleive most people are the same way-- so although it seems to take longer and be more smooth/less streamlined to expect students to develop their own understandings, it actually takes less time in the long run, because it's not just one more thing to memorize, it's not just greek to them, it has significance/meaning. Better that than repeating myself, or having them bomb a test and break my heart.