How do you deal with a child who understands what he did wrong and doesn't mind being punished?

My 5 year old is a really sweet and nice child, we never really had any type of behaviour problem with him. He's really curious and independent so sometimes he'll just try to do everything on his own and it won't work as he wanted. He's also pretty determined, so if he wants something- there is no stopping him.All that sounds pretty normal, except that recently he's been really bored at school and just doing his own thing. So when the teacher asks them to stop a project, he prefers to continue it and elaborate it instead of napping or coloring. We've spoken about it (us- parents and the teacher) and I insisted with my kid that he absolutely needs to follow the rules, even if it's not fun. He did great for a few weeks, but then he started getting bored again and not really listening.The teacher kept giving him "warnings" which obviously we talked about. We also told him that if he had more than one warning per week, he wouldn't get the famous "freezie" (MR Freeze that we need to pay for) at the end of the week. All good, he had no warnings at all until yesterday when the teacher left a note on his agenda saying that she caught my kid hiding the warnings that she'd been handing out to him and switching them for "good notes." She also said that when she caught him, he immediately said he understood what he did wrong, that he is sorry and that he will give all the notes to us.I felt really embarrassed when I read that and when we spoke about it, he looked embarrassed too. He wrote to his teacher, apologized again, he told me why he did it (apparently he didn't like getting warnings and it having consequences and he thought they were useless) and he said he wouldn't do it again.When I told him that he wasn't allowed to play with Lego for the whole evening (which is what he does after school all the time) he looked sad but told me he understood and nodded. Instead he helped me make dinner and drew a few drawings for his teacher and friends.I don't even know how to process all this. I don't know how to keep him stimulated at school when he's bored. It's clear to me (that's also a teacher) that he's just too advanced in some fields and that he loses interest quickly in stuff that is easy to him, but I also know that there is absolutely nothing to do with that and that he kind of just needs to try his best anyway and to keep pushing through it. The teacher is there for the whole class, not just for him. He also seems to understand this.I also don't know how/ if/ when to punish him. I'm a big believer that if a child realized what he did wrong and tried to fix it, I let it go, but this is recurring and whatever I'd do as a parent or as a teacher isn't working with my own kid. I've tried reward systems, punishments, consequences, talking.. I've spoken to his teacher...Anyone else ever dealt with a child like mine? via /r/Parenting http://ift.tt/2p2go3u