Sorry, I still disagree, I think. (Though your last paragraph could be something I would write, so maybe I'm misunderstanding you...)
Many GT kids are ready for algebraic problem solving, for example, before they have memorized their times tables. Keeping their advancement on hold until they memorize the chart isn't the best strategy for keeping them engaged with math. You lose them. What's more, they often learn the times tables without much effort once allowed to do algebra because at that point the math facts become useful to them. So in that case, the facts get into their heads only after they get to use the higher level skills.
I think you're right that learning styles and personality are at work here. I have one son who is memorizing the times tables at 5 because he wants to and it's fun for him. OTOH, my 8yo needed to be doing algebra before he was ready to learn his times tables, and he's still not quite 100%. (Those darn 8s!) But frequent use is making the memorization happen in a way that drill-and-kill did NOT.
I like the comparison of math to art that I read somewhere, (though I think you could use this for any concept vs. fact situation): what if you weren't allowed to put pen or crayon or paintbrush to paper until you had memorized every color in the 128-crayon box and got them all right on a series of tests? And then you got tested on styles of brush strokes. And so on. That doesn't make any sense to us. You learn those things by doing. I would argue that treating grade school as memorization-central is much he same thing.
Please don't misunderstand: I'm not anti-knowing things. And I do believe there are some things you just really ought to memorize. But I don't believe that facts *have* to come before concepts...not ever, really. Maybe with reading, just because I don't know how you can read a word without knowing the letters and phonemes first. But if there were a way for a child to get the concept of reading without those letter/sound facts, then I can't see how that would be a bad thing.
