Although it would seem to be one of the most basic aspects of skating, the mechanics of stroking -- progressing forward and backward across the ice between moves -- shows a lot about your polish, and also has a sublime influence on your elements.
Plus it's a pleasure to watch. When you see a skater with smooth gentle strokes it is like chinchilla fur on silk. Every push kisses the ice with such gentleness you can hardly tell exactly when the blade makes contact. It is soundless, rhythmic, and magical. It is fully controlled all the way down.
Just like specialty jump classes, some rinks do have a coach who can offer stroking classes. From what I recall the training is fairly brutal, as physical as running an hour of wind sprints but concentrated on those specific sets of muscles in your legs that position and push.
The immediate influence of this quality is that those who are accomplished at stroking have extra speed to help with balance and stored momentum when approaching jumps. The more sublime influence however is those accomplished at stroking gain this additional velocity without a gain in energy expenditure. Or the other way to look at it is: a skater who strokes smoothly and efficiently can get the same ice coverage as one with rough strokes, yet will be 25% less tired at the end of her routine.
