Study groups in mathematics
and group work in my courses

I have said (I hope I remembered to) in class that assignments can be submitted by groups of people. I guess I will make the limit on group size FOUR people.

This means that on any assignment in a course of mine, you may work with any number of other people from 0 through 3, and together submit just ONE paper

WITH ALL YOUR NAMES CLEARLY ON THE PAPER

AT THE TIME IT IS SUBMITTED.

Adding a name after the assignment is graded and returned will not work. It is academic dishonesty, and anyone who is a party to such nonsense will be prosecuted.

Designate ONE person ahead of time as being responsible for picking up the paper in class after it is graded. That person's name should be UNDERLINED on the joint submission.

Here is the way things are supposed to work in a group submission:

ALL members of the group are supposed to make a serious effort to solve ALL problems on the assignment. This is the only way people learn any mathematics.

I have run across some students who actually seem to think that the purpose of a group submission is to make it possible for each person in, say, a group of size four to do only one problem each on an assignment that has four problems, instead of having all four do four each. That is either amazingly stupid or disgustingly dishonest, or both.

No. When a group submission is made, the FIRST step is for ALL members of the group to try ALL the problems and get as far as they can with solving ALL of them. Only after this stage does the group meet (once or as many times as necessary) to discuss the problems and solutions and come up with joint solutions and write them up in a way that is acceptable to all members of the group.

DO NOT GIVE free rides to people who have done no work at all, who have not contributed at all to the process of jointly solving assignment problems. If student H has pretty clearly worked hard at solving the problems, has some ideas that are not completely worthless or silly, then I guess that H's name can go on a group submission even if H has not contributed large amounts of solutions to the problems. But if H has done no work at all, or is so far behind or clued-out in the course that it has contributed nothing at all to an assignment's solution, then allowing that person's name to be put on a group submission is academic dishonesty in a class of mine, and all people involved in such a submission will be prosecuted if I become aware of the dishonesty and can prove it. Also, an H who listens to explanations of a group solution and UNDERSTANDS all of the solution is very different from an H who does not listen to such or does not understand them, or an H who just appears at the last minute and begs a group's REAL members to let it add its name to a group submission with which it has had nothing to do. ("It", above, of course, means "she" or "he".)

I had an experience, a few years ago, in a course of mine, which illustrates a strong reason why you should not give anyone a free ride by putting its name on work you have done:

There were several weak students in a class who latched on to one or two strong ones and got free rides from them on assignments. Disgusting. Wrong. There was also one young lady who was not a weak student at all but who was also not an A or A+ student. She did not ask anyone for free rides. She did her own work and got her grades. These grades were lower than the grades gotten by some of the dishonest weak students who got free rides from some also dishonest quite strong students. This is not fair. It is true that at test and exam time she did far better than the weak folks who got free assignment rides. But it was still not right that her assignment grade, which was part of the course grade, was lower than theirs. [end of anecdote]

If you are not clear as to what my rules for group submissions are, from the above, ask me specific questions to make things clearer.

A group of people making a group submission in a course of mine is an example of a "study group". Study groups can also just be groups of people who meet and talk mathematics to help each other out, to benefit from the presence of more than one mind, more than one viewpoint. Female-type people especially seem to benefit from learning environments involving two or more people; males in general seem to like this less -- but there are MANY exceptions to these statements -- many females will want to work alone and many males thrive in study groups; I have seen many dozens of exceptions over the years; the generalization is not worth very much.

Good luck with the formation of a study group if you have interest in forming one! There is no easy or fool-proof way to form a group with members who get along great with each other or who are well-suited to each other in terms of abilities at mathematics. All one can do is try people out -- maybe you knew someone from before the course began, or maybe you form an impression of someone after a few classes and approach it to form a study group. Anyway, groups can shrink or grow, or trade members or disappear entirely, or spring up from people left after other groups dissolve; they are quite fluid. You are not MARRIED to any of the members of your group (smiley here). No one is stuck with anyone.