Grading exams

In many universities there is a tendency to eliminate the personal element from the grading of exams. That is, it is considered as a good thing to have an exam (or assignment) written in such a way so that even a machine can grade it. In fact, many argue that an exam should receive exactly the same grade regardless of who grades it, be it a machine or a human being.

To do this, administrators have taken all or some of the following steps:

1. Exams have become anonymous. So the grader does not see the name of the person who submitted the exam.
2. There are committees which decide, months before the exam is given, what the exam should be.
3. Solutions to the exam are written and they are supposed to be model solutions, predicting the exact steps the examinee will or should take.
4. The notion of partial credit has been established and sanctified. 

The intention of such rules may be good (you don't want to end up with a teacher who, for some special reasons, has the power to fail every single student). But this is hindered by the rules and regulations which are supposed to be uniform across university departments (e.g., the same exam rules should apply in the Department of Mathematics and in the Department of Theology), but also across universities in the same country or across countries. The latter is something that politicians in Europe decided they want to have, essentially advocating the Doctrine that all basic university degrees in a particular field should be equivalent, in the sense that a student with a BSc degree in Physics from the University of Bari Aldo Moro has the same knowledge as a student with the same degree from the University of Manchester. But politicians are politicians and we know why they can be so mistaken, willingly or not.

Back to the exams, however, I want to argue that *some* personal element in grading them is desirable in Mathematics, and, perhaps, in many other fields too. Here are some arguments:

1. A student screws up in a question so badly, that it is absolutely clear that the student is in the wrong field. For example, a student who reports negative probabilities, or adds fractions by adding numerators and denominators separately, or cannot find the area of a triangle  (cases taken from personal experience) should not be encouraged by partial credit. In fact, the opposite: negative credit should be given for answers which are so wrong that do not even fall in the category of "acceptable" mistakes.
2. On the other hand, suppose that a student is doing about average in all parts of the exam except in one question where he or she has a brilliant idea. An idea which shows that the student can think outside the box (that politicians, administrators, etc. want him or her to be in). In such a case, why not assign a mark which is a fraction larger than 1 of the intended mark? I would, and I will, whenever I can.
3. I can also argue that anonymous marking takes away the picture a teacher builds from a student by seeing how he or she participates in the classroom. Why, is it *only* a final exam or some written homework which will determine the eventual potential of a student? What if the teacher sees that the student has an ability which cannot be measured in a written exam? 

These are some arguments based on personal experience. I am fully aware that they are, in particular the last one, quite sensitive. No rule, whatsoever, can quantify the percentage a teacher can award a student for positive impression. But then, could the problem be in the very fact that we insist on numerical values of grades?

I am also fully aware that, given the current stupidity of European laws, none of the above arguments can be considered. However, they are all very reasonable and, moreover, rational!

Let us look, as a gedanken experiment, what could happen; what should, in a rational Society, take place in order that these changes be implemented.

First and foremost is the fact that, in wanting to make degrees from different universities equal, one makes the (wrong) assumption that all teachers are equivalent. How can this be corrected? By educating the teachers or by assigning them roles roughly equivalent to their level. This is not the case, in general. Once someone has, say, tenure, as a professor of Nuclear Physics, then nobody can raise the issue that this person may, at some point, not be able to teach his subject well. The university has no means of making sure that its teachers have the skills (real skills, not degrees) they claim to have. Has anybody ever considered giving an exam to a professor?

Second thing that should happen is to openly acknowledge that not everybody can go to university or that not everybody can go to a particular field. Not all people have the same intellectual abilities, much in the same way that not all have the same physical abilities. Everybody, of course, should have the same opportunities, but the two are not equivalent. The fact that I did have the opportunity to go to training to become Olympic athlete in boxing is not equivalent to my having the skills to do so. In fact, I never had. Likewise, the statement that anybody has the same opportunity to become a theoretical physicist is not equivalent to the statement that anybody has the same skills to do so. Human brain is just an organ. Muscle is another. It is easier to accept inequities in the latter, but not the former.

Discussing these things is like asking for Democracy to become real. It won't. (Hint: a necessary condition for real Democracy is the implementation of Ostracism.) But it doesn't hurt to discuss these things. This is why we have freedom of speech, don't we?