"I used the word full Natural Turn"

Actually, QUICKSTEP, you didn't.

REDRIDING did. Are you unable to keep track of your multiple personalities?

"because I could see that to you a Natural Turn is only the first three."

Apparently you aren't aware that the second half is nothing but a role reversal of the first...

"I also added that in a class of beginners it is possible to do a series of steps which has a nice movement about it, keeps moving, and has less turns it. "

Sure, you could also dance quickstep. But neither one would expose you to the technqiue of the 3/8 turn waltz figures... which is SUBSTANITLALY DIFFERENT than the technique of 1/4 turn waltz figures!

You could also teach them the rhythm foxtrot instead...

The whole idea of the teaching is for a class of say 12 couples all beginners not to do the 3/8 of a turn otherwise they will have to do the other 3/8 of a turn and this we dont want. The rhythm dancing you mentioned is always taught first in the first half of the class. Followed by the quarter Turn Waltz. This is a method I have seen which works. And everybody goes home happy.
I' ve also seen the other way and that is trying to teach a group of beginners a Change Step Natural Turn a Change Step and a Reverse Turn. Which the next morning no one can remember. Isn't that right. This other way I have seen them left to themselves to practise after the class and managing very well. This four bar group is so easy to remember that the next time in they dont need to re-learn it. They are dancing straight away. So now they have time to do a Basic Cha Cha as well as the Rhythm Foxtrot again. Method Method tried and proved.

Sure, you can teach a simplified waltz with fewer steps, however:

- at some point they'll have to learn a more complete set of elements.

- full natural and full reverse turns are a complete set, with a first-approximation symmetry that aids memory

- spin turns and impetus turns add extra, unique physical challenges and complicate the overall progression

- so do a whisk and chasse - suddently you have to add concern for CBMP, lowering with the feet apart, and a much more complicated floormap.

A Whisk and a Chasse is taught on the third week and continue with the quarter turn after the man has stepped outside. By this time some are already enquiring about private lessons
Its such a long time ago but the very first steps in dancing I took was in a private lesson although I did have some help from my parents. In my lesson I learnt the Quickstep first up to the Spin Turn and V,Six. and a Quick Open Reverse. I can not remember having to do a Natural Turn when I started the Waltz because I already new what a Spin Turn was from the Quickstep. Thats why from my own experience I would as they always did teach the Quickstep first.
How about that. A dead heat for first place in the World Swimming men' s 100 metres Freestyle. What a race.

Focusing on the closed manuevers had the same effect for us. It is really hard to do a lot of the closed manuevers without fairly good technique. I think that forced us to focus more on technique and really helped our smooth dancing.