Comment by Aurornis
> Memorization of, like, multiplication tables gives us a poor view of the more interesting type of memorization.
Memorizing multiplication tables is the first place many children encounter this strategy: The teacher shows you that you could try to memorize all of the combinations, or you could start learning some of the patterns and techniques. When multiplying by 5 the answer will end in 0 or 5. When multiplying by 2 the answer will be an even number, and so on.
I think there may have been a miscommunication somewhere on the chain of Mathematicians-Teachers-Students if that was the plan, when I was in elementary school.
Anecdotally (I only worked with math students as a tutor for a couple years), that math requires a lot of the boring type of memorization seems to be a really widespread misunderstanding.