Here's a really simple idea. Put the horse before the cart.
What we used to do was hold out a reward in front of a child and ask him to do something. Call it a demand, a stimulus, a command, but it was rarely anything so mild as a request or suggestion. The child was then expected to follow with the proper response. If he did what was asked, he got his reward. The rewards were deliberately chosen from things the child really liked - candy, stickers, soda pop, TV or computer time, even money. Naturally the thinking was that if what we were offering was highly motivating, the child was more likely to do what we wanted. The rewards could be immediate (a single piece of candy) or a little more delayed (earning chips to trade in later for something special).
If a child wasn't behaving as we wanted, we would often take away privileges. Again, we tried to use things that meant a lot to each child. If he liked to play with trains, that would be the first thing we took away when his behavior wasn't acceptable. And for kids who loved recess, we might even take that away. We thought we were using behavioral techniques that should be effective. Sometimes they were, but often things got worse. We had a lot to learn!
Putting the horse before the cart was an idea that came from a wonderfully wise occupational therapist who helped me learn so much about kids, behavior, out-of-whack sensory systems, and the value of sensory integration.
The simple part: give them what they need/want, as much as they need/want (within reason, and as long as it's good or at least harmless). Let them have their fill, and then try some meaningful work or requests for particular performance goals.
Instead of using time on the swing as a reward for finishing the first grade math work, let the child swing first and work later. If the child is hungry or thirsty, give him what he needs before asking him to sit and listen. If Disney movies are particularly motivating, watch one segment then work, watch another segment to help them organize themselves before leaving for a class that might require them to hold themselves together for a longer time than usual.
We ended up running a classroom that was much more like a therapy room - swings, a mini-trampoline, music playing, a wide variety of toys and games. We helped the kids learn to play before asking them to work. We kept our "demands" to a minimum, trying always to be sure there was a valid reason for what we were asking kids to do - never just busy work, and certainly never just to establish their compliance.
We were ever on the alert for signs that a particular child was dealing with sensory issues that interfered with their success at school. And then we tried to intervene in the most appropriate way. What I learned from that particular O.T. was that most kids will seek what they need in the way of sensory input. If they need a quiet place with little stimulation, they will run and hide. If they need more activity, they will bounce, run, rock, whatever works for them. If things are chaotic and overly stimulating, if a situation is particularly anxiety-producing, they might scream or become aggressive. If their needs can possibly be met in advance, the chances for undesirable behavior are greatly decreased.
It's a powerful combination: meet their needs and make sure we making reasonable, meaningful requests.
We gave up the candy, chips, and soda pop. We did away with "time-outs". We didn't need them any more. Everyone was much happier. School became an OK place to be.