On 8/3/2007, Science published a research study entitled "Defusing the Childhood Vocabulary Explosion". This study examines a core process in language acquisition, the so-called vocabulary explosion (or word spurt). During the word spurt (which typically happens during the middle of the second year), children seem to transform from slow word learnings (learning maybe 1-2 words per week) to extremely efficient ones. "Defusing the Vocabulary Explosion" suggests that this may be the result of fundamental mathematical principles, not specialized learning mechanisms or radical transformation on the part of the child.
There is a very good summary of the research here in nontechnical language.