Test Taking Advice for Proof-Based Mathematics
One of the unfortunate things about proof-based mathematics is that heavy emphasis is placed on big ideas, understanding, and an elusive “bigger picture”, yet evaluation of student performance is still conducted through exams that often require an additional set of test-taking skills. In addition, many instructors are aware of the difficulties accompanying a transition into proof-based mathematics, but they place additional focus on describing how to learn and necessary shifts in thinking patterns rather than the low-level mechanics of just being a student (e.g. studying, taking notes).
There is already a great corpus of test-taking advice on the internet, but such advice is typically broad, general advice that applies to any testing environment or advice that is tailored for more mechanical and computational math courses. Such advice can be great, and I do not intend to subsume it in what follows. However, it seems that advice that is pertinent specifically to proof-based mathematics is generally lacking, and hopefully I can provide some tips and pointers that are helpful.
I think the following advice generally falls into three categories that address different environments: learning in and from lecture, studying at home, and actually taking the test.
Keep in mind that this collection of advice is really more a slurry of opinions than anything. These little tidbits were guided by the habits that worked for me and the mistakes I’ve made along the way. Exercise your own discretion before following them blindly! Feel free to let me know if you have suggestions; if you have strong disagreements you are welcome to express this through textual assault.
- Take good notes in lecture.
- Treat your attention as a finite resource and be selective of what you’re writing down.
- Avoid “fixing” the lecturer’s notation, even if you’re used to a different convention.
- Be ready for when you fall behind.
- Committing theorem statements and definitions to memory is necessary but not sufficient.
- Know thy proofs at a high level.
- Prepare examples and counterexamples.
- Get lots of practise.
- Time yourself working on exercises or practise exams.
- When doing exercises, try to understand the writer’s intent.
- Don’t be afraid to ask for help, either from classmates, instructors, or the internet. In particular, don’t spend too long being stuck.
- On test day…
- Eat something and caffeinate carefully.
- Write your solutions iteratively by starting with the most important details or arguments and filling in the gaps if you have time.
- Avoid writing unnecessary details, especially imprecise ideas and heuristics.
- Use scratch paper to work out simple examples or ideas.