critiques of parent word-count studies?

[galey modan]

I recently read the NY Times opinion piece, linked below, about studies
showing that the number of words parents say to their children in a given
time period is linked to socioeconomic class and is a predictor of future
academic success. Although I'm not a language acquisition specialist, these
seem like bizarre and linguistically un-sound studies (at least from the NY
Times piece, it seems like all they're doing is counting words, rather than
looking at any content or structure.) Does anyone know of any recent
linguistic/ ling anth critiques of this kind of work, other than the
somewhat related Ochs and Heath?

thanks,

Galey Modan