Recently, someone asked me if I still had those pre-test dreams, you know, the ones where you show up to the exam late and in your underwear. After some thought, I realized that I hadn’t had any dreams like that since I started teaching. I do have pre-test dreams, of a different type: the ones where I show up late to GIVE the test, the exams are blank, and I’m in my underwear.
I often wonder what it is that makes exams so stressful, not only for students but for professors. I guess I wonder less about why it’s stressful for students. Being evaluated is no easy task. And when things like the all-important grade in the course depend on your performance in a one-hour time span it becomes that much worse. But why do I still get stressed out? I like to think it’s because I want this inherently horrible experience they go through to be worth it.
A friend of mine (who’s also a math professor) recently said that he hates exam day because he feels he has to trade his “educator” role for a “policeman” role. In a way, he meant that he didn’t like going around the room making sure no one is cheating, but beyond that I think we all feel we go from being the students’ allies to being enforcers of some sort.
So this leads us to the most basic question: what is the point of an exam? Do we give people exams to gauge how much they know? As someone who has bombed a few math exams herself (and who is simultaneously pretty confident of her own math abilities) I think exams are a flawed way to gather information about a person’s knowledge on a subject. So what really is the point? I do think it is a convenient way to check how much people are understanding the material covered in the class, but that makes the exam only useful to us, and potentially harmful to them (there are many reasons students bomb tests that might not be knowledge-related). I still remember, back in grad school, listening to Dr. Bob (one of UT Austin’s teaching gurus) talk about this very topic, and I will never forget those two words:
This is the mantra that makes everything fit together. Sure, tests are useful to US as assessment tools, but the main reason for having them is for the students. THEY are getting something out of the experience. The mere process of taking the exam is a learning opportunity. We are not policemen. We are always educators.
But of course, this philosophy only creates more challenges, at least for us. For one, writing an exam is already hard enough. You want to cover certain material, you want to be able to have problems of varying difficulty, and you want to write “good” problems. But now we want to think of an exam that is going to be a learning experience as well. To me, that has always meant “focus more on conceptual understanding, less on algorithms and computations”. This also tends to make the exams more difficult, because students believe that a math exam has to have a lot of computation, and get very confused when a question asks them to write a sentence or paragraph. Another professor friend of mine told me today that a student complained that his exam “had no math, it was all concepts and writing”. What he meant was that there weren’t very many computations. But I feel (and I think many people out there feel this way too) that if a calculator or computer can do it, I don’t want to bother asking a student to do it. Sure, comfort with computations is always a good thing, but we are training people to be critical thinkers, not calculators. So I say focus on the critical thinking instead. However, I have realized that I tend to pick too many difficult problems, because they are “nice” problems. This is an easy trap to fall into when using the “tests teach” philosophy. I still need to learn to find that right balance of difficulty levels, and learn to let go of the really nice problems and assign them as homework problems instead. There is a certain amount of thinking that most of them just cannot do under that much stress and with a strict time limit.
After the exam-taking comes the grading. Ideally, we would write thoughtful comments for each of the problems we grade, as a way of giving useful feedback to the students. As I recently found out, this is a doable task when you have a class of 25 students, not so much when you have 70. For my last exam, I actually wrote very little on the exams, and instead wrote up solutions to the test and posted them on our class webpage. I then told them to make sure they read the solutions I wrote and compare with the solutions they wrote. Of course, many of them will not do this, but many of them would not read the thoughtful comments either. The point is to give them the chance of processing the feedback. I will see soon enough if they take this opportunity (this is the first time I have done it this way).
A great way to have the students process feedback is to have them write test corrections for extra credit. I have done this many times in the past and it has worked well on many levels. First, they love getting a chance to get extra credit. This also forces them to read the comments we so carefully wrote. A pleasant side-effect is that not very many people try to negotiate their grade if they have this other way to change it. Finally, and most importantly, it really makes them think about the problem that they missed in a way that they are not likely to forget that concept again. Of course, we have to grade the corrections, effectively having about twice as much grading to do as we did before. This semester I decided not to do corrections and I’m actually regretting it. I think next time I have these many students I will shuffle other grading around so I can still do test corrections.
These are only some of the ways in which one could incorporate the “tests teach” philosophy into our test writing, test giving and test grading process. I think it really depends on the class and on the instructor, but I definitely believe that this is a good perspective on things.
The “tests teach” mantra is something I keep repeating to my students in class too. I think that if they believe this, they might actually be less anxious, or nervous, or defeated if they don’t get the grade they wanted. This is part of a learning process, not the ending. And maybe once this shift happens, I will stop feeling like the policeman or the torturer, and back to being their ally.
I invite you all to post ideas on how to make tests less scary (take-homes, orals, group tests, answer in the form of an opera*?), to post your own testing philosophies, and to share your test-taking or test-making nightmares!
*This last idea was taken from and episode of the show Futurama (which has several mathematically trained writers). In case you’re interested, the episode was called “The Duh Vinci Code”, and in one scene one of the characters says of a Calculus class: “It was so hard. We had to answer every question in the form of an opera!”