Researchers have found that babies under a year old actually learn word patterns (ie grammar) first, contrary to initial belief. They are looking for indicators as to what type of words might be coming next. So if you say "It's a..." the baby will already recognise that you will say the name of an object next. If you use a word followed by "ing" then the word is likely to be an action. They use these clues to build up their vocabulary, rather than the other way around!
That strongly suggests that teaching some of those basic rules and phrases should be part of the initial language lessons for children.