@Thomas,
It's very cool actually! Exactly parallel -- handshapes = phonemes, or something (too long out of grad school, but I remember the gist). Main point is that babies babble with the component parts of the language ("ba ba ba" or mushing a hand against her face repeatedly), and then through feedback it's refined.
At any rate, sozlet would "babble" in ASL, and I'd do the motherese thing of taking the close babbles and repeating them "correctly" -- "'Mama', right, did you say 'Mama'? that's how you say 'Mama,'", etc. (All in ASL.)
I'd speak too though, so I did both. Toggled back and forth between ASL and spoken English, and sometimes both at the same time.