Supposed to be an old planting rhyme.
William Wells Newell, 1883, "Games and Songs of American Children," said it is a favorite in France, Provence, Spain, Italy, Sicily, Germany and Sweden but is "unknown in Great Britain." Known to Froissart (b. 1337) and Rabelais (B. 1483).
The game from New York:

The ring circles, singing, about a child in the centre-
Oats, pease, beans and barley grows,
Oats, pease, beans and barley grows;
How you nor I, nor nobidy knows,
Oats, pease, beans and barley grows.

The children now pause, and sing with appropriate gestures-
Thus the farmer sows his seed,
Stands erect and takes his ease,
Stamps his foot, and claps his hands,
And turns about to view his lands.

Waiting for a partner,
Waiting for a partner,
Open the ring and take her in,
And kiss her when you get her in.

The boy selects a girl, and the two kneel in the ring and salute-
Now you're married, you must obey,
You must be true to all you say,
You must be kind, you must be good,
And make your husband chop the wood.

Newell says the basic game is fairly constant, but there is "an amatory chorus," which varies greatly-
And now you're married in Hymen's band,
You must obey your wife's command;
You must obey your constant good,
And keep your wife in hickory wood-
Split the wood and carry it in, (2x)
And then she'll let you kiss her again.

He gives some variant lines, and discusses French, German and other versions.

Black walnut, hope this helps. I hope more are posted.
It does appear in some 'Mother Goose', but apparently only late compilations.