I would add that it worked that way for potty training here too. People always think I'm crazy when I say he potty trained himself (at 18 months). He insisted that he needed to use the potty (no prior experience) at 18 months. I finally gave in and held him on the much too big potty and he peed and pooped. We bought underwear and that was that.
Math was more the bang your head over his lack of one-to-one correspondence then in 6 months he progressed from counting to multiplication, division, square roots.... and still going.
I am really struggling to explain that yes we were at point such and such so many months ago and yes we are way out here now. Moving target is so right! My phrase has been "his growth isn't really linear as much as sudden enormous leaps". So hard to pin down and plan for!
