The landings were under a parachute canopy.

I believe I thoroughly answered the original question.

really don't know the # of landings... but I know when I did my PPL in 1978.... solo'd at 10 hours... took my PPL check ride at 43 hours.... passed...

In UPT... solo'd on flight 9 for T-37s ... and about the same for T-38s.. really not much leeway there.. .its in the syllabus... and you are either ready or you bust the ride...recollection is that there was basically a 2 hop window to be ready.... yes we did have some guys who didn't make it and never solo'd.... total class stat's..... 66 started pilot training... 28 graduated.

The biggest problem that I see with new CFI's is them trying to do touch and goes before the student has grasped ground effect.
Stop trying to get the wheels on the ground every approach. Work on getting the student to fly the low approach getting stabilized in ground effect. Once the student has a solid grasp on ground effect, the plane will land itself. Teaching this way, also instills the idea of, if something doesn't look right, go around instead of making a bad landing and potentially having a big insurance bill to worry about.

Trial and error causes headaches and a sore lower back.

try this method if not already using it, and I bet you will see a change on your students success rate.

I think within limits, a student has to use trial end error, stray towards the limits to see what happens, you have to teach them right, but if you never let them mess up they'll never experience what happens at the limits and won't understand what happens there or why it's bad. More than often I've had someone that would fail to control the plane at the limits, simply because they'd never had that experience before (taking over with a student for another instructor). This isn't a haphazard "let the student go on his own" approach, but trying to make everything fit into a perfect box can really mess someone up when they are on their own and something abnormal happens. IMO, many students, CFIs and even commercial pilots, don't really understand landings and the dynamics involved, which makes it take much longer. Cue points given are often vague or make no sense when you use critical thinking, some of the directions just don't make sense to a student that lacks the common understanding. It was always rewarding though to get a new private student landing better than a commercial or cfi student that had trained with someone else. The great thing about private students is usually whatever they do, good or bad, is a direct reflection of your instruction :)