I am new to this SIG and would like to add a bit of myunderstanding about the topic.
Understanding mathematical facts allows for easier memorization. In fact, I think that it follows almost 'naturally'. It is when the math facts are 'played with' in the mind that new understanding and insight emerges, that new theories are developed and proven, with the facts ready at hand. Rote memorization to me means mindless storing of facts - the mind does not comprehend the facts and therefore the 'learner' can do little more than reproduce the facts as they were stored. A person who understands the facts she/he learnt can recombine them in novel ways to produce new insights.
But I think there are limits to what one can expect students to memorize. I think it would be unproductive to expect students to memorize long lists and tables of formulae and data. For example, memorizing long lists of calculus formulae and topics like the periodic table of elements seem to me a waste of time. Time would be better spent to truly understand the rules about how the things fit together than committing all the various elements to memory. The same with the formulae.