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On Difficult Exams

Nov 9, 2007
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This has been the subject of a lot of debates, especially since I’m teaching Mathematics. The usual impression is that we give difficult exams. No, let me rephrase that: we are usually being reprimanded for giving difficult exams.

Now, how does one say that an exam is difficult? The usual notion is that if more than half of the students failed the exam, then the exam is difficult. Personally, I don’t think that it is fair to classify exams as being easy or difficult based on this statistic alone. Let me illustrate my point. Suppose that you have a calculus exam and you gave that exam to two classes: one composed of sixth graders and the other composed of college students. You will expect to have a high failing rate on the class of sixth graders compared with the class of college students. So can you say that the exam is difficult? You don’t have enough data to make that claim.

Let us first look at the reason why we need exams. The main objective of an exam is to determine how much a student has learned. In general, a teacher does not give questions that he/she has not discussed. How can a teacher ask something that he/she did not teach? Will a teacher in mathematics ask a question about music? It is not fair. There might be a few items in the exam when a student has to do a little trick (personally, I call it “magic”) before he could answer the question. These questions are important in determining who among the class deserves a high grade. But the tools needed to solve the problem are there, and it is up to the student on how he/she will use these tools to answer a problem. So if you are comparing two exams created by two different teachers, and you see that one exam seems to be more difficult than the other, then one has to look at the teaching styles of these teachers. Most probably, the one who gave the difficult exam taught his/her class how to answer these types of questions. As an effect, this teacher will demand more from his/her students.

One might argue that the students don’t really understand what the teacher is saying, and yet the teacher is expecting that they will meet his/her standard. I remember one teacher of mine from my undergraduate years, and there was this one teacher who has this really terrible reputation of giving failing grades to around 80%+ of the class. But in retrospect, we are partly at fault. Given his reputation, we did not really take him seriously and just let him speak of all that nonsense without even attempting to understand what he is saying. And since no one is asking questions, he kept on babbling and babbling, thinking that we can understand what he was saying. And indeed, out of 30+ students in his class, only five of us passed the course.

What is the moral in this story? It is important to ask questions. Even a brief reaction would suffice. The teacher is not a mind reader; he will not know if the student understands the topic or not if he cannot get feedback. Believe me, it is a discouraging sight if you are speaking in front of a group of people who just stares blankly at you. If you didn’t get it the first time, ask your teacher to repeat what she said. If you cannot follow his/her logic, then ask him/her to explain further. Asking questions does not imply that you are weak; it means that you are interested to learn more, and you want to clarify certain things. Don’t be too shy to ask questions, because it will also serve as a feedback to the teacher whether the students understood the topic. If this is done, then the exams would be a good measure on how much a student has learned.

Another reason why students tend to fail the exams is because they tend to cram. This is especially true in mathematics because it is skill-based. I would always tell my students that if they want to pass the course, it is not enough to read your notes right before the exam. Also, I would advise them to ask a question immediately if there is something that they don’t understand. You will not be able to handle more advanced computations if you don’t even know the basic. Practice is very important. You will eventually memorize the quadratic formula (for example) if you have solved a dozen or more of these types of problems. Try it.

There are many different factors to consider when we are looking at failing rates. In my opinion, the one teaching the subject can assess if the exam is really difficult or not. If the teacher believes that he/she has done everything to teach the students, and yet the results are bad, then the teacher should not hesitate to give failing marks. For me, adjusting the grades (like lowering the denominator or “curving” the grades) is tantamount to admitting that there is something wrong with the given exam, or there is something wrong with the way you teach. Failing a student means that the student is not yet ready to take a more advanced course, and that’s why there is a need to retake the subject. Besides, I don’t want my colleagues to criticize me and say that I have former students failing in this particular subject because they did not learn what they should have learned in my course.

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