Cindy:
I agree with Carolyn.
I want to add too that a lot of horses take off because they are out of balance and do not know what to do - it is more comfortable for some of them to go to the gallop instead of canter. They are two different gaits. There is a gallop and there is a canter. The canter is slower and 3 beat and they really need to engage their hind end and collect to a degree to balance. This is a new thing for them. So the walk-trot-canter working in a 20 meter circle and cantering for only about 5 strides at a time is a good idea because you can use the circle and the transitions to help him find his balance. The circle because he should be bending his body around the circle - the transitions because practicing transitions up and down help a horse engage his hind end and get it under him. I would practice the transitions up to trot and down to walk and halt and then walk and trot and then down enough so you start to feel him react to the aids quick through those transitions - his body will be more on the aids and more balanced then. Then try the canter. I would open you hips - sit deep but light in the seat of the saddle (light because you do not want to hurt his back) and open your shoulders up - give a light half halt and then cue the canter and use a verbal cue. I personally use the cue UP instead of the word canter because it is a single syllable. Make sure the outside rein is secure and that he is bending on the circle. I bring the back foot behind the girth and the inside at the girth and nudge there. Once the horse steps into the canter, you might think to yourself with the rhythm of the steps - 1-2-3, 1-2-3, 1-2-3, 1-2-3, 1-2-3, 1-2-3 and then relax your body, open your shoulders and say TROOOOOT - give the word a downward slowing enunciation and after you cue for a second with your body and the word, then add a little rein. Give him the benefit of a slow transition the first few times and then see if he catches on to your body and your voice and starts transitioning quicker. I hate to snatch a horse in the mouth BEFORE he has had a chance to learn how to respond the way I want - but also be ready because you do not want to get hurt either - this is a reason why a round pen or small arena is very useful - not just because there is not room for him to take off in it - but also to give you a chance to relax and not be anticipating him running away! THat is working against yourself!
The reason I saw to count the steps of each stride is - as time goes on and you know your horse's rhythm, you can use your body and mind to slow his canter by changing the rhythm of that 1-2-3, 1-2-3, 1-2-3. But if it is overwhelming to do it - don't yet. Some people learn better if their mind has something to think about and some people learn better when they can just focus on one thing only.
-Lara