I base all of my groundwork exercises off of Clinton Anderson's Downunder Horsemanship program. I've had excellent success with these methods. I can create a respectful and responsive horse in just a couple of weeks. These groundwork exercises can transform any stubborn or unruly horse into soft, supple, willing to work, and ready to start in a safe, consistently effective manor.
Desensitizing is something I generally use as the initial exercise with each horse. I don't want any horse to fear my training tools or myself, so I teach him to relax and be comfortable with my training stick and rope. Later I also progress desensitizing to more literal things, like exposure to crossing bridges, walking across plastic tarps, carrying bags of aluminum cans, being sacked out with feed bags, etc. Desensitizing is literally the act of applying pressure, and not releasing the pressure until the horse is relaxed and quits moving. Whereas sensitizing is exactly the opposite - appling the pressure and releasing as soon as the horse gets the right answer by performing a manuever.
Disengaging the hindquarters is the first sensitizing exercise I use with every horse, sometimes I start with this exercise for the most unruly horses. The goal is for the horse to pivot on the forehand, and cross his hind legs under himself with each step. This teaches the horse to get his butt out of your space - it's hard to get kicked when the horse's butt is facing away from you. It's also the exercise that I will use when first teaching him to lunge. I will use this exercise again when I first climb in the saddle to get the horse to take those intitial steps and then to whoa him as well. Later, if a rider encounters any safety issues, disengaging the hindquarters will take away the horse's forward motion and even stop him from bucking.
Backing up is a sensitizing exercise that I develop multiple cues for. I teach a horse to back up with body language, which will save you from getting run over by a spooked horse, or just get him out of your space; and also from direct pressure on the halter, which will be how a rider would back him from the saddle.
Yielding the forehand is a sensitizing exercise that teaches the horse to keep his shoulder out of your space - we've all had that horse that uses his front end to push us around. This will also be a tool to teach your horse to lunge and change directions, and move him around during saddling and grooming.
Lungeing is a sensitizing exercise that I use to teach a horse his gaits. I used to free lunge in a roundpen, but I've learned to prefer online lungeing. There's a greater deal of respect and softness required to lunge a horse on line as opposed to in a roundpen. I don't use lungeing to tire a horse out. It is merely a means to establish all three gaits. Once the horse is solid on the lungeline and will walk, trot, canter, change directions and whoa, I repeat with the saddle.
Flexing is easily the most important sensitizing exercise of all. This make a horse soft and supple, creates the steering wheel, the break, and the reverse. First I flex with the halter, and then with the snaffle. Here, I'm flexing Chase with his ear - something that is trickier to teach a horse, but is just one more method of getting your horse soft and respectful.
Saddling is a desensitizing exercise and is introduced as soon as the horse is solid in all the previous exercises. I use the disengaging hindquarter, backing, forehand yield, and flexing exercises to keep him from panicking and exploding when saddling and cinching. Once he's relaxed enough to move out, I lunge him. If he can walk, trot, and canter on the lunge line consistently and fluidly without bucking, he's ready to ride.
Sidepassing is a sensitizing exercises that stems from the forehand and hindquarter yields. It is not necessary to safely start a horse, but if you can teach this from the ground it's 100 times easier to establish under saddle. I do not use this exercise with every horse I train - many of my clients do not want a push button horse (usually trail riders and beginners), so for those particular horses, I avoid all leg yield exercises such as sidepassing, with the exception of the forehand and hindquarter yields necessary to start the horse undersaddle.
The key to a happy, willing horse is reward. The art of training horses is not in how the pressure is applied, but rather how quickly you release the pressure and how often you praise the horse. I use my stick to ask for each exercise, and always rub and praise the horse with the stick the instant he makes an effort in the right direction. Proper timing and reward, along with lots of love, affection, and respect from the handler, creates a horse that will be happy to continue trying and ultimately enjoy his job.
If the desensitizing and sensitizing exercises are balanced, your horse will not walk on you. He will not push you around, scratch his head on your shoulder, or slam into you at the gate. Nor will he be naughty for the farrier, refuse to attempt scary new obstacles, kick you, bite you, or dance around for saddling. He will not be headshy or afraid of flyspray. He will not jig, or paw impatiently. Nor will he run from you in the pasture when you want to catch him. But he will be quiet, alert, and patient while he waits for your next cue, ready to give you his all each time you ask.

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