An ASL program "Mother Goose" is basically a collection of nursery rhymes and stories for infants, toddlers, and children to help with language acquisition and literacy development in signed language.
In speech, rhymes come with the repetitions of sounds in words. In sign language, rhymes are done with the repetitions of visues in signed words (e.g. handshapes, movements, etc.).
The unmarked "5" handshape is the earliest phonological unit of ASL that appears in infants' early linguistic development in sign language. A video below shows an example of the ASL nursery rhymes produced by Canadian ASL native signers.
In the video, the mother narrates an nursery rhyme called, "Peekaboo Animals." Let's inspect a couple of the elements:
The "5" handshape is repeated in all ASL words of animals before and after peek-a-boo: lion, tiger, bear, monkey, and spider.
And, the location parameter of each of these ASL words of animals is in the order from the top (head) to the waist level.
Baby may enjoy this rhyme especially with the anticipation of the last animal that will tickle her/him.
As the two months old baby Juli was listening, I was improvising a nice little ASL poem with similes between "blue eyes" and "blue sky", and between "white glowing lights in the eyes" and "sunshine in the blue sky" (ASL rhymes also). And, the "black bird flying" in circle.
Taking an advantage of the visual-spatial nature in sign language, I can transform an imagination into reality. For example, I produced in ASL: a black bird flies in large circle in the sky and the circle becomes smaller and smaller as it gets closer and closer to the listener.
This intactile imagination transformed into a tactile experience of physical touch through ASL. Baby at this stage is fascinated by spirals and by coincidence I could incorporate this shape into language.
You can compose your own ASL nursery rhymes using some ASL words with the same handshapes.
Also see parentese in sign language: child-directed talk.