You replaced the rote recitation of faceless homework with engagement from an authority. She was not interested in the sequence of numbers, but interested in your interest. She loves you, and is reflecting your engagement back at you in hopes of getting more validation. Children do that a lot.

You describe the homework as

> basically lots or practice in basic arithmetic

Which is absolutely what you need for these sequences to have any meaning. There is no "pure math" to have a game about, without the "pathetic" examples of Lucy's 5 apples and Tom's 2. If somebody hadn't (brutally) drilled the concept of numbers into her skull, the sequences of random symbols would not mean anything to her.

Engaging with your child, who has already been partially socialized, is not proof that this socialization wasn't necessary. For that, you would have to have locked your daughter in the basement for those 7 years, and then find that she was spontaneously able to do multiplication. That is not going to happen.

> No, you really, really should not be brutal to little children.

I hope you understand that _brutality_ as spiritual. It's the brutality of going against nature, of putting a monkey in a suit and locking it in an office for 8 hours a day to feed itself. You don't beat math into your children, but they sure as hell don't learn it from eating candy and watching Minecraft let's plays.