Now that he's 5, he also has the verbal ability and the confidence to express mathematical concepts. Turns out he has a really good spatial mind.
For example, yesterday he was in the kitchen playing with a toy sled that's about 2 feet long. There were two chairs on opposite sides of the kitchen. He held the sled up, like the beginnings of a bridge between the chairs, and said, "It would take about three of these sleds to make a bridge between the chairs." Just eyeballing it....so casually. And he was right. Anda and he measured, and it took about 3 sled-lengths (3 1/2 to be exact) to reach from chair to chair. He could just SEE that. I am so bad at distances, so I was duly impressed.
But then today I was even more impressed. I was explaining to him the concept of paying postage by weight for an overseas flight to get his picture to his Grandma on the other side of the world in Portugal. He listened and comprehended. Then he held his hands up as if he were holding an imaginary ball. "The easy way," he said, "would be to slice the world here, right in half." He showed me with his hand, cutting his imaginary ball into two pieces, pole-to-pole. "Then just turn this half around, and we'd be touching her and could just give it to her." He showed me with his hands, manipulating the pieces in the air so deftly that I could see what he was seeing. Practical? No. But the fact that his 5-year-old brain could dissect a world and manipulate the pieces so that two points on opposite sides were closer together--that's some impressive geometry. Especially for a guy who is just supposed to be learning that you can combine groups to make larger groups.
He says he wants to grow up to be an architect. I believe him.