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!”
Great post! I want to share a strategy that has worked very well so far with my calculus classes.
Before each exam, I write a practice test for my students. If I’m planning to ask a question where the format might seem unusual to students, I try to give a question with the same format on the practice test. This gives students a chance to get used to the instructions so that they don’t have to focus on that part during the actual test – they can focus on the content of the question (which will be quite different from what was on the practice test). I find that students are a little less nervous when they know what about half of the test will look like prior to taking it – even though they are still working on problems that they’ve never seen before.
For example, on an exam covering sequences and series, one of the questions will require students to read mock student solutions to some series convergence problems, and find the errors in the mock student’s reasoning. Of course, you never run out of misconceptions about sequences and series, so there were plenty of errors for me to put a few on the practice test, and a different few on the real test.
Of course, the practice tests help focus the students’ efforts while studying, and they convey the message that the best way to prepare is to work on problems. They take quite a bit of time to prepare, but I think I’ll find them very nice to have around when that magical time comes when I get to teach a course that I’ve taught before. =)
I must admit, that whenever possible, I opt *out* of giving final exams and assign projects instead. In some classes (e.g. Calculus) I can’t get away with this anymore, because as a department we have instituted some uniformity in content and structure for these classes (which has been a GOOD thing!). For the tests and quizzes I *do* give (and, like you, I believe they are important teaching tools) I allow “cheat sheets” which students are also required to hand in. I believe making these sheets up is a good way to study. One downside is that *some* students check their brains at the door when they have one of these sheets, and spend too much time looking around on their sheets for brilliant answers, instead of *thinking* — but they might be looking into space instead, without them. In general, this does seem to relieve a lot of stress, at least many students have told me so.
Good discussion. After this, you may dream about being late to write the blog and a policeman shows up in your underwear.
Asking the students to write test corrections is a great idea. I’ve tried this in the small class I’m teaching. My marking system for the corrections was that the students would get 1/3 of the points they lost in a given problem if they wrote the full solution to the problem correctly. In this way, the students who did poorly and who had to do more work would had more reward, and yet their mark would never be greater than those who did well in the exam. I think it worked fantastic. Of course, the marking is a nightmare.
I do the same as Matilde, but they can earn up to 1/2 credit back. This makes me feel better about writing harder tests, decreases grade-grubbing as Adriana suggests, and for some students presents real learning opportunities. I’m always very, very depressed when I grade several pages of exam revision and the student earns no points back, though. What a waste of their time and mine!
I like the idea of test corrections, but I’ve found that not only the added grading but grade inflation becomes a concern. I’m trying something new this semester that is working great. I give a quiz about a week after the exam with the highly missed exam questions on it. The students know there will be such a quiz and it forces them to read those comments.
I had a dream once that I had to administer a calculus test… on an airplane, in-flight O_O
I’ve had those dreams too. Everyone’s staring at me, and I say “Umm… I’ll write the questions on the board…” and wake up not long after.
As noted above, practice tests teach too. One benefit of having your “nice” questions on the practice test is that it ends up more difficult than the actual test, which (I would like to believe) leaves the students less stressed at the test, pleased to discover that it’s not actually so difficult.
About the calculation questions vs. theoretical: I still remember vividly my first semester in graduate school. On the final exam in my real analysis class there was an integral! An actual integral that I was supposed to evaluate! We had done all this theoretical stuff all semester… measurable sets and the existence of non-measurable sets and so on. And he wanted us to calculate an integral! I was aghast, and slightly panicked. But when I settled down and worked the problem, I noticed it really asking us for a straightforward application of Fubini’s Theorem… but I guess grad students are like the anti-calculus student?
My best test giving experience has been in the intro to proof class for early math majors (post calculus, but pre just about everything else). I give a proof-based take home exam and a more computational in-class exam, with the take-home done first and due the day of the in-class exam. That way I don’t have to worry about time constraints on the proof-y part of the exam, and working on that theoretically helps students study for the in-class part. I was happy with how well it went, and several students wrote on their course evaluation that they really liked the structure.
I just have a very hard time guessing how hard an exam will be for students. I err in both directions with great frequency, and rarely hit the “just right” target. Either my students are leaving after blowing through the test in 20-30 minutes, or the whole class is desperately trying to finish as time runs out, and they glower at me as they leave. Sigh.
Adriana, I have had a same pre-test dreams… Now not anymore . I don’t even know why I was so stressed out about it.
I remember a course I taught that met every day. I gave a *lot* of 5 minute pop quizzes, on average, once per week. However, these quizzes could not hurt the student. Either they earned 100%, which replaced one homework problem (I gave more homework than quizzes), or that quiz didn’t count. By the end of the semester, the students were very familiar with the type of concepts for which I’d be testing and didn’t seem to be all that stressed out. I also got great teaching evaluations. The best thing, though, was a scene I never thought I’d witness: a young woman came rushing into class late one day and burst out, “Did you give us a quiz today? I hope I didn’t miss a quiz!”