My kids haven't been tested, but I'm interested in this thread because my kids both seem to excel at math, and I'm not quite sure what to do with them!
Things that make me think my kids are good at math:
-Had one-to-one correspondence for numbers early
by age 2 to 3 - and not just a few, but large numbers (like able to count out 32 objects accurately).
-Understood the concept (if not the facts) of multiplication by age 4 or so (saying things like "three 3s are 9, right mom?" or "we have to wait 30 minutes! That's 3 10s! I can't wait that long!")
-He's had a good understanding of time, e.g., that hours are divided into minutes, minutes into seconds and each of these are 60 unit measures since he's been about 3-4. When he was 4, I drove into the parking garage where went to daycare. We were supposed to be there by 9 am. The clock in the car read "8:49". Ds announced "We have 11 minutes to get there." (ironically, he still can't tell time with an analog clock!)
-He was able to play board games with accurate counting out of moves from about 3. He could play Monopoly Jr and accurately handle the money aspect from about 4.
-He's always been very good at recognizing patterns
Now he's in 1st grade and his teacher has him doing some 'challenge math'. I need to find out more about it. He's always the first to finish his math work in class. He LIKES to do math problems. He tries to help out the other kids at his table.
Interestingly, he gets the concepts more easily than the details. He's not very careful with details, so his homework/class work isn't always accurate. I need to figure out how to handle that.
Dd has a similar trajectory, if not more accelerated in some areas.
-She's been able to play games where she needs to count out spaces from about 2 1/2.
-She's been able to link the spots on a die (singular of dice) with a number since she was 3. She'll roll a die and say "3" or "5" and always be right.
-When I look at the PBS kids web site where they have the developmental trajectories, dd is doing at 3 1/2 a lot of things that they say 6-7 year olds should be doing with regard to number knowledge (1-1 correspondence for numbers up to 20 (she can do up to 45+), if you ask her what number comes before/after 25 or 32, she can answer, she can count by 10s to 100 (though she tends to say "ten-ty" for 100, it shows me she's got the pattern!), she recognizes simple patterns).
-Her operations on numbers (adding, subtracting) aren't as advanced (probably more a 4-5 year old level), but we haven't worked on it (she doesn't' seem interested yet). We played games with ds at this age to work on these.
-She's very good with puzzles (does 40-50 piece puzzles when she cares to.)