I had a day lesson with one of the popular instructors on here, and while he did have a lot of good information, he attempted to completely change my stroke to a pendulumn, where I had many years of muscle memory with a piston stroke. Straight back and forth, even dropping the elbow on exaggerated follow throughs.
I say that, to clarify that he did mention to me, I was one of the very very few people he had taught that was dead on center ball when I lined up on the ball.
And how did I get that way? Stroking into a bottle/Buddy Hall cue guide, until I could pretty much do it with my eyes closed, without touching the edge at any point.
What I think this does for me, is it forces me to align my head/stance in the proper locations to be able to both aim along the correct line, and deliver the cue straight upon that line. So I am not really just training my arm to move correctly, but also forcing all elements of my stance into a configuration that works for my vision center.
Now.. To those who will immediately dismiss my training method... Keep in mind that I played with Little Joe Villapando a few years back at Derby, and he specifically comllimented me on my game, and I asked him about the piston stroke and my training method, and he was of the opinion that you do what works for your body, and pendulumn versus piston doesn't really matter if you make the ball and the cue ball goes where intended.
So, to the OP, I guess this all depends on what your student's stroke looks like. If it incorporates a piston type movement, then using my method will force everything into the right planes. If he has a pendulumn stroke, totally ignore everything I said, because it won't work for him.
Short Bus Russ