I had my Calculus students each write a paper on single function. I was pretty happy with the results, not because they were so great, but because they really exposed some weak spots in the group's grasp of some ideas. When the whole class is working on the same problems, its pretty rare that mistakes go uncaught and uncorrected. I think that this is often a good thing, but it was becoming apparent that the same students were correcting the same mistakes that kept being made by the same students (that sentence can't possibly make sense, can it?)
When forced to work independently, each student was faced pretty directly with their weak points. Some of the randomly assigned functions were more difficult to work with algebraically, but in today's Wolfram Alpha and Microsoft Math world, finding and simplifying derivatives wasn't the issue... interpreting them was. I'm now starting to get some second drafts, and its pleasing to see them wrap their heads around the relationship between a function and its derivatives.
Here is a copy of my work, which I gave to show my expectations.
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