If he's counting physical objects, perhaps add and remove objects until reaching 0 and explaining to him that this lack of objects is called 0?

People almost always start "stopwatch" counting at 1. If you time how long a juggling ball stays in the air, or how long it takes to run a short distance, a stopwatch will read 0.9 or something meanwhile most people start "1, tw-.." and then say 1.5 or so.

He just will one day. It was my 2 year old's favorite number after a sesame street episode about it.

Yeah, it's pretty incredible, isn't it? Makes you realize that it's not just the training of the brain, that brain is growing and it is simply able to comprehend more as it grows, no training will do that. For some things, you just wait.

Yeah, I think I posed the question just to get ideas for how others think about it. I don't have a need for him to learn it per se, I just wanted to start a discussion about how zero is a difficult concept to teach. Heck, humanity had to "invent" the concept of zero.

I alluded to this in another comment, but what astonishes me about my son is how rapidly he grows and changes. Every night, my wife and I talk about how amazing he is, etc. and I can't help but think about the fact that 1 year ago, he was barely able to roll over, and that he's now running around, "reading," eating solid foods, and a full-blown chatterbox. If he's doing this much now, what the heck is he going to be doing next year?

It's forced me to reevaluate my own life. If my son can accomplish all of that in one year with proper support, nurturing, and guidance, and we are genetically related (i.e. 50% of him is me), then what could I do in the same amount of time?

I've resolved to find that out.

It sure can be motivating. But unfortunately we do not benefit from any growing or our "hardware" anymore (or not as much at least). Where your son get some extra ram and CPUs plugged in every month,we have to make do with what we have.

> He's got 1, and 2 down, [...] He can say the numbers 1 to 10

That's extremely amazing for a kid that is exactly one years old, rather than, say, 1.x years old for high values of x.

He's actually 17 months if we want to get specific. On his 1st birthday, I managed to get him to answer the question "X, how old are you?" with "Wah!", which only became an articulate "One!" around Christmas/16 months, which was also about the time he started being able to say 1 to 10.

He actually is a pretty amazing kid. He's miles ahead of other kids his age, even some who are older. I wasn't expecting to be able to teach him counting until next year, so I'm being very relaxed about it right now and making it fun. He's 1, not 5, as far as I'm concerned, he can do what he wants, but if he's into it, I'll teach him.

Seems like a very technical way to say “almost 2”.

Consider P₁ ∈ H and P₂ ∈ G where H is the set of HN posters, and G is the set of persons in the general population. Let p(P U) be the probability that a person, P, will produce an utterance, U, using mathematical terms and/or notation. Let q(U) be the probability that U will be better understood in mathematical terms than in plain language.

For any U, p(P₂ U) ≤ q(U) < p(P₁ U)

How many candies do I have? Knowing the difference between nothing, one, two, three may be easier than memorizing a set of numbers.

(Although kids can pick up on memorization very quickly)

How many apples do you have when I give you 0?

I’m an embedded C programmer who typically avoids dynamic allocation... so I know the answer is zero apples... but it doesn’t matter because I have to hold my hand out making a space for an apple to go just in case some day you do decide to hand it to me.

>C programmer who typically avoids dynamic allocation

Me too. But the problem is, maybe they'll give you a few. Probably not more than 10 or 20? Say 20 to be safe. So I'd keep an empty box ready.