When I was a kid we spent we spent a lot of time working on our feel for the water by sculling. For me, an average swimmer at best, it was something that really helped me develop distance per stroke and a really good catch in all of my strokes.
As a 20 year veteran in the art of coaching swimming I spend a lot of time reading swimming texts, watching swimming videos, and researching swimming websites. One thing that I have noticed over the years is that sculling is not often mentioned as a drill for teaching/coaching in swimming. It is something that I think needs to make a comeback.
Sculling helps kids learn how to apply a continuous force on on the water...from the catch to the finish. The simple act of laying on your back and sculling (without kicking), head first really does promote the feel for the water. Using a large pair of paddles will help encourage athletes, somewhat like fins during kicking, by increasing their velocity (sculling is not really a fast drill).
Once sculling on the back is mastered, then additional styles can be employed to further develop and enhance swimming skills. Sculling on the back (feet first), sculling on the stomach head first (hands deep and slightly in front of the shoulders), etc.
Regardless of the style or equipment used during the drill, I think it is important to bring sculling back. At least once a week...if not more.