<p>A problem for some students who have a very good intuitive sense of math is that they don’t “show their work,” i.e., the intermediate steps in solving a problem. A teacher will generally mark those test results down, whether out of concern the student somehow copied the answer or that the student just made a lucky guess. One piece of advice I would offer students is that they take care to show all their work. (Way back in 8th grade when my son was in a statewide math competition, he finished tied for 2nd but was awarded 3rd place. The tie-breaker was that he didn’t show his work, even though he had the right answer! Nowadays, as a journalist he shows a lot more of his work than most journalists do – I think he actually learned from that experience in his youth.)</p>