For some time now I have been trying to teach my 10 year old TB gelding to jump. By nature he is very nervous and excitable. Everything I have taught him so far has taken a lot of time and patience. But jumping has been the worst experience yet. After every fence he takes off at a wild gallop, at the same time throwing his head up and down, and occasionally bucking. This makes it very difficult to stay on and forget negotiating toward the next fence.

I commend your patience and previous accomplishments with your horse. Your horse galloping off and bucking is connected to poor bit communication. Bucking is a forward motion, your horse must change his weight from the back to the front. To stop your horse from bucking never allow him to change his weight. When your horse does change his weight, you need to return his weight back to the hindquarters. This is accomplished by applying bit pressure until he returns his weight back to his hindquarters. You may have to stop or circle him to a stop. A high excitability situation is not the place to teach your horse to back off bit pressure. Your horse needs to be very responsive to the bit to correct your problem. I realize jumping requires a horse to be less sensitive to the bit to avoid being unintentionally stopped by a rider while jumping, but there must be a balance. So you will need to search for this balance between to hard and to soft. As you are practicing riding require your horse to respond to a lighter cue at a low excitability level. Practice backing more often, most people only practice forward movements. Your horse responds to the same cue for slowing down, stopping, and backing.

It also sounds like your horse is uncomfortable with jumps, so try backing up to the basics. Try jumping a single low jump and stopping afterwards with a lot of rewarding. This way you will be lowering the excitability of jumping to avoid losing control. Then slowly raise the jump height each time your horse gains confidence. By working slowly with relaxation and reward your horse will be more inclined to work with you, rather than fleeing from what you are doing.