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Let's say a group of students decides to study an existing subject X collectively without a professor. What general guidelines should be followed so that the group can make the most out of it?

I am mainly interested in things like

  1. What should be the ideal size of the study group?
  2. Should all the members do the same thing or different things?
  3. Should there be a categorization of members, like should some members do fundamentally different things than the other ones?

etc.

(for context: subject is math)

2 Answers 2

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I don't think there is an ideal. Lots of things can work if people are committed, though continuing commitment will be an issue for most.

I'd suggest asking a professor for some guidance, especially initially. They can suggest books and papers to read.

More than six in a group will start to get unwieldy. Two is fine if both are committed. But the process will differ depending on group size. I'll suppose closer to six than two in what follows.

Someone should take the lead in scheduling meetings but that is probably enough.

One way to make it work is for everyone in the group to study the same material for a week (or so), but one of the members (rotating) is tasked with making a presentation to everyone on that material. That can include both an oral presentation and a written summary. Everyone else is expected to read and actually put some effort into the same material, but that will probably be the hardest part to maintain.

But someone needs to be the "leader" for any given meeting; the presenter. If no one leads then little is likely to happen.

The presentation of the material includes a discussion of it with corrections suggested. To really do a good job of it the presenter then produces a second written report that includes updates from the presentation. This is distributed to everyone.

People could volunteer for some set of material or the "organizer" can assign people, say in round-robin fashion.

Let any of the members suggest new material. Check back with the professor on occasion, perhaps by showing them the reports.

Since this is math, don't neglect the fact that a lot (most?) learning takes place while doing exercises. A group can be used to get feedback on individual attempts at problems - especially difficult problems. It is easy to be misled as to your level of knowledge if you don't test it with application to problems.

Note that this isn't limited to students. A group of professionals can do the same thing.

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First to answer your specific questions.

  1. The group size is going to depend on how effectively you can choose active contributing members. Three useful members will be better than any number of unhelpful persons.
  2. Uniform activity for some phases and type of group, individual for others.
  3. See point 2.

The primary thing is to get people who will work and not simply coast. If you can find more people who will be active and contribute meaningfully and usefully, then more is better. But each person in the group who does not help is worse.

Keep in mind that project managers nearly all say that if you are going to fire a project member, you want to do it early rather than late. Early replacement means you have more time to make up for the problems. Ideally you want to filter out the bad apples before any work at all gets done, but that is usually impossible.

Once your group is selected, then what is the goal? Is it to keep everybody motivated? If so, how? Maybe you set goals, set each other tests or homework assignments, kick each other's chair if the other person starts to slack, or whatever. Make sure everybody knows the goal and the method that are to be considered acceptable.

Or possibly the goal is to perform some practice task. Will that task be one-person sized and done by everybody? Or broken down into different one-person sized tasks that build up the complete task? Each of these now involves some degree of management. You need to decide these things very early. And you need people to understand and agree to the plan.

Getting this far will give you some idea of whether you have the right people. If you wind up not completing this, you are probably doomed. Pay attention to who doomed you, keeping in mind it might have been yourself.

Just some possible models for a study group.

  • Quiet study time. Get your study material and go to the same place as your study group. The group is empowered to push people back (shush them, etc.) to keep them working. If somebody gets stuck on some question then ask your neighbor.
  • There are many variations on the previous one. For example, it might be possible to hire a tutor. The tutor could give a quick lecture on a topic, then quiet study time would start. The tutor would circulate and answer questions as required.
  • Get old exams. Divide the questions and each person or set of persons do some part of the exam. Then when everybody is ready, regroup and compare answers. Record which types of question gave the most difficulty, and use those to guide where more work is needed.
  • Get a textbook (or other document such as a research article, etc.). Assign each person some part to read, chapter or section or whatever. Then regroup and report to the others on your portion. If your portion is too easy, go ahead and read other parts. After each section there should be practice problems. These could be done individually or taken up as a group.
  • Pick a subject. Each person (or sub group) researches some part of that subject and prepares a report. Then regroup and give presentations on the reports. The trick here is choosing the right sized parts of the subject. And again, there should be practice problems.

Of course there are many other possible patterns. You need to decide what and how based on the people available, the level of work you are prepared to do, the time available, and so on.

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