When I started doing substitute teaching here in Florida, back in 2006 or so, I worked in various elementary schools nearby and learned many things. I learned about FCAT, the standardized state testing system. I discovered in person that Physical Education classes are held outdoors unless the weather is very, very inclement. There is a roof over a large section of concrete where some games can be played or where activities can be held in a light rain. I learned that different schools handled things like lunch and dismissal and traveling around the school as a class group, each in their own way.
Universal in all of the schools was the direction: Criss-Cross Applesauce. Often for story time when the students are called to come to a piece of carpeting in the otherwise linoleum tiled classrooms or in the media center or in the combination lunch room/auditorium area for an assembly or in that covered PE area for roll call. You must have guessed by now that the direction means for the students to sit on the floor, cross-legged.
When I was in elementary school myself, nearly a million years ago, we sat in small chairs at the front of the classroom for reading group. I have a recollection of very occasionally doing a project where we needed to sit on the floor to be able to draw a large picture or make a poster or map or some other group work that was larger than our desks. Occasionally for PE we sat in this cross-legged style and were directed to sit "Indian Style" which is likely the reason it had to be changed. One of the perceptions about Native Americans at that point in history was that they always sat in their tepees or hogans or igloos. or around the fire smoking the peace pipe in a cross-legged fashion. They may have, I really don't know for certain.
The Criss-Cross Applesauce phrase, I learned by Googling, comes from a rhyme, supposedly said to babies. I have never heard anyone use this rhyme. I can only imagine that it came into popularity during the 10 years I worked in Nursing Homes rather than schools. I was also reminded by Google that this sitting position is sometimes referred to as sitting "tailor style" as well.