An oft-quoted line from teacher to student is “There is no such thing as a stupid question”, which I think is a good sentiment to alleviate the fear of asking questions. Although I believe a good deal more than that is required to ensure that students are comfortable asking and answering questions in class, this is not what I plan on talking about today.

Today we’re going to talk about a special kind of stupid question. Of course there are stupid questions; Why did you lock your keys in the car? Would you like free upgrade to first class?  What’s your star sign? Should I go to grad school? What’s that smell? And many more… Then there are things like these beauties from the Australian Academy of Science. But if you’re observationally gifted, you may have noticed that this post was filed under education. Today we complain about education again.

Far too often, I’ve seen test questions that I don’t remotely agree with. I don’t disagree with the solutions — I just don’t believe that the questions achieve their purposes. Since I’m not nearly at a point in my career when I can carelessly insult specific questions that I’ve come across, I won’t. But this kind of stupid question is so prevalent that it wouldn’t be fair to isolate any particular culprits anyway. The kind of stupid question that I’m talking about is one requiring unnecessary complicated calculations or assuming that the student is familiar with some particular example. And here I’m referring to test questions only — timed tests should be approached differently to assignments, where plenty of unstressed thinking time is available. Let me illustrate what I mean with some fictional examples:

• Testing l’Hôpital’s rule with an example that requires 6 iterations before getting an answer. That is, the student must perform the same technique 6 times over before arriving at an answer.
• Testing primary school geometry by asking what the interior angles of a stop sign are. Not knowing the shape of a stop sign is different to not knowing what an octagon is.
• A separable first order ODE that requires a page of working to evaluate the integral.
• Asking students to reproduce a proof that was included as an optional exercise earlier in the semester. Students will do a different random selection of problems each; you’ll just be measuring which students picked the same question that you did.
• Having a needlessly ugly solution to a problem — Like $4736\sqrt{17}-Log_e (7)\pi^{1/4}$. Many students will assume it’s wrong and either start again or abandon the problem entirely.

Credit to this dude, who has a page full of these drawings.

These problems don’t only cause students who understand the concepts to get the questions wrong, they can also make students waste time and become unnecessarily stressed. And just to reiterate the point, I think these are terrible test questions but perfectly good assignment questions. Test questions should test concepts, not who was listening to the example given in lecture 17 or who can perform pages of computations the fastest.
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