Sparrow, got a swimming question for you.
I counted my strokes yesterday: 26 - 29 strokes / 25m. I watched another guy doing freestyle and he used 16 strokes after an initial kickoff, so probably about 3 or 4 more strokes.
I think this high number of strokes was quite revealing and I am going to mention this to my swim coach once we get started. Obviously, the way to increase efficiency is to minimize stroke count. And, the way to do that is to increase hydrodynamics and propulsion, right? I won't be able to fix the hydrodynamics without a coach watching me, but I have intentionally backed off on kicking to save my legs for the bike and run (as recommended in Total Immersion).
I did work on my rotation and it seemed that when I intentionally "reached out" my shoulders rotated. But, I also noticed that I rotate moreso on the breath strokes than non-breath-strokes.
Any suggestions or is this all coach/pupil stuff?
that was a good idea you had counting your strokes. Its really the tell-all method when considering one's efficiency in the water.
I have found that rotation is absolutely key. Without rotation you will be using your shoulders primarily to pull which will get you little endurance OR efficiency. Those are weak small muscles compared to the big ones in your back.
One thing you can do right away to help promote the rotation is take your legs away with a buoy. If you don't have one, put a kick board between your thighs and make most of it stick "up" as you are laying down in the water, like a shark fin. When you rotate the extra board will slap down on the water and you will be "coasting" on the flat side of the board. If you don't feel it touch down, you're not rotating enough. The arm out front is like your lever. You have to let it ride out there for a bit before you start your pull. It glides on the water and makes you streamlined. If you take a stroke by entering the water and immediately pull down instead of gliding out, you will be trapping air bubbles with your stroke instead of pure water. Enter the water, rotate to the side so the front of your body is perpendicular to the bottom of the pool and that will be the greatest reach you can achieve.
When you breathe you will naturally rotate more to that side. The goal then is to tune into how much rotating you're doing on that breathing side and try and mimic it on the other side you aren't breathing on.
Another thing you can do with the buoy is to go many strokes with NO breath. This makes you more even and you can clue into how much you're rotating. Exaggerating your rotation for a while will make it habit more quickly. Don't worry about the speed part of anything. Get your mechanics down pat and you will be fast. I promise.
Last thing I have to say is note where your head is. If its buried under the water or up too high (like you're staring at the other end of the pool) you will have a hard time rotating properly.
wait one more thing

A great set to do for this is something I call "mini maxies" and everyone giggles when I say that

you will count your strokes for an entire 2 laps (1 arm is 1 stroke) and then ADD it to the exact time it took to do the 2 laps. Repeat as much as you want and try to lower the number. the lower the number, the better the efficiency. You will have to play with speed, technique, streamlines, kicking etc. to lower that number. Its not just one thing that comes into play. A good goal for you is to get under 100