Since this is community wiki, I'll feel free to share a possibly relevant anecdote; feel free to delete if you don't think this is an answer.

I once had a freshman calculus student ask me if they'd be required to learn the "Greek method" for calculating derivatives. When I looked puzzled, he explained to me that the "Greek method" involved taking a limit as $h$ goes to zero, and that this was the method the ancient Greeks had used back before anyone realized that all you have to do is bring down the exponent and then lower it by one.