Many riders find that jumping horses or ponies is an exhilarating sport.
The initial training of a young or older horse to jump should be done gradually, beginning with ground poles spaced apart to fit the length of stride of the animal. This can be graduated to using cavaletti, which is simply a pole set on 2 x's that give you three training heights: 7", 12" and 17" for gymnastics. Four to six cavaletti set in a line at the lowest level can improve a horse's trot; and set at the highest height they can make a small bounce jump.
Used reguarly, cavaletti can be an integral part of your training. Variations can be set up to keep the horse/pony interested in the work.
Later, once horse, pony and rider have accomplished these varying heights without over practising, they can move on to small jumps with a few poles and a ground pole. A ground pole provides the horse or pony with a distance marker to judge when they should begin to jump. A ground pole set too far from the jump confuses the horse or pony and there may be an accident where the rider and animal crashes through the fence.
Before raising the height of the jumps or cavaletti, it is of benefit to make a spread jump in the early stages. It is easier for a horse to jump wide than to jump higher.
Often, riders think they have prepared their mounts properly at home before shows. If a rider jumps their horse or pony too much, the animal will become "sour" (not wanting to jump) and will often act out their frustrations in the show ring. Apart from being embarassing, the rider could be bucked off resulting in injury. Also, jumping a horse/pony too high too soon before it becomes comfortable with an easier height will often cause refusals at the fence.
It takes time to train a horse/pony to jump properly and consistently, which is why the jumping levels at shows: pre-green hunter/jumper, green hunter/jumper, are set at graduating levels to prepare a rider and horse for the next level. Often, I have seen riders and horses not ready for their level and need to take more time at home with practice which should include long hacks to break up the intense training. Horses need breaks from their work just like humans do. Too much repetition makes for cranky, reluctant workers: humans and horses or ponies.
The video section shows what happens when rider and mount are prepared or not. Another good video of using bounces at a show in practice can be seen on You Tube: Girl Doing A Bounce.