My Nan (Grandma) and I used to sing that song together when I was small. It kept her entertained. :D
We learned it in the first grade (five/six y.o.) as part of our “enrichment” before the gubmint got hold of the education system. That also included learning how to dance (in the winter when it was too cold or the snow was too deep for us to go outside) and learning how to shoot rifles. Not to mention shop and home economics in the upper grades...
Anyway, it was a fun song, and I think we even had a play that had the Teddy Bear Picnic as a main theme... These days, I wish I could have seen it from the parents point of view!