Thanks for the replies everyone.
ColinsMum, it's nice to hear confirmation that my son is not alone with his combination of characteristics. I basically agree with what you say about how to nurture mathematicians - both parents have Maths PhDs and we know what mathematics is about - but that doesn't mean we know what we should be doing so we are very much open to suggestions. I agree with the sentiments in "The Calculus Trap"
http://www.artofproblemsolving.com/Resources/articles.php?page=calculustrap and "Why Discrete Math Is Important"
http://www.artofproblemsolving.com/Resources/articles.php?page=discretemath so we certainly want to do many things outside the standard American K-12 Math path. AoPS itself certainly has some interesting such courses, e.g. Counting & Probability and Number Theory, but if someone had courses on set theory, logic, graph theory, etc., then we'd be interested in those too. Mathematics competitions will provide a challenge, and will better gauge where he stands relative to his peers. We will keep accelerating him though, which is easy in a virtual school with its individually paced online courses, until he "officially" gets to (Middle School level) Algebra, and will then diversify into all the other topics and activities.
Dottie, I think you're right that since he could do the timed Math and Reading tests at a good speed, then he should have been been able to do the PSI subtests more quickly. He would know what it meant to do familiar things like Math and Reading quickly, but perhaps when it came to the unfamiliar and novel PSI tasks he'd have no basis for choosing what speed to go at. Perhaps he could have gone much faster, and scored higher (despite making more errors) but he'd have no way of knowing this at the time. This makes me think that PSI is not a robust method for measuring what it's supposed to measure. It's too dependent on a child's choice of speed and how well that choice balances speed and accuracy to maximize score. That's my off the cuff theory anyway. So I'm not going to worry that there's a slow processing issue.
qxp, the WJ-III report did not have the type of information you mentioned. We'll try to get more information. (The WJ-III and WISC-IV were given by two different testers FWIW.) You're right that the combination of scores doesn't seem consistent, so we at least need to put put some healthy error bars on all these numbers. I would (wildly) guess our son is 3 to 4 SD above average in Mathematical ability for his age, so I'm taking the very high WJ-III Math numbers with a grain of salt. I think future Mathematics competitions will give a more accurate picture. On the other hand, the WISC-IV VCI and PSI numbers probably underestimate his abilities, but they could still be his weaker areas. So I would think that if you decrease the higher scores and increase the lower scores, then that would give a more accurate (and plausible) picture. So I'm not thinking the score disparities necessarily indicate some kind of "issue" though I can understand why the concern arises.
