I know we are not drill sergeants, but last I checked, parents are supposed to give directives. They are supposed to tell their children what is not safe, fair or kind, not ask them. Half the time, the kids ignore (or laugh at) their parents' statements and I wonder if that would be different if parents just spoke more firmly. Of course, I can't test that theory properly because almost everyone I know ends their sentence with "okay."
The last few paragraphs of the (snootily titled, yet interesting) article Why French Parents Are Superior touches upon this as well. The French woman is recommending firmness and I bet that the American mother was saying, "Don't run outside the gate, okay?" If that is the case, then it's good news. That means that we don't have to be French to be superior, we just have to stop asking our kids to do as we say and start telling them. Okay?
*My neighborhood is so diverse that I have yet to meet a kid named Jimmy, Sally or Bobby at the playground. They sound like imaginary kids from the 1950s.