Just joined today after a few months of browsing. This site is the first place I'd encountered the term "math facts." What a horrible idea, particularly for a gifted abstract thinker. Math Concepts and Processes? Yes. Facts? No.
An abstract thinker learns quickly by understanding and creating robust active connections. Drilling creates hazardous ruts and lays down the wrong pathways (being bored and hating is a survival instinct for the precious part of the brain that is trying to save itself from being mis-wired.)
With high perceptual reasoning, they should be drawn to the patterns. Help them discover patterns. Eventually they will have very fast paths to the answers, and when the numbers get larger they'll use the same processes just as quickly while those who had "math facts" hammered in will fumble with no learned process to back them up.
I find so much at fault with your post that it's hard to know where to begin! Learning and teaching math facts is a fairly frequent topic on
websites and in
scholarly journals about education; your lack of knowledge of this is not evidence that the idea of math facts, or the learning of them, is educational nonsense. Increasing arithmetical fluency is not at odds with increasing conceptual knowledge; in fact it may reduce the cognitive load necessary to do the "grunt work" of a problem, and thus increase a student's ability to focus on the conceptual. And by increasing the speed of working a problem, it can give any student with speed issues, gifted or not, a better chance of keeping up in class.
Meanwhile, your own apparent strong focus on rote problem-solving procedures
is at odds with becoming strong in math, in my opinion. Math-- taught correctly, and at its heart-- isn't about learning a set of steps that one then successfully applies to bigger and bigger numbers. There isn't enough room here to go into what math education is or should be about, and I'm less qualified to weigh in than many here, but it certainly isn't that.
Drilling in and of itself doesn't create "hazardous ruts", though it may bore someone who doesn't need the drill. There cannot be any math-fact-avoiding survival instinct, since cavepeople didn't have math facts to avoid, and if they did, avoiding them wouldn't have avoided death before procreation.
