Caveat and disclaimer: The exercise assumes that you are on reasonable terms with your horse and that there are no major disobediences. I cannot stress too much that this web site offers ideas and not prescriptions. Please always be mindful of the potential for injury that accompanies all riding!
The action priority in training is forward-->straight-->through done in iterative cycles. What I mean by iteration is that the output of one cycle of training is input for the next, so that improvements may be advanced while consolidating the gymnastic and emotional foundation. Because horses are living works in progress, trainers are never free of having to consolidate a foundation for athletic performance with each ride.
In a training session (or warm-up at a competition), I work on relaxation combined with stretching. There is a key response I look for every moment I am in the saddle: a soft munching at the bit in response to my lower leg at the girth. The image below indicates the anatomy that connects a rider's lower leg to the base of the neck, tongue and jaw. A useful check on relaxation of a rider's seat is that legs hang along the horse's sides as though they were wet towels and thigh muscles should be soft enough to roll gently across the thigh bone.
Without a trained and reliable connection from the lower leg to the neck and jaw combined with an independent seat, the horse will be somewhat tense and down at the withers, even if he appears quiet. I do not even trot until I have a soft, steady connection to the rein which goes through the entire horse. Some days this takes longer than others, but my horses have come to know the way to approach this part of a ride. Vulkan, as Mister Conservation of Energy, likes the stretching part of a lesson! Max is focused on every exercise and is much quicker to chew softly at the bit than Vulkan.
Depending on the feel of the walk work, I may go directly to some canter circles and broken lines, combined with walk-canter-walk transitions. This turns out to be tougher to do properly than flying changes and addresses ALL the issues of fowardness, straightness, throughness.
Here is the "change of bend" exercise
(may be done on serpentines, straight lines or on 20 meter circles depending on the training of your horse):
WALK in left bend to left CANTER (12 strides or so) WALK 5-6 steps left bend
<change bend in 1 stride>
WALK 8-9 steps right bend to right CANTER to WALK right bend 5-6 steps
<change bend in 1 stride>
WALK in left bend and repeat the series.
You need to change bend with your lower leg while maintaining a neutral rein connection. If this turns out to be blocked, then the block(s) can be identified as the specific problem to solve.
1) PROBLEM: Your horse contracts its neck, comes above the contact.
SOLUTION: Dropping the withers and contracting the neck means horse does not respond to leg by relaxing jaw and lifting withers, so needs work in walk-trot serpentines and broken lines until you can CHANGE THE BEND WITHOUT ANY CHANGE IN TRAVEL ALONG A STRAIGHT LINE OR CURVE. Then go back to walk-canter transitions.
2) PROBLEM: Your mount lurches forward (falls against the hand) in the transition from canter to walk.
SOLUTION: Ask for the walk transition out of canter by closing the fingers (NO pulling, please!) on the inside rein at the same time you step straight down in the inside stirrup. If you have a problem with the leg aid, check to see you do not turn your toes out (locks the hip joint so your seatbones cannot follow the pattern of the back muscles in the gait) or clamp with your knees (disables your seat and locks the horse's shoulder blades).
3) PROBLEM: Horse gets indignant at being asked to change bend promptly. May slow down or give some other indication of being not forward (behind the leg).
SOLUTION: If the horse is genuinely behind the leg, a light tap with a whip behind the inside leg that gives the aid for the bend is appropriate. Spurring may involve tightening the seat or leg and is problematic if you are not expert in subtle use of spurs. Horses can also learn to ignore spurs or riders become dependent on them rather than revising their position. Check to see that you do, in fact, reverse the aids, which means you must reverse the relative position of your seat bones (inside at the girth, outside 4 inches behind the girth). If you can't do this easily, YOU are stiff and need some relaxing and stretching before you get in the saddle.
4) PROBLEM: Your horse (and you) rush through transitions.
SOLUTION: The major problem may be that tempo is too quick. Dressage transitions (level balance, promptly forward, fluent limb swaps between gaits) depend on long enough ground contact time with stance limbs so swing legs have an optimum chance to reposition for the next gait. This requires strength, flexibility and endurance. There needs to be time to develop STRENGTH plus ENDURANCE to lift the withers and manage the limbs in the transition. Practice of transitions should recognize that they are potent developers of gymnastic capacity while at the same time being fatiguing. A few well done will build confident balance while avoiding making a horse tired (and resentful).
If a transition to canter needs refining, try to leg yield from the quarter line to the long side, then pick up the canter at the long side (helps with inside leg at girth). In the down transition, try it on a 15 meter circle so the circle helps with bend and balance. Leg yield only works if you perform it with the inside leg at the girth. A yield done with the inside leg behind the girth produces a leg yield, but does not connect with the canter depart.
Advantages of this change of bend/half halt exercise for troubleshooting are enormous, because it increases throughness in a posture which is possible for the horse given its level of training. It also keeps the poll up because of the natural tendency for the horse to come up when changing its bend. The upward half halt on a rein can lead to evasions that are hard to correct. A subtle change of bend without changing the line of travel is a very effective half-halt (call for a rebalancing change of posture of the whole spine).
As the horse becomes more forward and straight, it is more through (meaning there are no blocked movements in the entire spine either longitudinally or laterally). The poll position is maintained because the rider uses a neutral or supporting rein plus the lower leg for adjusting posture (some call it "frame," but I like "posture" because it means adjusting the spine, not just the outer profile).
Oh yes, there is the issue of suspension. It turns out that there is a worship of suspension in some quarters of the dressage community. Expressive gaits are elastic and cadenced (marked tempo which gives limbs time to complete their motion with out hurry or tension). Gaits which are cadenced may have little suspension (passage) or none (piaffe). The canter with the most suspension is the extended canter. Medium canter should show some "jump." Collected canter, school canter and pirouette canters have the suspension absorbed into leg contact times. The issue is too long to go into here, save to say that the only thing a horse or human in the air can do is fall back to earth, and the longer the fall the more the concussive forces on limb structures. At the acceleration of gravity (32 feet per second per second), time in the air with all four feet off the ground is so brief that it does not contribute much to cadence in collection. Footing and conditioning become serious issues in considering suspension.
So even if you are getting comments on your dressage tests about 'needing more suspension,' get some videotape of your horse and with your VCR step forward through each frame so you can see exactly what your horse does. Sometimes Morgans, Lippizaners or Friesians have limb angles such that they move with less sweep and more flexed joints. The consequence of this is that their timing is slightly different than, say, a Thoroughbred. Their canter may be "flatter" or with less "jump." If you are getting comments about "4 beats" in canter, this can be checked on video. Some judges tell a rider that they observe a flat canter but do not have time to explain what a flat canter is (a dressage test is not a lecture or a riding lesson). A "flat" canter is one with minimal time in the "silent" or suspension phase (see movie HERE).
The exercise above will help build the strength plus endurance that your horse needs to manage its legs in swing phase (off the ground). Once it can do this, transitions and straightness will be better. Your horse will be more comfortable with throughness, because it will have the athletic foundation which makes maintaining the "up through the withers" possible. Remember, the horse has to lift its withers with you sitting just behind them! Real strength training is involved!
Look for gradual, rather than sudden progress. This is indicative of solid conditioning and non-injurious changes in ability to stretch. And no matter how well trained, a tense horse is not straight because the muscles of its stronger side will hold it out of equal alignment.