THese discussions remind me of two stories by Asimov, both quite to the point. Alsa, I don't have good references for either, but I'll bet someone does.
One (I think) is called Power! Both are frequently anthologized.
One is about a society where people DO use calculators for everything, and then one genius finds a way to make calculations with paper and pencil -- a procedure that always gives the same results as the calculators! Asimov makes it believable that this is a radical idea that nobody believes at firts, and has a neat (very '50s) logical consequence.
The other is, I think, earlier. This is a bout a society in which people learn by having the knowledge placed right into their brains. Once at about 6, you learn how to read. Later, you get a profession "injected" -- the profession is chosen based on what your brain is best able to absorb. The protagonist is someone whose brain is untrainable. (I just realized, incidentally, that there's a nice subtheme about local funding for education that teachers will enjoy!)