Apparently Button Knows Addition?

Sometimes I attempt to teach my 3 year old things. It's usually well after everyone else's 3 year olds are doing the same thing, and I suddenly remember that there's more to raising a child than force feeding them meals and building super awesome lego pirate ships. Somehow or other he's learned all the things I figure one ought to know by 3, though, so apparently fly-by-the-seat-of-your-pants style teaching just works around here!

Anyway, so today I decide to teach Button addition. He's got counting down. Yesterday he surprised me by counting all the way to 30, instead of twentyten, so I suppose I was inspired by that. I figured I would simply introduce the IDEA of addition (that adding more things means you have more of them; combining two numbers gives you a new, bigger number, blah blah blah). I thought it out. I planned a strategy. We've counted piles of legos and put them together before, so this shouldn't be too hard, right? I talked myself into it, secretly fretting that I'll never be able to communicate such a complex idea to his little mind and he'll be doomed to math failure the rest of his life.

I decided the best way to introduce this would be with the chalk board. He likes the chalk board. It's the only way I ever got him to write a letter! Apparently sitting down with a pencil is asking a LOT of an active little boy... I probably should have assumed that, but I digress. So I wipe off the chalk board and begin. I draw one star and ask him how many stars there are. He counts, and tells me, "Five." I realize he's counting POINTS on the star, not the star itself. I convince him there's one WHOLE star, but am thinking this is already not going too well. I draw another star and ask the same question. "Ten", he answers. Shoot, he's counting points again AND already added the points on the two stars. He's a bit ahead of me, I think, but we move on. I reiterate that we're only counting whole stars, and when he says "two" I rejoice at our progress.

I decide at this point to abandon the stars and just write 1+2. I ask him "How many is 1 plus 2?"
"Three!" he answers happliy. Lucky guess.
"1 plus 3?" I ask.
"Four!" he exults, with his head cocked nearly upside down.
We get all the way to "1+9," with him answering correctly each time before I figure he's probably just counting.

"Alright," I say, and go back to drawing out stars. I draw two stars with a 2 next to them, then below that I draw four stars with a 4 next to them. I know I've got him now, but I figure I can use the bigger numbers to teach the concept. "How many are two stars plus four stars?"

"Six," he replies after looking over my star scribbles.

"Go play," I concede. No point in teaching him what he already knows.