...I find it troubling that their definition of mathematically talented is 95th percentile (or even 99th percentile). Dr. Stanley's work focused on children who were really at the extreme tail (even well beyond the 99.9 subtest standard used by Davidson). At the nationally competitive level, that's who we are dealing with.
Even my DD, who is not mathematically talented, is consistently at above 99th percentile. She is just not at the extreme like her brother or even her mother.
Performance on a standardized test or in a math competition seems like a narrow definition of math talent to me. Both of these things require speed; what about people who prefer to approach problems s-l-o-w-l-y and consider many different aspects of an idea?
Many things in our society (including chess competitions, tenure decisions, and so) reward speed (e.g. how fast can you make your next move?? How many publications can you get out in the next 5 years??). IMO, when we fail to let people move slowly, we fail as a society in a very important area.
Actually, Val, I don't disagree with you on this point. The standardized tests and competitions are one way to catch many of those with math talents. Certainly, some are missed, especially twice exceptional kids. At the same time, speed does matter in some situations. It may seem unfair, but if I were hiring, I would give preference to an applicant who can think and act fast, all other abilities being equal.
More to the point, my post is consistent with yours to the extent that I don't believe doing well on a standardized test or math competition (at the 95th or even 99th percentile) necessarily translates to math talent. That was my point regarding DD. My judgment was not based just on standardized test scores and math competition awards but on more informal demonstrations of DS versus DD's innate abilities from toddlerhood. DS ponders independently and arrives at math concepts without being taught. DD needs to be taught - she learns very quickly and is very bright but that innate talent is missing. Incidentally, I am not so presumptuous as to assume that DS will ultimately fall within that extreme tail either as he is no Terrence Tao - only time will tell whether his minor math talent develops into a significant talent as an adult.
