Someone has got to seriously define the line between learning and memorizing. I've heard many complaints from teachers that students study for a test and forget the information months or even weeks later. Maybe that's not their fault. Maybe the brain can't keep up with all the knowledge being stuffed down its throat, those regretted tattoos that you remove because you don't want them anymore, you don't need them anymore. The only difference I can see between writing and erasing those facts on your brain and writing and erasing those facts on the back of your hand is that one will get you a 0 for cheating. Facts are being written or tattooed or memorized but they aren't permanent. The tests we give only give students an outlet to vomit up those stupid facts, sick of them bouncing around in their uninterested brains.
Tests with provided answer choices restrict in-depth and out-of-bounds thinking. Never give a student a 25% chance of getting an answer right. Give them unlimited choices and unlimited opportunities That's the way students learn.
Then again, tests that aren't multiple choice or matching or fill-in-the-blank are super stressful on students. So, if you can, make sure your students actually understand the content before you shove a quiz into their face.
As a student, I know how hard it is to remember EVERYTHING you learn in a year, and then summer happens and you forget it all. You remove those tattoos your teachers drew into your brains and you look back on all of that wasted time. So don't test a student's memorization skills. Test her learning.