One of the best ideas I have found for how to form groups that work effectively comes from Professor Molly Lindner, of Kent State University. The article from which this comes can be found here. She suggests using the metaphor of a quintet (or a trio). She starts off by telling the students “about the qualities of a variety of musical instruments and the roles they play in producing the whole composition. Each instrument makes vital contributions; none is more important than any other. However, each has distinctive characteristics.”
She then gives the class a handout in which each instrument and their characteristics are listed, and asks them to mark the one that they are most of the time, as well as the one they are like some of the time.
The students hand in the completed questionnaire. My version of this document can be found here. The teacher then looks them over and forms the group, ensuring that each group has one of each instrument and never more than one “lead instrument”.
At the same time that I give students the instrument form, I also give them a schedule sheet on which they indicate their availability for group work.
Armed with that information, I first form groups by instrument, then look at the availability factor to tweak them. That way, students are temperamentally suited to work together well, and there are no excuses for why members can’t meet.
While no method of group formation can ensure that every group works perfectly, this method has proven itself to be very effective in my classes, and students seem to love it.