Thoughts on Collaboration

It's the first week of school, and I put in some time rewriting my course policies to articulate why, when, and how to collaborate on problem sets.  This issue is particularly crucial in my advanced Geometry class, where students solve college-level problems, not just exercises. Feel free to use some version of this in your own classes, and -- even more important -- to let me know what you think!
------------------

Collaboration, Research, and Hard Problems

Contrary to stereotype, mathematics is best done as part of a community—not alone in a study.  I hope and expect that students will frequently discuss problems, ideas, and solutions in and out of class.  Some guidelines:

·         Make sure that when you are “working with” someone else, you are both really working and contributing.  Contributions can take many forms—clarifying, questioning, justifying, and restating, to name a few—not just coming up with “the idea”, but each of you should leave the collaboration feeling good about what you, and the other person, contributed to the session.

·         One test for how much you did in solving a problem is whether you can reconstruct the entire solution on your own afterwards.  If you need to look at your notes extensively, or get lost in the middle, you probably should have collaborated more actively.

·         One time when it is useful to be alone in your study is to check for your own understanding.  I recommend that students start problem sets by themselves, to see what they can accomplish and what ideas they can generate individually before working with other students.  I also recommend that students finish and write up problem sets by themselves, to make sure that they really understand the work they and their fellow students did together.

·         Give credit generously: it doesn’t subtract from the points you get (and in the real world of “karma points”, giving credit almost always adds to your own).  Write “Wolfgang suggested this auxiliary line” or “Credit to Seraphina for spotting the similar triangles.”  Taking ideas from other people without attribution is plagiarism; taking ideas with attribution is research.

·         Finally, unless specified in a particular project or assignment instruction, please DO NOT do research on the web (or in books, if you still remember those).  The essence of this course is learning to reason mathematically by solving problems and thinking through solutions, not regurgitating theorems and ideas you learned somewhere else.