I am a mom of a very strong willed 6 yr old son. I have learned that the best way to discipline him is not to be more powerful and have control over him (boy is this a hard way!) but rather to have power in partnership with him and set things up or teach him how to behave and still meet his needs. When you have punishments it is a win/lose situation and that doesn't seem to phase my son. When you have training then its a win/win situation. My son has walked through something so that its now his idea and he is for it.
With regards to the classroom, perhaps the style of classroom is clashing with his personality. He probably isn't a 'line up and follow' type of person and if that's what's expected, this is a hard place for him. My son went to a public school that had a large section of the kindergarten day as "choice time" where there were several stations of learning opportunities he could pick from. Then there were other times where all kids followed along with a (very talented) teacher (who really "got" 5 yr olds). This is all new to them.
I am a big admirer of a classroom structure that is taught by Jane Nelsen that teaches kids to find the answer for problems. The kids help each other to succeed. If that isn't a great dynamic, I don't know what is. I found a youtube video that goes through it if you're interested: http://tinyurl.com/29fl2g8
Being strong willed can be a wonderful trait - it gives someone the drive to do the impossible or become a great leader. However it's tough when you're the parent. One book that really helped me was "Raising your Spirited Child". I should say that I read Dr. Dobson's book on strong willed chidren and when I got through, summed it up for me by the parent needing to be the strongest one and dominate. I didn't want that. I wanted my son to be able to think through something and come up with the best course of action, led by his inner guidance (christian morals) instead of my outer parenting (rules and punishments).
I am really happy I took this style. Some days are really hard when he is difficult, but most days are good and his God-given temperament is still there and as strong as the day he was born.
Good luck! It may not be your son, but rather the school approach or their expectations that are out of line.