He's a boy in a school system that has been re-designed from the ground up to ignore the needs of boys, to instead focus on the needs of girls. How much recess does he get? How many chances to get a bloody nose, or dirty clothes, or wrestle to figure out pecking order? Boys need all of that to function well, they need to be able to challenge, and learn about losing, and striving to overcome. Boys don't need gold stars, or rainbows, or any of the other rewards many little girls live for.
You want him to behave, he needs to be worn out. Do you spend time rough housing with him? Playing football, tossing a ball, wrestling on the lawn? If not please get him into a program that will challenge him physically. His mind will follow. Jiu jitsu has done wonders for my buddies shy little brat. He is now an animal on the mat, has a ton of friends, and has learned discipline, respect, and most importantly, how to deal with losing in a mature way. (And he is now an A student who listens to his teachers.) Get him into weight lifting, no six is not too young, just make sure he isn't pushing any limits. Swimming is another great one. Get that boy exhausted daily. Then love on him. MY dad was a hard ass, but when he hugged me, man I was on cloud nine; that love goes a long way.