Like Bluemagic, I cannot "memorize" anything. It's worst with digits/values-- those, I can't even hold in working memory for long.
I can ONLY memorize information through writing it. So I recopied any lists of terminology, reaction schemes, etc about three times, and then I could more or less reproduce the visual information in the list.
I have to use a bit of random information (like the definition of an esoteric term, for example) about three times before it "sticks" for me, and I'm not as bad as I used to be.
Yes, recognizing patterns can help, or having a very strong visual, or auditory memory can. DD has to say what she wants to remember and to write it as well.
Oddly, it sounds like my weakness here is the opposite of bluemagic's-- I can recall vocabulary words far better than I can math facts or digits (like phone numbers). I'm amazing with faces, but horrible with names.
I remember things by making jokes or dirty mnemonics of them. That's the truth.
Timed math facts tests were a nightmare for me personally in elementary school.
I did go on to earn a terminal degree in a physical science, however, so it's not like it prevented me from learning higher math, or using it, either.
My personal feeling is that a child who understands the "why" of it all, and can more or less calculate what s/he needs probably just doesn't see any pressing need to make the (extraordinary) effort to memorize them, and I didn't force DD to. There's my confession. She learned them anyway over a period of about five years, but it wasn't until she was in Algebra I that she truly knew them cold. It happened through use, and through use alone. All the effort in the world wasn't going to get her there faster.
Honestly? I didn't really much see the point of rote memorization anyway. I still don't.