I subbed in PE today and observed something quite amazing. We played Cornhole (bean bag toss) with two people to each pair of boards. I told them we were playing to 21 - 3 points for going in the hole and 1 point if it stayed on the board. Fourth graders were first, and I noticed some pairs were adding the scores of both players to see how high they could go. The next group of fourth graders did the same. They cheered as much for their opponent as they did for themselves. I decided to tell the rest of the classes they could score either way. A large majority of third graders, second graders, and kindergartners chose to go for one big number. They didn't even compare numbers with other pairs, and they all had a fantastic time.
It was a wonderful example of kids opting out, on their own, of a win-lose game and playing just for the fun of it. I set up a competition and they turned it into a partnership. Score one for those who believe cooperation should trump competition in school.