I have a new 1 year old and foster parented a 10 week old kitten 6 mns ago.
The kitten did the agressive biting thing while "playing". Now my 1 year old does it, but not as much. I read a cat book and it explained if the kitten is taken away to young they don't learn how to inhibit their bite from their mum.
The book suggested the moment the cat starts to bite, DO NOT TOUCH IT, for they might see touch as affection (and therefore reward), but replace it with a toy about their size. You want to teach that is OK to be aggressive with a toy, but NOT with people.
My 1 year old is getting better. As soon as she starts up I either put a finger on her forward with a stern NO (which she doesnt hear for anything else) and I dont touch her and ignore her, even if she is still on my lap. I'm hoping she learns that no biting will mean more hugs, pats, and kisses from me.