Answer

By Your Horse

Dressage rider and instructor Claire Lilley says…

To help improve your mare’s canter, you could move on to lungeing her in side reins. Use plain ones rather than elastic ones, as these don’t give the horse any support. Fasten the side reins so her nose is vertical to the ground and her poll the highest point.
If your horse lowers her head too much, use small tugs (half-halts) on the lunge line to raise her head to the correct position. This way, she has the best chance to work correctly through her back and take weight on her hindlegs, which she must do in order to canter slowly. She needs to get the idea of cantering slowly for a few steps, then trotting again on the lunge.
When riding, you need to be firmer in your back and stomach muscles to prevent your mare going too fast. Maintain a steady contact with the bit, without dropping the contact or pulling back, so she learns to accept it quietly. This should follow on from lungeing her in side reins. 
Circle work, ground poles (single ones) shoulder-in and leg yield are all useful exercises to help her become more balanced and able to collect. It can help to ask for canter from walk (it doesn’t matter if she trots a couple of steps first).
Work on large circles rather than straight lines, as this makes it easier for the horse to balance initially, as well as enabling you to spiral in on the circle to help your downwards transitions.