Even if you have to show your work, a lot of students will just blindly try a few canned approaches until they get something that looks about right. Actually u

Even if you have to show your work, a lot of students will just blindly try a few canned approaches until they get something that looks about right. Actually understanding what you're doing is definitely more efficient, but a lot of people muddle through without really understanding the reasoning. One of the worst examples of that mentality I saw in a first year university course was a multi-part question where one part had the student calculate something and the next part had the student do something to sanity check the answer. One student got the first part wrong and then fudged the working in the second part to get it to say that the first answer was correct. Of course, this completely misses the point of checking the answer. Worse, they came up to me after class and argued that they deserved full points because the second error was "a consequence of" the first one. They seemed totally perplexed that I didn't agree.