While writing Smart Flash Cards, I read several articles about which was best, Rote Learning or Reasoning. Reasoning is being able to figure out the answer and Rote Learning is memorizing by repetition.
I think the answer is obvious. You need both. First Reasoning then Rote Learning.
Why you need reasoning.
If you can reason you will never be stuck. Let’s look at the example 9 X 12. If you know 9 X 11 = 99 (Rule 5) and you know that multiplication is simply repeated addition(Before You Begin), then then you will know 9 X 12 = 99 + 9 = 108. Everyone needs to be able to do that. If you can’t Reason then Rote Learning will be very difficult.
Why you need Rote Learning.
Reasoning steals focus from the concept you are trying to learn. If you are studying Geometry your focus should be on the Pythagorean theorem not reasoning out “What is 8 X 8?” The multiplication table should be automatic. You should know the answer to every problem like you know your own name. It saves time, reduces mistakes and allows you to focus on the current lesson.