OP: I think the interest and the speed with which your ds picked up the concepts seems advanced. I don't know anything about education, though, and my only frame of reference is my own ds6 -- not ND for math! I don't think later interest necessarily means less GT for math; my own ds's reading was much earlier than his math.
Which leads me to ... this is an interesting discussion, as I consider ds6 pretty mathy.
He was a pretty early reader -- sight words by two, slowly growing to a big sight word vocab by 3, to the point that he was reading new picture books (not easy readers) by 3.5; he didn't really have a BOB books phase and didn't read much Dr. Seuss stuff either. Captain Underpants fluently by 4.5, now flying through A Series of Unfortunate Events. Prefers non-fiction about severe weather and natural disasters.
In math, he was doing simple addition and subtraction by 3.5yo and reading digital clocks by 3yo; I honestly didn't think much of it because it seems pretty intuitive to me! I didn't think he was too into math and thought he was more verbal until he was about 4.5yo and started counting piles of change, understanding the concepts of decimals, doing double-digit addition in his head. It just sort of went through the roof. Now he's doing late third grade math at school and doing well there. He could move faster on his own, but so could most kids at school.
What I find interesting, though, is that his strength seems to lean toward calculation rather than concept. For example, on the Cute Quotes thread, I wrote:
He plays a game designed for older teens/adults; there are 80 levels total, and he got to level 20 today. Very pleased with himself, he said, "Whew! I'm a quarter of the way done!"
Since he started it
I said, "Congratulations! What's another way to say that?"
"Umm ... I'm 2/8ths of the way there!"
I said, "That's right! Or ...?"
"Or 3/12ths! Or 100/400ths! Or 400/1600ths! Or ..." here he got a naughty little grin, "or 16/64ths!"
But thinking about it today, I realized that he probably didn't really understand the concept -- that you're multiplying top and bottom by the same number to *get* those equivalent fractions. So I asked him, "*Why* is 2/3rds the same as 4/6ths?" He couldn't explain, so I tried to explain it to him ... I *think* he got it!
Is this unusual, that he'd be able to do the computation without realizing how or why?
