Actually, tlkng1, you don't agree with me at all!!
Teaching the horse to "skip" leads or "swap" by doing fewer and fewer strides of trot in a simple change through trot will not teach correct changes and more often than not you will end up with a rushed horse that is on the forehand.
It is important to perform all movements correctly, always. This means the simple change through trot should always be performed with 3-4 strides of trot (more on a green horse), and the simple change (a true simple change, through walk) always with 3-4 steps of walk (more with a green horse). The important thing to remember in any kind of simple change is that there are two distinct transitions and three distinct gaits. As riders we have to focus on maintaining the balance, the quality of the gaits, the quality of the transitions and THEN worry about the change as a whole. If you don't have a good canter coming into the change, then don't even bother with the first transition! If you don't have a good canter-trot (or canter-walk) transition, don't even bother continuing in the change, etc..
As well, putting a pole on the ground will teach the horse to change one stride late behind, flat and imbalanced - on the forehand. We call these "lead swaps", not flying changes as they are not correct.
A correct flying change is taught through the use of exercises, body control, timing and feel. The quality of the canter is paramount and must never be sacrificed by rushing the horse through a simple change or putting him over a pole while drastically shifting your own body weight and "hoping they land on the new lead". As in anything, the rider must stay still in the center of the horse and teach the horse a quiet aid, correctly. The flying change is simply an aid for the horse to pick up the canter. The only difference from a normal walk-canter or trot-canter transition is that he is already in the canter, on the other lead. He must understand the aid for a flying change (!!) as simply a canter aid and then he will be able to move his ody crrectly through the movement. Chucking him over a pole or running him through a simple change does not teach him an aid!!! It only serves to teach lead swaps where the rider has to flail herself around, knock the horse out of balance and then "hope the horse does a change". It doesn't look nice, it's not correct and it teaches the horse nothing but to canter around on the forehand, crooked.