I think achievement REALLY matters. Whether it is great reading capabilities or math ability - that achievement is important and can indicate giftedness, IMO, in and of itself. I don't think IQ tests even claim to measure everything that goes into talent or achievement; rather, I think they only look at certain aspects of what MIGHT make a person become an achiever. They are but one measure. Achievement, on the other hand, speaks for itself. That is, if a child is consistently high achieving, but has lower ability/IQ scores, it would seem the ability/IQ test is missing something (or perhaps identifying something that the child struggles with, although they STILL manage to achieve).