A piece in the NYTimes (http://opinionator.blogs.nytimes.com/2013/04/10/the-power-of-talking-to-your-baby/) highlights the classic Hart & Risley study showing the huge difference in quantity of child-directed speech that different babies experience, and its correlation with socio-economic status. If all parents could speak more with their infants and toddlers, then perhaps the achievement gap would disappear or at least shrink. The NYTimes article mentions a few studies being done with the LENA recorder to see if measuring the number of words spoken helps parents to be more conscious of their speech patterns and talk more to their children.
The Slate post (
http://www.slate.com/articles/health_and_science/science/2013/09/children_s_language_development_talk_and_listen_to_them_from_birth.html) describes more specifics about one of the projects, the Thirty Million Words Project, using LENA as well as specific training for the mothers about the significance of their words and the impact that their speech can have on their child's future.
Annie Paul Murphy's post (on her blog, on Creativity Post, and on Mindshift) makes the extremely important point that it's not just the quantity, but also the quality of the speech that matters. One aspect is the positive vs negative ratio of what the parent is saying, but more relevant is the interaction, the back and forth, the 'turn taking'.
Another Slate post (http://www.slate.com/articles/technology/future_tense/2013/09/baby_app_ftc_complaints_are_missing_the_big_picture.html) talks about how 'baby apps' can be a positive influence on children - if parents use them as an interaction point! The apps and videos don't make a difference (and may even have a negative impact) if the parent just sets their child down in front of the screen. But if the parent engages with the child and the technology, asking questions about what's happening on the TV, helping the child to use the app and talking about what's happening, then this screen time can contribute to learning. Also another study (Skype Me! Socially Contingent Interactions Help Toddlers Learn Language) finds that young children can learn new vocabulary through screen time, if the people or characters on the screen are responding to children in timely and meaningful ways - aka grandparents interacting through Skype.
Interaction and participation makes all the difference - talking with your child, not just at your child, can give them a head start in life.