Adventures in being a mathematician and having small children: my 6yo has a habit of doubling numbers. If a number comes up in conversation, he'll routinely just say what it is if you add it to itself. In a video game today we caught a fish that was 99cm long.

IMMEDIATELY he says "huh, 198" and I'm curious to know the steps he took, so I ask how he did it. "Well, 9 times 2 is 18, so there you go" he says, with the beatific look of a 6yo with a cute mop of blond hair.

"Sure", I say, "2 times 9 is 18 so 2 times 90 is 180 and then 2 times 9 is 18 and 180 plus 18 is 198, is that how you did it?"

"haha no"

"how then"

"I dunno"

He refuses absolutely to answer any further questions. He just "likes to double things". Ok. We don't press. Later, my 7yo is doing subtraction problems for a math-y video game, which she greatly enjoys. She seems to struggle with a two-digit subtraction problem so I try to help.

The problem is 85 - 47. It's hard for her only because she insists on doing it in her head; I write it down on paper and she very awkwardly and slowly, but correctly, writes first the 8 and then the 3 to make 38. I ask her how she did it. She doesn't appreciate the question.

"I usually just count down with the numbers" she says, pointing to the row of digits on the laptop keyboard (which has zero at the END which is WRONG but not the point today (there is no point today)) and I am bemused as always. I try to get her to explain the paper calculation.

"Well first I do 5 subtract 7 which is 2 minus, and 10 is 8 but 2 minus, and then I do 8 subtract 4, which is 4 but not because of the minus, it has to be 3, because 4 minus is 3, but you don't write that, in fact you don't write anything until you have the 8, and then the 3."

I am just barely holding on to the varying uses of "minus" (esp. funny since she resents when I use the word "minus" as a binary operation, that word is "subtract", thank you VERY much). I ask her why she doesn't use paper, since it's easy, and the problem seemed hard before.

"The laptop numbers are right here though" she says, vaguely pointing at them again. Precisely how she uses them remains vague. My suggestions that I might teach her a method that would work all the time, even for big numbers, is met with disdain. Who needs big numbers?

You'd think however many math degrees would give you more lead time on your kids finding better ways to do every calculation and then not letting you in on how they did it, but nooooo.