Good points, Rowan.

I smiled at your comment about me doing notations for children's handclap rhymes. I would love to have some dancer or another person who is more detail oriented than me document how the handclap routines and other movements routines I've collected are done.
But, when that information is shared, I would be careful to add that this is a pattern that was observed at a particular place in time with some particular children. I would also say that, although the pattern appears to be very fixed in that particular locale with these particular children, the pattern of performing that particular rhyme may be different elsewhere.

I have seen x and o notations written above specific words in some books on children's rhymes. They are difficult [for me] to follow, though other people may "get it". I do better with word descriptions. However, my concern would be that some people would think that this is the only way these specific rhymes can be performed. Of course, it isn't.

That said, there does seem to be a basic pattern that I've seen children do for two, three, and four person handclaps. And I've also observed some basic patterns for group handclaps {some of which by the process of elimination, become two person handclaps}. I have also observed two basic patterns for foot stomping cheers {my term for identifiably formulaic patterns of rhymes that are chanted by groups of girls while they perform, synchronized, syncopated bass sounding foot stomps, individual handclaps, and body pats}.
I believe that for the historical/folkloric record these movement patterns should be documented in print and in video. But, I would not want any person to think that these were the only ways to say or to do these rhymes or cheers.

I've found that children are usually very inflexible when it comes to making changes in the performance activity and text of any rhymes or cheers that they've learned. However, I believe that we adults who have an interest in folk culture can help to lessen this inflexibility if we ourselves are more flexible.

My sense is that in time an increasing number of children & teens will be posting their examples of children's rhymes, cheerleader cheers, and footstomping cheers on Internet message boards, blogs, and discussion forums. I hope that we adults who also post to and/or moderate those Internet websites are proactive in explaining the concept that "variations aren't necessarily wrong" on those Internet forums as well as whereever & whenever we interact with children & youth.

In repeating this message we can help children & teens & adults learn to respect & appreciate their own traditions and other people's traditions.