Write Solutions Iteratively
Date Written: June 19, 2024; Last Modified: June 19, 2024This test-taking strategy may or may not be specific to proof-based mathematics, and I suspect that it is.
When writing out solutions to homework problems, I personally expect a significant amount of detail. However, this level of precision and thoroughness is not a reasonable expectation for exams, and this seems to be cause for stress (especially when exams are timed). Note that these expectations can change for take-home exams.
If you’re finding yourself pressed for time, or if you know that a complete solution will take far too long to write out, start by writing out an outline. Express the kep steps of your solution, cite the theorems that are necessary, but omit the (relatively) smaller details. If you have time at the end of the exam, then you can go back and fill the details in.
This process is more of an art than a science, and there’s no good way to pin down which details stay in and which details don’t. Ultimately, the underlying principle is that some parts of a solution are worth more than others: the key ideas might net you most of the credit, and the messy computations might only be worth half as much.