My elementary school (I'm 28 by they way, so this is some two decades ago) actually had a program for students like that; one day a week , you would be pulled out of normal class for an alternative class where the material was taught through projects and discussions, logic was explicitly both encouraged in thinking and taught as a skill, and there was basically no rote memorization. We learned games like chess and Magic: the Gathering (I had no idea how huge that game would go on to become; I wonder if the teacher still has those first-edition decks?) during our breaks from "actual" instruction, and there were basically no tests.
It was a ton of fun, but I only stayed in it for one year; the other four days a week were still boring me out of my skull. After the year in that pull-out program, I transferred to another school that had a fully accelerated / "gifted" curriculum. That was less boring - the material and pacing were both better, but I was still the top math student in the class and frequently bored there waiting for others to catch up, for example - but I missed the one-day-a-week program from the old school.
As for what I did during the mind-numbing classes, I read. Fiction mostly, but some non-fiction - I really loved "The Way Things Work" books when I was about Alex's age - and I usually tried to make it not-entirely-obvious what I was doing. The teachers knew, of course, but as long as I didn't flaunt what I was doing and kept my scores up, they didn't generally care. I was bad at the participation / stupid games stuff in those classes, but I learned to read stuff way "above my level" and got way more benefit out of it that I would have from listening to the teacher drone on about how to do long division or whatever.
My school board did similar - I did the full-time gifted class, my brother did the one day a week.
I also got accelerated to a rather extreme degree - I skipped 3 grades, and started highschool at age 10. It was a mixed blessing, frankly - it got me past the "kids are pure evil" years, and turned me from the obnoxiously nerdy kid into a curiousity, which got me picked on a lot less. The material didn't get much more interesting - once you catch up, it's being taught at the same pace. And on the downside, it made me a lot more awkward in highschoo...
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A list of some posts that are pretty awesome
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