Nobody likes difficult exams. After all, the professor might ask us questions we haven’t seen before. He might ask about ideas we haven’t considered before. Difficult exams can tank my grade. That wouldn’t be fair, right? Unfortunately, I would argue that those are actually “good” things.
What is the purpose of an exam? Exams are meant to test your understanding of the material. I’ve had many exams in college that are just refreshed versions of previous semesters’ exams. Change a number here and there, change some units, and voila! New exam question. I’ve also had exams where the professor goes out of their way to tell the students what will be on the exam. Why are these things “bad”? Well, they go against the purpose of exams, which is to “test your understanding of the material.” Using similar questions incentivizes students to memorize a particular method of solving questions. It promotes a surface-level understanding of the material, since getting full points is usually the only goal when taking an exam. Giving out the test format allows students to narrow down what they have to study. In other words, you’re incentivizing students to only understand specific portions of the curriculum.
Let’s define what a difficult exam is. A difficult exam is an exam that challenges your understanding of the material. It forces you to apply your tools in ways you might not be familiar with. It makes you think about how to tackle a problem and introduces potential pitfalls that demonstrate an incomplete understanding. I’m not advocating for 250-IQ problems, riddles, or trick questions. There are obviously exams that are too difficult. But, with my experience in college, an alarming amount of exams can be considered overly-simplistic.
So, why are difficult exams good? Well, forcing you to apply your tools in new ways shows that you actually understand what you’re working with. You’re not applying formulas to known situations, you’re analyzing a problem to see how a formula can be used. This mimics real life. You’re never going to get a problem at your job that clearly defines a physics problem with initial conditions. It won’t be labeled with “kinematics question #1” or “solve using the quadratic formula.” You’ll be forced to understand the problem at heart and learn how to apply your knowledge.
This is all in principle. I like easy exams as much as the next guy. I like having high grades and formulaically studying for an exam I already know the format of. It’s simply way less stressful. But in principle, easy exams don’t really challenge students’ thinking. It doesn’t force them to use their critical thinking and problem-solving skills. In high school, I had a math teacher (Mr. Schwartz) that gave us exams with problems unlike those on our homeworks. He would write the questions in a way where we had to think about how to apply the tools we learned over the semester. It was tough. But, I think his strategy incentivized deeper studying and understanding of the material. Doing well on an exam was gratifying because you felt as though you earned your grade. It wasn’t just handed to you on a platter.
Problem writing is a skill. It forces experts to come up with new ways of asking essentially the same question. It forces humanity to approach complex and novel problems. It’s way harder to do than simply refresh old questions. In the math olympiad every year, the world’s top geniuses come up with ways to ask new questions. The strategies remain the same, but the solution is never trivial. Imagine if they just copied last year’s questions with different numbers. What a joke that would be.
At the end of the day, this is the professor’s prerogative. Students shouldn’t be at fault for figuring out the best ways to play the game. But, if that game has an easy strategy, it’s not a challenge for the students. Professors who challenge their students will end up providing a lot more value in the long run. Once they’re out of school at a job or doing research, they will be prepared to take on the problems that come their way.