The birth of the Hokey-Pokey, recorded for posterity.

Well, they might be learning to kick, but they look a lot more like "Hudson River Dance" than they look like the Rockettes.

It's a Busby Berkeley musical!

I'm a little teapot,
        short and stout
This is my handle,
       this is my spout
When I get all steamed up,
       hear me shout,
"Tip me over
       and pour me out!"

...was a farmer's tan apparently.

As jnc said they are practicing the side stroke. Specifically, the scissors kick and the "picking apples off the tree" hand stroke.

At the University of North Carolina in the mid 1960's, you had to pass a swimming test (four laps of the pool using three different strokes) in order to graduate.

One singular sensation..

Looks like they are all trying to do "the tree." It's even harder when you don't hang on to something.

the purpose of this "flamingo" pose?

Practicing the sidestroke.

Look at the third sailor from right, he looks like a mere boy. I doubt he is a day older than 15!

I the mid 1960s, when I joined the Navy, you couldn't complete basic training without passing a swim test.