I did learn my math facts in grade school but it wasn't exactly by rote. It was more that I repeatedly thought about them until the answers were clear. For example, 7+8=15 because 8+8=16 and 7 is one less than 8. This process builds upon itself--i.e. at some point I had to become convinced that 8+8=16 before I could use that to conclude that 7+8=15. After a while, I felt that I could skip the reasoning part and just go straight to the answer.

Exactly! This is exactly what Dr. F was saying! If you get it, then the doing is easy and you learn math facts just from daily use. If you don't get it, then you're forced to rely on rote memorization for the doing, and that's painful for a GT kid. Better to start with the concepts and let the knowledge of the math facts come naturally from there.

My point (I think I have one

) is that verbal reasoning can be used to understand math as a language for representing real problems. This is SO important for kids to understand. The way math is taught in school you would think that the math and verbal domains were completely seperate.

I think that GT kids have the ability to intuit this connection. Mathy kids don't need to have things translated for them this way. Exposing kids like this to math is like immersing them in a foreign language. They will soak it up. Exposing them to calculus at a young age is like letting them read books with big words in them. They may not understand them right away but that's ok.

EXACTLY! This is something Dr. F said, too, almost verbatim! That's why he believes ALL GT kids are naturals at math, even if they're highly verbal. Because language and math are not separate entities. Our brains don't divide math and language that way.

Oh, Cathy, you're explaining this SOOOOOOO much better than I did! Thanks!

This kind of enrichment is beneficial to kids at all levels--without it, math just seems like an arithmetic wasteland to them and they lose interest.

Again, right on the money. Dr. F said we should, in effect, aim high with these kids. If they don't get it all at age 6, so what? They've got years more to pick up what they missed on the first exposure! But showing them what's out there, what math REALLY is--and it ain't workbooks!--captivates them, shows them that math is beautiful. We don't teach kids to read by diagramming sentences, so why would we try to teach math by starting with arithmetic. Teach them to love it first, then the nuts-and-bolts will come.

You rock, Cathy!

You made that a whole lot clearer than I did!