In fact, in this case (412 divided by 17) what you did is exactly what the long division algorithm would have you do -- try to divide 41/17, which is really 410

In fact, in this case (412 divided by 17) what you did is exactly what the long division algorithm would have you do -- try to divide 41/17, which is really 410/17, and take the closest-without-going-over multiple of 10 -- 20 in this case, then recognize how much you actually "used up" -- 340 -- and then divide into what's left. So it's even worse than you imagined with your ignorant teachers -- you were doing long division after all and they didn't recognize it.