I was born in 1957, in Peoria, Illinois. One of my earliest childhood memories is my mother singing this version of the song:

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Into the air, junior birdman
Into the air, upside down
Into the air, junior birdman
But keep your eyes upon the ground.

And when you see junior birdmen
Flying high, flapping their wings
Then you will know the junior birdmen
Have sent their boxtops in.
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Many of the other editions posted earlier are richer and more sensical in both story and rhyme, but I think this short simple version also has its charm, especially for youngsters. Indisputably a catchy tune! And, as others have remarked, nice to learn it is widely known and remembered.