I think ebeth's point is an important one: math concepts are great, but math skills are necessary too. Developing the skills shouldn't be particularly difficult for the HG+ kid, but it still requires a certain amount of practice. For some of our kids that process of acquiring and perfecting a skill is itself an exciting thing - I think our DS, for example, gets a real thrill out of getting the right answers. But perhaps this changes with age. Still, perfecting the skill is only the very first stage of real mathematical understanding; the deep and wide aspects are really much more important. (Terence Tao's father seems to have recognized this relatively early on, and he is a good advocate for the view.)
Not to pull the thread off-topic, but I would be interested to know if anyone has any experience with Math Circles. Properly done this seems the right place for developing deep and broad acquaintance with math, and there really are a lot of them sprouting up. DS is joining one in the Fall, and we have high hopes.
BB
