The Use of Old Exams

University libraries often keep a file of old exams, at least for those courses whose professors approve of the idea, and make them available to students. As best I can tell, there are two reasons they do so. One is to help students study for  exams they are going to take. The other is to prevent students who have access to old exams from other sources, a friend who took the course the year before or a fraternity that keeps a file of old exams provided by its members, from having an advantage over students who lack such access. My own practice is to cut out the middleman by webbing some of my old exams and linking to them on the class web page.

I have, however, some reservations about the practice, having to do with how the old exams are used by students. The way I want them to use the exams is as a way of checking on how well they know the material, so that if they think they understand part of it and don't they will discover the problem before, not after, taking the final. My usual suggestion is that, after studying, a student should take one of the webbed exams and use my answers, if they are there, to check his. If the answers are not there, he can at least go back to the book to see whether what he wrote fits what it said.

What I do not want the student to do, and am concerned that many students may try to do, is memorize the answers to all the question on past exams on the theory that those are the questions that will appear on the next exam. One problem with that is that you can memorize an answer without understanding it. Another is that the exam questions, even from multiple exams, cover only a fraction of what the students are supposed to have learned; an exam is a sample of the course, not a summary. If I limited my exams to questions from the old exams that I have webbed, a student might be able to get a reasonable grade by memorizing answers to those questions, but the grade would be poor evidence of how much of the course he understood. Memorizing answers is analogous to the practice of going through a textbook using a highlighter to mark the five or ten percent that you believe you actually are supposed to learn—or at least will be tested on.

If I try to avoid including in the current exam questions that were in the webbed past exams—which is mostly what I do—a student who studies by memorizing answers will not only waste his time in a long run sense but in a short run sense as well, since not only will he not have learned the subject and be unlikely to remember much of it a year or two later, he will not even get the good grade his effort was intended to produce.

My problem as a teacher is how to get the benefit of making it possible for the student to use the exams in the way I want him to without making it too likely that he will use them in the way I do not want him to. I do not have a really satisfactory solution. I tell my students how I want them to use the old exams, but students, reasonably enough, may suspect that my objectives are not identical to theirs, hence that advice it is in my interest to give them may not be advice it is in their interest to follow. I also warn the students that I try to avoid putting questions from the webbed exams on the current one, which may be more effective, providing they are paying attention, believe me, and remember.

One element of the problem is the question of whether to web answers as well as questions. One of the problems in economics, in my experience, is that because it deals with features of the world that students are familiar with and uses ordinary language, often with specialized meanings, a student may go through a course thinking he understands everything but the fine points and end up having learned almost nothing. Having done so he might answer all the questions on an old exam to his satisfaction but not to mine. Providing answers makes it easier for a student to tell whether he actually understands the subject—by how well his answer fits mine.

The disadvantage is that students may take the opportunity to memorize the answers instead of learning the course material.

At some level, my response to all such issues is that it is my  job to make it possible for my students to learn, theirs to make it happen. If a student chooses to ignore my advice and devote his efforts to memorizing answers in order to get a good grade on the exam, rather than learning ideas in order to understand what the course teaches, that is his responsibility, not mine. Along similar lines, I make no attempt to enforce compulsory attendance. But I would still prefer, so far as I can manage, to teach the course in a way that will make it more likely that students end up understanding the ideas it covers.

Having discussed at some length one issue associated with giving exams—it is, of course, that time of year—I will take the opportunity to mention two others, starting with a policy I adopted years ago designed to make taking exams a little pleasanter for students, grading them a little pleasanter for me, and the resulting grades a slightly better measure of what each student knows.

Imagine that you are a student taking an exam, and after answering all of the questions you know the answers to you still have some time left. It is tempting to spend the rest of the time answering the questions you do not know the answers to, in the hope that something you write will fool the professor grading the exam into thinking you know the answer, at least in part, expressed it unclearly, and deserve at least partial credit. Doing this wastes your time writing, my time reading, and adds some additional noise to the signal that exams generate, since there is a risk that I will either be fooled into giving you credit you do not deserve, or interpret some other student's poorly written answer as entirely bogus when it is not.

My solution to this problem was inspired by Socrates' explanation of why he was, as the oracle told him, the wisest man in Athens. He was initially dubious, since he didn't know anything. But, after extended conversation with his fellow citizens, he concluded that they didn't know anything either—but thought they did.

On my exams, knowing that you do not know something is worth twenty percent. That is what you get on a question for not doing it. So if you suspect that the best bogus answer you can come up with will be worth less than twenty percent, you are better off leaving the question blank or writing "I do not know," going home early, and saving me the hassle of trying to figure out which answers are or are not entirely bogus.

My other policy, adopted several years ago, is to give short exams, exams which I expect most students to finish before their time runs out. My original reason for doing so was my dissatisfaction with the common practice of giving students who can persuade the relevant university officials that they have some invisible handicap, some sort of learning disability, extra time on exams. While some of those students may suffer from a real problem, I suspect that in many cases all that is special about their situation is having parents willing to pay a professional to produce the needed diagnosis.

I did not like being a party to what I regarded as legalized cheating.  I had no way of preventing it, but I did have a way of making it ineffective. If everyone can finish the exam before time runs out, having an extra hour is no longer an advantage.

That was my original reason for trying (not always successfully) to write short exams. After I had been doing it for a while, I concluded that it was a good idea on its own merits. Being able to do things fast is sometimes useful, but in most contexts getting the right answer is more important than getting it quickly. An exam that most students find it hard to complete rewards speed by more than I think it should be rewarded.

It occurs to me that there is one more policy of mine with regard to exams at least worth mentioning. I only write the exam after the last class. That way I do not have to worry, when students are asking questions in the final review class, that I might be giving away the answer to an exam question, unduly advantaging those paying attention at that moment and reducing the ability of the exam to function as a random sample of the student's knowledge.

And, for a last comment ...  . I like to say that being a professor is better than working for a living, except when grading exams. One reason is that grading exams is a pain. Another is that it is when you find out that you have not done nearly as good a job of teaching as you thought you had.