When I was at the eye clinic recently (fine, fine), I was passing the waiting time for my eyes to dilate by reading Scientific American; there was an article by Alison Gopnik on how doctors (et al) have misunderstood children's ability to learn during the years they are not talking fluently (my word there) yet. Fascinating, but I only got to the end of the second paragraph and fuzzball eyes when I was called. Didn't just lift the magazine later on because the doctor walked me out... (laughs, would I do that? No, I might ask for a photocopy of an article).
Anyway, I want to look up that article. I'd figured as much from reading recently, but want to read Gopnik's descriptions further.
Aha, this is it - it's from July 2010. http://www.scientificamerican.com/article.cfm?id=how-babies-think
Anyway, your daughter's smarts reminded me about that article.
Edit, I'm now thinking Sozobe may have spoken about this before and that I forgot.