I'm an English major, so I'm not sure I'm doing a great job of teaching math myself.
But I did find the math guy's approach to be useful to me in how I *think* about teaching math, at least.
The gist of the guy's teaching theory as I understood it is that you teach kids to love math and to explore it first. Then you worry about getting the facts down. Just as you don't make kids memorize every color in the rainbow and all the sizes and names of all the paintbrushes in the world before you let them paint, so also you don't have to be sure that kids know every fact. Fact memorization is a tool for doing math, but it is NOT math! If you look at most elementary schools today, I don't think you'd know that.
He says that facts are necessary, but especially with GT kids, they'll come with time. When they need to know and when they can see a reason for knowing their times tables (or whatever), they'll learn them. Until then, give them plenty of *real-life* reasons to use them and learn them.
That is, use science to teach math. Use blocks to teach geometry. Introduce concepts like calculus early on in a simpler form through pendulums and other physics work. Don't get boxed in to thinking of math as only numbers and equations, but as a way of looking at the world and a way of solving problems. Mathemeticians have to be creative people! You'd never know that from most elementary school approaches that I've seen. And I think this general approach is why many GT kids get good grades in math but decide somewhere along the line that even so, they're not good at math. (True confessions: that describes me.) It's because they never get to really see math, let alone do it! Arithmetic isn't all there is to math any more than grammar is all there is to poetry.
Am I living this? More than I was last year, but not as much as the math expert I'm citing does. The stuff he does with kids is incredible. Eventually I hope to get DS7 into a class with the guy, one way or another. But at least I can say that DS7 loves math this year, whereas it was not a big hit last year when he was doing workbooks. So that's a big key to me. Honestly, I didn't think he was a mathy kid for a while there, but now I've changed my mind. I think he is. And, to top it off, he's learning his times tables, happily and without any problems. The hands-on, guided play kind of stuff we're doing is a huge hit, and he's learning a lot from it. Blocks and pattern blocks are our friends! We got a new math card game called "1-2-3-Oy!" and that's popular with both DS7 and DS4. Dice games are fun learning opportunities. Physics experiments and graphing on Excel is going well. (With and assist from DH the engineer on that!) Stuff DS7 can see and touch and use seems to be working a lot better for him, as the math guy said it would.
DS7 is also seeing connections between things this year, and I don't think I did that in any serious way until college, so I feel pretty good about that.
I'm still learning how to do this--not to mention probably really learning to understand math for the very first time in my life!--and I know I'm not doing a fantastic job. But I think it's going okay. DS7 likes math now and he's learning and problem solving. So I think it's working. I think! I hope!
I don't know if that little ramble is any help to you at all...
