I had experience with both American schooling and European one where memorization was a big part of the learning. I was struggling to memorize things. The American way worked perfectly for me. I think that schools should not encourage memorization.

A learning process where you remember all the facts and recite them exactly, you get a good grade is bad. That doesn't mean you actually understand and can apply your knowledge. There was this article on HN a couple of days ago about the medical paper where the author had reinvented the integral. That's the result of too much memorization.