An effective strategy that I've used was inspired by Allen Mendler's, Discipline with Dignity. Essentially, whenever two children have a disagreement or an argument, a mediator (at this age, likely the teacher) pulls aside the children or takes them to a relatively private spot.
The mediator asks one child to tell his or her side of the situation, while the other child listens, and then the other child takes his or her turn to voice a point of view. Establishing rules for this exchange is essential and a good skill builder in active listening; the other child cannot comment while the other child is speaking.
The mediator then retells what he or she heard each child say, i.e. "I hear Joe saying that ___ happened, and he feels ____ about the situation. I also hear Sara saying that _____, and she feels _____." The next step in the resolution process seems a bit contrived, but it's an important one. The teacher, as the mediator, asks one child to think of one thing that he or she really likes (a personality trait, a skill, etc.) about the other child, and vice versa.
Some children may raise their eyebrow at this one, but once they start to share, the magic is released. Most tend to forget the negative feelings they were harboring over the situation, and instead focus on the compliment given them and on the positive attributes of the other person. The mediator can then suggest a solution for future situations, or pose this question to the students. Last but not least, the students must look each other in the eye and shake hands.
Though I didn't start to use this idea until halfway through the year, I can see the distinct advantage and benefit in promoting this approach early on in the year. There are a plethora of ideas, if one is willing to seek and discover. I recently also found this free article on conflict resolution at the elementary level through Scholastic. I am eager to try some of these approaches out next year, to experiment and look for children to start independently applying these strategies. What a triumph if students are able to self-regulate and use these on their own! I am a firm believer that the start of a better world CAN begin in the classroom.
Of course, I have those moments where squabbles and disagreements break out in the middle of a transition, or in line on the way to lunch. It is in these fast-moving situations, where there's not ample time, or even a good 5 minutes, to focus on structured conflict resolution. All the more reason to build these skills in the beginning of the year. I've taken to using the simple phrase, "be the bigger person", with a reminder to breathe and let go of the little things, like being "cut" in line.
These aren't necessarily small things to a child, which is important to remember - but having some sort of quick verbal and visual reminder for kids in these instances is key. Better to try defusing and neutralizing than to wave a hand and leave those students feeling angry and discouraged!