How do you deal with an immature boyfriend?

Hi so I have my boyfriend whom I love so much, but we both have our quirks, which can make eachother a bit mad or annoyed. I'm working on mine, but it doesn't seem like he's working on his very much. Basically when he gets mad he pouts and won't talk to me and so we spend half the day being mad at eachother or I'm just distraught because I have no clue what I can do to help him. We're in highschool and he does this in class. I find it a bit embarassing when he does and I've told him but usually he just pouts about it. He knows he acts this way and I don't appreciate it, but he does it anyways. I look at it as an immaturity thing. He's not afraid of telling me things; he just doesn't and starts to sulk. I've talk to him many times, but I'm still at a loss of what to do. I love him to death and I hate saying I want him to change, but I think it'd be a change for the better. Just like me not being jealous anymore. How do I help him when he's in this state and is there any way to help him speed up this process of maturing?