To me, commitment means that I am committed to keep on keeping on, no matter what the results are on the first or second day I try it. It means that I have prepared the students for something new and different, and that I have enlisted their agreement to try it out for a couple of weeks and then evaluate it together. It means that I am expecting that it might take a few sessions before we, instructor and students, are comfortable with the format of the activity, and I am expecting that I will have to tweak it a little as I go along.
What is an appropriate activity? There are two aspects to take into account here, the kind of group skills required of students and the difficulty of the math content. When students have strong group skills, when you and they have established a safe atmosphere for taking risks in learning math, then they can, in pairs or small groups, take on some investigations of math beyond their comfort zone, that is, math that is truly new to them, not simply a confirmation of what they already know or have experience with. Such group work requires students to be able to show leadership in a group, to keep a group on task, to disagree without devastating conflict, and to compromise for the sake of accomplishing a task. All of these skills need to be learned, and, in my experience, it is rare to find a random group of math students who come equipped with them.
For the classic group activity—give a group of three or four students a new kind of math problem to solve together and make a presentation on their joint solution—I’d wait until my class had progressed to the point where they were confident about their math skills and liked to solve problems. I’d wait until they had worked in small groups enough to develop good communication skills and to learn each other’s strengths and weaknesses. I’d wait until they wanted to get into a situation where they had independence of action. (If other teachers were also interested in working with these same students in groups, we might get together to teach some of those group skills.)
Before they reach this rarefied state, I like to introduce them to group work by doing math activities that are social. Social activities provide opportunities to share math knowledge and experience, and to talk about math, without requiring students to have a highly developed ability to articulate concepts, negotiate meaning, disagree diplomatically, or provide leadership to keep the group on task.
In many of the activities that follow, the teacher is leading the group and relatively few group interaction skills are required of the students, so they are good activities to use if you have not asked your students to do group work before. Furthermore, because the teacher is leading the activities, it is relatively easy to adjust the level of difficulty of the math as you go along: you can make it more difficult when the students have understood the concept, or stop the process for a moment to teach something everyone seems to need; you can plan for some whole class or one-to-one teaching before the next group session, to clear up some misunderstandings or pave the way for what you want to practice when you have them all working together again.