Maths exams are typically structured with the easiest questions at the beginning and hard questions at the end. The standard advice is to start at the beginning and get as far as you can before going back to check your answers. This assumes that either you can do a problem or you can’t do it and you’ll know soon after starting a problem if you can solve it.
I don’t agree with this assumption. When you examine it closely it’s clearly untrue as all teachers know students who did problems perfectly in class only to go to pieces on a test. However more than being false I think this assumption is very harmful as the idea that either you can do a question or you can’t turns a momentary panic on seeing an unfamiliar question into proof that you can’t do maths. The belief that they can’t do maths destroys students motivation, and becomes a self fulfilling prophecy.
So how can we improve the situation? Explain to students that it may take some time to solve the harder problems. Recommend that they start by looking at a hard problem that looks interesting. If they solve it first time, great. They should give themselves a high five and move onto another hard question. If they don’t solve it first time then after a couple of minutes if they find themselves stuck they should take a break to look at an easier problem. It’s important that students understand that they haven’t failed at the hard problem and they certainly aren’t giving up. They are taking a break to give their subconscious mind a chance to work on the problem. Once they’ve worked on an easier problem they move back to the hard problem.
It may take several attempts before they solve the hard problem, or they may not finish it during the exam. But by looking at it early they have time for more attempts than if they left it to the end, a better chance of solving the hard questions and a much healthier understanding that hard maths problems take persistence to figure out and an initial feeling of confusion is not a sign that you can’t do a problem.