I studied my kid from day one. Since I had to stay home in the evening, I read after bedtime, and part of what I was reading was Piaget... back in the early 70s. So I played with Piaget's ideas on the carpet with M. Piaget rarely dealt with language per se. Most of his work was conceptual and spatial. Babies and small children obviously don't understand half of what you say to them. What I discovered was that they certainly do understand all sorts of physical stuff through what psychology calls kinesthic learning. Wrestling out of their diapers for example. M enjoyed this kind of stuff as well as fake wrestling, being handled well and nicely and all sorts of physical activities, like being chasted while crawling away madly flayling. I enjoyed all that stuff too. In our family division of labor, the ex did all the `school' stuff like going through picture books and talking, naming things and animals from pictures, letters, numbers, etc.
So, the point is that language skill, under the poverty of input theory, can lead to an alternate conclusion. A child's language capacity and skill is vastly augmented by their physical activity. I found that to be so true, I started deliberately working through physical manipulations and games, like taking apart a broken tape recorder with little and so forth. I used a sort of spontaneous play, nothing too systematic...
So, I see a problem with only focusing on language, as language. Such a focus obscures the whole realm of kinesthic learning, as well as the later social interactions and relationships, and that sort of learning, etc, etc. My suspicion is that all that non-verbal stuff becomes incorporated into the linguistic sphere but later through some system we don't understand. M was a late talker and at first that worried me----geeze, I over did it. But once he started talking of course he wouldn't shut up...
CG