Ahhh… the doodling. Of all the things people have mentioned, that's the one I'd personally most like you to understand if you were the teacher standing in front of 14yo me.
I realise that for some students, they doodle because they're bored and then they get involved in the doodle rather than paying attention to you. I guess it's probably pretty difficult to give this student the support they need by not allowing them to doodle, while allowing the student next to them to doodle as much as they like. But doodling is almost essential for kids like I was.
It's like… inside your head, there's a menagerie of animals clamouring for attention, fighting each other, getting into mischief and just generally looking for some way to cause havoc. If you want to get anything done, you need to organise the chaos a bit — get the monkeys into their enclosure, set up a ball-throwing machine to entertain the labradors, occupy the guinea pigs with half a watermelon to eat, and mollify the cat with constant fusses (until it suddenly decides it's done with you, lashes out and stalks off). If at least some of the noisy, demanding, distracting creatures can be temporarily engaged in some other activity, you have a much better chance of success at the thing you actually want to do.
Doodling in my books occupies my hands, my eyes, and several different mental functions that aren't required for listening to and understanding a teacher (like limited spatial planning, motor coordination, awareness of physical sensations, aesthetic judgement, and so on), freeing up some of my limited attentional resources.
If I'm doodling, I'm listening to every word you say, and will probably be able to tell you your last three sentences verbatim, if you decide you'd like to try to humiliate me for "not listening".
If I'm not doodling, I might be listening, but I'm just as likely to be distracted by all the things I can see, or by some sensation I'm experiencing, or by thoughts flitting and skipping through my head.
Doodling is a technique I use to occupy enough of my head-menagerie to free up my attention for you. It doesn't matter how many times you tell me off or make me pay 50p for a new roughbook because you think my doodles are wasting paper, I will keep doing it because the alternative is a skull full of shit-flinging monkeys and labradors eating guinea pigs.