. Geometry, if taught using proofs, is the first REAL math class. It is shame kids have to wait until 8th grade to get to it when many are clearly ready for "proofs lite" by the 3rd grade.
What the GT kids get excited about is number THEORY and algebraic theory - things THEIR minds can sense but which ALL elementary teachers are totally ignorant of. If a kid can grasp series, summations, and then limits, then they are ready for Calculus as well.
Kids can be slow computationalists, BUT they get the THEORY and get it spades.
This is what I saw with my son this summer at the Epsilon math camp. The 8 to 10 year old kids did proofs and really understood them! I remember proofs in geometry and I just memorized them. But I didn't get a chance to "fall in love" with math because I didn't get to even be exposed to the real math you are talking about until 9th grade or so. I'm so happy for son getting to see some of it now...even though his school curriculum doesn't provide it, I learned what he needs so I provide it outside school as well as I can.
