Often, on exams in particular, reverse trick questions are posed. These are questions which look tough, complex, and pompous, but are actually easy and can be solved by applying some basic method. I give an example later.
Why are these used by professors?
I think they are very inappropiate, since they put the smart student at a disadvantage, and the less smart at an advantage. If you ask a question which is designed to seem difficult, the smart student mentally approaches the problem as a difficult problem, and therefore gets ready to use the more complicated tools at their disposal. Thus, one might be working for a considerable time trying to apply a complicated technique on a problem, which could be solved in seconds if one spotted the easy ‘hidden’ method. This is in particular a problem on exams and tests, where time is an important factor.
Meanwhile, the less smart and stupid students approach the problem as they approach any other: “well, here’s a problem which concerns topic A, I only know that one basic easy method regarding topic A which they taught the first day, so might as well apply it and see where it gets me even though it seems unlikely to work, whoops, it actually did work!“, and they might be done with the problem immediately.
So, what do you think?
Here’s an example of math. I was once asked to take the integral of a very ugly looking function, it was a fraction, with both numerator and denominator looking like the spawn of the devil.
I spent some time trying to simplify it, so that I might get an idea of what sort of method would work best. I already disregarded integration by parts, since it was obvious that it would lead to many complicated terms that I wouldn’t want to bother with. Ultimately, this did not work.
Turns out, the actual solution is to not simplify it, not look for an appropiate method, but just blindly apply integration by parts to the expression in its original form. This method, by design, leads to many complicated terms disappearing and making the integral way easier to solve (something which was impossible to predict). This was of course intentional by the professor.
I think this is a question which smart students will take longer to solve (since they know more methods and are better at creative simplification), while less smart students will solve immediately (since their first and only thought will be to just apply integration by parts).