My mother taught us the tongue twisters that she learned growing up. My favorite is “the mistle thrush whistles in the thistle bush”. There are mistle thrushes in Europe but not in the United States. It is also found in temperate Asia and North Africa, here.

A counting rhyme that we learned is this:
“Intry mintry cutetry corn
Apple seed and apple thorn
Wire briar limber lock
Three geese in a flock
One flew east, one flew west
one flew over the cuckoo’s nest
Sit and sing, by the spring
One, two, three
Out goes he.”

Here is another version, from 1920: https://etc.usf.edu/lit2go/74/nursery-rhymes-and-traditional-poems/5204/intery-mintery-cutery-corn/.

We also learned some of my grandfather’s songs. A piece of this one:

Only we learned it as “chop, chop” not clap, clap. It’s like a 1960s line dance, isn’t it? Shirley Ellis, 1965.

For the Ragtag Daily Prompt: whistle.

And here is a version with the clapping:

I would bet that there are way more elaborate versions of the clapping.

Before that, a song called Little Rubber Dolly was recorded in 1930.