Yesterday Natalie finally managed to count apple bites correctly. A couple of months ago she was able to recognize the numbers one through eleven but she had little understanding of counting: Whenever I asked her to count some items, she'd point at them randomly and say one, two, three, etc. Sometimes she would stop at the right number but most often she would not.
This weekend I showed her that she could move one apple bite to the side with each number. And repeatedly she was able to figure out the right number. It made us both happy: me because she could count and her because she got so many apple bites.
About fourty years ago I delighted my father by listing all powers of two up to 8192. To show his appreciation he gave me some money. It was the first money I ever earned. Years later I got my master's in math. So today I gave Natalie a present: a jigsaw puzzle of Thomas the tank engine.
Can't wait to teach her differential equations!
