Recently I had an opportunity down south to teach a class where a young lady who never held a fly rod asked for instructions.
I did not start by teaching the dynamics of loop control or confuse her with words like loading the rod, etc. I gave simple instruction how to place her feet, pivot the body and required arm motions. I try to teach what she might instinctively do if she never had instructions. For the backcast I handed are a small toy asking her to throw it sideways up a hill to me. The first attempts she stopped her and hand in the wrong direction and the toy didn’t come to me.I explained that would be the direction your fly line would have gone. Soon she began stopping her arm and hand so the toy traveled toward me. I got behind and took her hand telling her to look at the tip of the rod and I began false casting suggesting she try to make the line crash into the rod.
I made sure each time she took the rod well back so the tip followed a curve path and when she attempted to hit the line on the rod she created a tight loop. After a minute or two helping her I had her try it alone. She threw perfect loops.
Then placing the line on the grass I repeated the procedure but taught her to pull on the line during acceleration. In perhaps three or four minutes she was making perfect double hauls. I had her false casting. In 15 minutes this lady who never held a fly rod before was throwing tight loops and false casting and with a big grin. I have done this many time over the years.
I have been teaching casting since the 1950s and I think it’s wonderful for the instructor to know mathematics, physics, etc,. But I think most instructors want to learn down to earth techniques that will help them teach.