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I just googled "elementary backstroke" and yeah... I'm in my forties, pretty proficient swimmer, and nobody ever showed it to me. I watch my kid's lessons and I'm sure I didn't see it being shown to them. They got into what I google as "backstroke" straight away, without the "elementary" phase.
I just looked it up and turns out that's my favourite stroke! I didn't know it had a name, I just called it the "Jellyfish" :) I don't think I was ever taught it. I think I just discovered it playing around in the water one day.
When I want to play around, I try swimming backwards. On my back, with my feet straight ahead and motionless, I stroke backwards with my arms so I move in the direction my feet are pointing.