By the time you have finished with an assignment, everyone in the group should understand the solution to each problem, and each group member should be able to explain how to solve each problem.
Only one copy of the homework per group will be accepted and graded. Each participating member of the team receives the same grade. The solution to each problem should have both symbolic and verbal explanations or interpretations. Diagrams, tables and pictures should be provided when appropriate. (This is sometimes called "the rule of three" or "the rule of four" after the Harvard/Michigan Calculus listing of algebraic, graphical, numerical and verbal aspects to problem solutions.)
For each problem set, your group should meet at least twice. During these meetings, every group member has a role:
The Scribe is responsible for writing up the final version of the homework to be handed in. S/he should write a rough draft of the homework, which all the group members should look over, both to be sure it is accurate and to be sure it is well-written. A Tip: if the Scribe word-processes the homework, it's a lot easier to revise.
The Clarifier is responsible for making sure that each group member understands the group's solution to the problems. S/he should also assist in describing and recasting ideas presented by other members of the group.
The Reporter writes a cover sheet for the homework set. On this page the names of the participating group members and their roles should be listed. (If a group member did not contribute, her/his name should not appear on the Reporter's Page and s/he will not receive credit.) The Reporter also writes a paragraph or two summarizing the activity of the group, such as how long the group met, what particular difficulties and successes the group had, and differences of opinion on solutions.
The Manager coordinates when and where the homework group meets, and arranges for or provides refreshments. (The Reporter often comments on such in the Reporter's Page.) If another team member is absent or ill, the Manager assumes that individual's responsibility. The manager is also responsible for duplicating the final copy of the homework and getting a copy to each group member, so that each group member has a copy to study from! Some groups choose to do this before the homework is graded and some choose to do it after the homework has been graded.
Whether working with the same group or a changing group, you should rotate roles between assignments. This should evenly distribute all responsibilities over the semester.
If you have doubts as to the utility of doing homework in groups, consider: most employers, when asked what abilities and skills they want in their employees, will list "works well in a team environment" as one of the most-necessary attributes. Group homework gives you good practice in working this way.