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I am an undergraduate at a respectable US institution studying mathematics. I am having a huge problem with test anxiety. It completely inhibits my ability to think clearly.

For example: I had a quiz this past week in measure theory, and to prepare I did every problem in our book. I got it back today and got a 50%.

Similar things have happened throughout my mathematical career. Many classes where I feel like I have understood topics entirely have turned into B or B+ grades because I cannot perform on exams. And, no, I am not cheating on homeworks.

What do I do?

Hugh Mungus
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    I've had students for decades who've had the same problem. The best advice I can give you is to stop worrying about tests. The more you worry, the worse it gets. Have you perhaps considered learning some relaxation techniques, like yoga? – Ted Shifrin Apr 07 '17 at 22:36
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    I have the same problem, though to a lesser degree. A shot of liquor before the exam (or quiz) substantially reduces the anxiety. – MathematicsStudent1122 Apr 07 '17 at 22:40
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    Test anxiety seems to be a real issue everywhere, and many universities have psychological counselling for it. Have you asked around about this in your institution? That may help...and, perhaps, also Retalin. – DonAntonio Apr 07 '17 at 22:51
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    @MathematicsStudent1122: but how does the shot of alcohol affect your performance in the exam or quiz? – Rob Arthan Apr 07 '17 at 22:56
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    The abominable practice of encouraging (whether explicitly or not) students to think that grades are the bottom line is probably the cause of most problems like this. – Michael Hardy Apr 07 '17 at 23:28
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    Speak with your professor and see if you can take exams during office hours or at Student Disability Services (or similar proctoring service). Extended time could help you relax. – Austin Mohr Apr 08 '17 at 00:44

2 Answers2

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This is a common problem faced by many mathematics students. I will relate how I dealt with it when I was an undergraduate student.

  1. Although it should go without saying, be prepared. If you know that you have not prepared adequately, you will lose confidence in your ability to succeed.

  2. When you first get the exam in front of you, quickly search the exam for the easiest questions. Skip over any which you do not immediately know how to begin working and put them out of your mind.

  3. Begin working the problems, working the easiest problems first. This will get a large number of the exam points and will give you the opportunity to calm down. As you are working the easier problems you will usually find that you suddenly get flashes of insight into how to begin the problems that you skipped over.

  4. When you have finished the easier problems, begin working the ones which you were less sure of, beginning with any on which you got flashes of insight in step 3. Keep reminding yourself that you prepared well for this exam and that you have the knowledge and ability to work the problems.

  5. When you find a problem which you cannot work, the worst thing to do is panic. When we panic we retreat to a safe place in our mind where our knowledge is no longer readily available and we may find ourselves unable to work even the easy problems.

One final point which I left out. Check to see if the counseling center at your school has any advice or assistance in dealing with exam anxiety. Larger schools, especially have trained counselors to deal with such problems. It's a wider issue than just mathematics.

John Wayland Bales
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    Yes especially reading through and skipping over is great advice. The brain can work on it's own munching on the more difficult questions while you are working on the easier questions. – mathreadler Apr 07 '17 at 22:51
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    As a comment from a grading perspective, do try to get at least something down for each question. Even if you don't complete a proof, giving some sort of a idea of how you want to approach the problem can help the grader justify awarding some partial credit. – erfink Apr 07 '17 at 22:58
  • @mathreadler 100% agree. I have had so many exams where on first time through, I think I can do 0 of the problems. Then somehow, by the end of the exam, I can do n>0 of the problems – operatorerror Apr 07 '17 at 23:04
  • @qbert by skimming through the questions all first and trying to estimate how hard they are for you you give your brain time to work on it in the background as you solve the problem. – mathreadler Apr 08 '17 at 14:41
  • @erfink whether that is beneficial or not can depend a lot on the grading culture of wherever you are taking the exam. Some places you get auto 0 for first mistake even if you show you have the theoretical understanding required to probably patch the errors you introduce. – mathreadler Apr 08 '17 at 14:44
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Math is like chess. You really improve by playing long games or solving tough problems. Tests are often about speed and not getting things confused. So you might want to step up a notch with challenging problems. It will make standard problems look much easier and less confusing. In my opinion you should treat them like bullet chess that is solving them as fast as possible with as few mistakes as possible. The only path is concentration on tough problems. Just like in chess: Playing bullet games don’t improve your strength at all; you feel they dumb you down. The same is with math tests where speed counts a lot. It feels like they dumb you down and only speed is required! The deeper you go, the more challenging things you do, the more confidence you’ll have. Just don’t focus on simple (test-like) problems. It’s just like focusing on bullet chess. You may play 10,000 games without much improvement. That might create anger, anxiety, and a lot of negativity. You work hard on speed (or on standard problems) and get no results. That’s terrible anxiety and it’s very discouraging. I mean doing a lot of problems without the necessary results on tests. Of course you will need to work on speed too, not too much though, but it is necessary. It is just like in bullet chess when you have to make a decision fast, although the move requires a lot more.

So, only real strength and superiority can boost your confidence and diminish anxiety. Playing fast won’t cut it (=getting only standard and confusing questions right in time trouble). Conceptual understanding, challenging questions and super subtleties will get you the results you want. Tackling anxiety won’t cut it, although it might help. I think you know that one textbook and one solution manual might be just the tip of the iceberg. Anyway I'm gonna emphasize here that sometimes you need a more advanced book along with a simpler book to get better results. Training for speed and tests are secondary, although it is important too. Treat tests like funny bullet chess games with haphazard results, and treat challenging problems and tough conceptual things and subtleties like real knowledge and strength.

Bottom line is you always want a serious book (+a simple one) and serious problems to tackle. A serious, challenging solution manual is a must too. If it is already tough as it is, well, the science is getting tougher and tougher all the time. More and more time is needed to cover all the bases.
Just my opinion.

A couple of funny quotes (New edit: probably should not have included these quotes as they draw attention to some humor and they are beside the point. They were not meant to create some negativity here or present any truth here, though they main contain something of the kind)

“A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street”

“Never listen to anything your math teacher tells you” (said by an anonymous math teacher)”

Really hope that my advice won't be useless to you.

Ken Draco
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  • My apologies, but I think this is misleading advice. But maybe it's just me. Mileages vary, and all that. Worldviews, too, apparently. – paul garrett Apr 08 '17 at 01:11
  • And how exactly is it misleading? What is misleading? Do you mean that it is okay for a math major to study math superfluously or to focus on dumbed down speed tests? If you say I'm wrong and vote me down at least there should some idea behind. Or it's just like that: Wrong. Period? Nice reasoning! – Ken Draco Apr 08 '17 at 01:29
  • No, of course I don't "mean" all the straw men you've set up. Math is not like chess, to begin with, in my worldview. Of course, others have other opinions. But I am, further, opposed to many of the facile cliches that pervade the mythology about mathematics. And, specifically, your answer addresses the issue by first accidentally conceding that the externally contrived context is legitimate... which I think is both unwise and factually inaccurate. But/and, yes, I do think my reasoning is generally quite nice... though that is surely not the question anyone cares about. Please relax... – paul garrett Apr 08 '17 at 01:53
  • And, yes, unfortunately, it is entirely reasonable to be skeptical of the pontifications of (e.g.) old white guys [sic] who are safe and in control of status and jobs and so on. That's not what I'd take issue with. It's the naive receiving of figurative quips as literal truth, for example. – paul garrett Apr 08 '17 at 01:57
  • Well, chess was for illustration purposes. The claim "externally contrived context" is factually inaccurate and unwise is based on what? Do you think playing bullet chess really improve the game? Or do you think making simplistic mechanical standardized test-like questions problems for speed tests (most tests are really timed) is conducive to becoming a good mathematicians? Seriously? Why dragging here some pontifications simplistic of white guys – Ken Draco Apr 08 '17 at 02:27
  • Why dragging here some "pontifications" - I can, though, I agree with that point. Funny quotes are of course not true but may contain some truth or helpful advice. Facile cliches and quotes you may attack. That was just a funny remark on my part but you should have said so, that is, if you hate those two funny quotes which are mostly grotesque exaggerations. I don't argue here. These are just funny quotes. I presume you have nothing to say about my reasoning except attack it without any reason. – Ken Draco Apr 08 '17 at 02:34
  • Sorry for grammatical olla podrida. While I was writing I exceeded the number of characters by a large margin and couldn't edit the comment because it was already clicked posted. – Ken Draco Apr 08 '17 at 02:41