I'm surprized that none of you have really understood the thumb over method. I am new to this board, so if you'll excuse my lack of knowing each of you etc etc. Also, I am just learning the TO method myself. I have been playing for about 4 1/2 years, 2 1/2 of them seriously. I've just instinctively done the TU because it was intuitive. First question, why is the TO method not taught as a regular movement? It's really quite simple. It can be compared to riding a bike. When you're a kid, you don't worry about bending down over your handlebars, you just ride your bike. And hey, it works just fine. But if you're gonna be a professional biker, you soon find out that you need correct body positions. In piano, the HUGE majority of teachers are students are your common hobby level musicians. Teachers that are primarily in it for the income, students in it because their parents make them, or for fun. So, most of the teachers are never teaching anyone over an intermediate level. The TO method is used for very fast scales and arpeggios, and so it is not needed in the beginner to intermediate levels, and so consequently not taught. Also, when we get to the professional and university/convervatory level, most students already know the TO method, usually coming upon it by chance, and so it also is not taught here, because it's a basic technique. So basically, it's not taught because it's generally not needed for the majority of the public.
Second, what is it? I was very confused at first also. The term itself is what throws everything off in your head. Instead of thumb OVER, think of it as thumb NOT UNDER. The convincing movement is easily seen. Hold your hand out in front of you, all fingers relaxed, with your thumb in a natural position parallel to the fingers. Now move your thumb up and down, which is how you hit keys on the piano. It is easily moves several inches. Now, while still moving up and down, slowly bring it underneath the fingers. It slowly loses mobility, eventually becoming essentially paralyzed. Now obviously you can still move it, but you're using different muscles and it is moving slower. In slow (read:beginner) passages, this is fine, noone knows. But when we get to the level that few attain and few need to be taught, it becomes a problem. So, we move to TO. The thumb takes on the same role as the rest of the fingers, we only use up and down, not left and right. If you do a B major scale (the scale Chopin started all his students on), it will be easiest to start. Play B-C#-D#, then move your whole hand (flick sort of) to the next set of four notes. Your thumb does not move under, or over, but merely moves with the rest of the fingers. Now all your fingers are in place, and you can play them as fast as you want. The major clincher is getting your whole hand over with no bump, which will not be a problem, as long as you practice it. If you practice TO as much as you would TU, you will be playing MUCH faster scales than you would ever imagine. It's hard to get the block out of your head, but it is essential. A lot of advanced students intuitively stumble unto some from of the TO method. I was not taught it, even though I was playing advanced pieces, because I practiced a lot of "block" playing, even for scales, and so my hand was already essentially playing TO, so my teacher never really mentioned it. Chopin taught both methods. TU is obviously needed sometimes, but whenever possible TO is much more efficient. That's the basics, for what it's worth.
-Kolby-