First of all, you'll want to make sure that your dwarves actually ARE training. You might have the schedule under the wrong alert, or you might not have a barracks designated for them to train at. How do they show up on your units list? What are the actual activities they're currently engaged in?
Second, a squad full of dabblers trains very slowly. They keep trying to teach each other things, even though they're no good at fighting, no good at teaching, and no good at learning, and that leads to slow progress. Could be that all those dabbling kicking demonstrations are doing more harm than good, by preventing good sparring.
So how do you train up your first squad? Combat. That could be a danger room (cheap as it may be), an arena (almost as cheap), risking their lives on the field, or sparring.
I'm not totally sure on how to get your dwarves to spar rather than go to demonstrations. I believe that a relatively smaller barracks helps. I also believe smaller class sizes and lots of idle time for your military helps. Sure, the procrastinators won't spar, they'll only ever attend classes, but you'll find a few dwarves getting skilled more quickly.
Once you have a couple of really skilled dwarves in a squad, the demonstrations will be much more effective, because they'll actually have some knowledge to share-- and then they'll become better teachers, and their squadmates will become better students as they become better fighters, and will eventually even become good teachers as well. Once it's time for your next squad, distribute the really good teachers evenly through the squads, and you'll see the second squad trains up much faster than the first ever did. Then-- guard your teachers' lives carefully
This can go a lot faster, I've discovered, by starting out with one or more proficient teacher military dwarves. It can also work in conjunction with other methods, if it makes it feel less cheap-- give a good teacher a wooden crossbow sans bolts and a trapped unarmed goblin to wail on, and he'll become a near legendary hammerdwarf fairly quickly, and then he'll be able to train the other members of his squad that much faster.