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As the title says, do you learn math faster by working on problems in groups, where you can discuss your solutions or by doing it all by yourself? I can't see any advantage of working in groups because if you get stuck on a problem, you can just ask the smartest person in group how he or she solved the problem which means you won't have to work as hard.

I want to know what professional mathematicians think. Are people (like me) who prefers to work by themselves missing out?

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    $\begingroup$ I found group study almost worthless as an undergraduate but quite valuable as a graduate student. As an undergraduate there are typically students who are just going through the motions who wouldn't contribute to the group and in any event the material was mostly computational and hence best done alone. In graduate school, the material was more theoretical and pretty much everyone in the groups I participated in wanted to learn. Some of the better study groups took on the flavor of informal seminars where nontrivial proofs were discussed in detail. $\endgroup$ – John Coleman May 18 '17 at 1:06
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There is evidence that group studying in college is negatively correlated with improvements in critical thinking, as measured by a test called the CLA (Collegiate Learning Assessment). This is described in Arum and Roksa, Academically Adrift: Limited Learning on College Campuses, p. 100.

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  • $\begingroup$ I like this answer the best because it references research. $\endgroup$ – Björn Lindqvist May 18 '17 at 12:37
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Keep in mind that this is a very personal question. Some people simply work better in groups and some people work better alone. We are all different, and we should embrace that.

From a more objective point of view, both of them have their advantages and disadvantages. What I noticed from people studying in groups is that they usually forget one basic thing: learning is an interior process, not an exterior one. It is you who has to take the information and internalize it, mix it in the already built web of knowledge from your mind. Study groups are useful only as long as they support this process. However, most of the times, study groups tend to shift the focus from each individual's gain to the overall gain, thus making it more inefficient for some.

Another aspect of the group study is fun. For example, I get very frustrated at times when I can't comprehend something or I don't manage to find a solution. Speaking to somebody once in a while helps relieve this.

Sharing is another advantage of study groups. The most helpful teachers for me were not those who taught me something, but those who opened doors for me by briefly explaining a concept/mentioning a resource/etc. I think this is the ultimate goal of a study group: study on your own, share your experiences, build upon other's experience. Unfortunately in practice doesn't always work this way.

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Let me answer your question from my own experience as a student, several years ago.

Studying alone had the disadvantage that I could take a time-off whenever I felt like it, which is bad for a person with less self-discipline.
Studying in group had the disadvantage that I could ask for explanation about the course, which could reduce my ability to solve my own problems, a skill which is quite crucial while doing a math exam :-)

Hence I ended up with the following procedure: I studied together in group, as much as possible, but there was the firm criterion that I only did this when none of the other people was studying the same matter I was.

As a result, I ended up studying with futur lawyers, agriculture engineers, nurses, architects, ..., and even mathematicians, but the latter only when they were following other classes than me :-)

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  • $\begingroup$ How did you find this sort of arrangement? I love it, but you would have to have similar types to you. Reminds me of the "run with a friend in the morning and exchange shoes". It prevents you from rolling over if tired because you know the other person is relying on the damned shoes! $\endgroup$ – guest Jan 12 '18 at 1:53
  • $\begingroup$ @guest: how do you mean? I just meant that I studied with friends where I lived with or whom I met during Spanish evening course. In my environment, it's very normal to live together (I mean in common corridors, but each having its own private chamber) with all kinds of students. $\endgroup$ – Dominique Jan 12 '18 at 7:25
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I think solo studying is way more effective. I would keep a little sheet or back pages of the notebook for prof questions, but would often figure them out by the end of the self study session. In the event I didn't, it was easy to ask the prof the next day.

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