Three functions of examinations

Once upon a time Vladimir Abramovich Rokhlin told me:

``Independently on intentions, an examination fulfills the following three functions:

1. determines what students will learn, will know and will be able to do.

This function is most important. Ultimately it shapes the society. The exams define the contents and quality of education and, ultimately, the future of the society. For a specific exam, this function may be amplified by a value attached to the exam: the most influential are exams which play an important role in the life career (say, if the enrollment to a college depends on its result).

Students are smart. They tend to learn exactly what is helpful at an exam. Thus if something is not needed for passing an exam, it is not studied.

Nonetheless, often this most important function is not taken into account. It is not taken into account on the national level. Often it is not taken into account even on the level of a single program in a college.

It is not difficult to realize what would be consequences of a change in an exam. However, to this end at least the question should be posed. Otherwise, people just follow an established practice and take the luxury not to think about implications.

2. tests and certifies what a student really knows and can do.

An exam is expected to differentiate students, to assign grades to them.

3. teaches a student extremely efficiently.

In a stressful atmosphere of an exam, learning is most efficient. This is what keeps exams in student's memory. I remember in detail some of exams that I had 50 years ago.

Of course, if an exam consists of straightforward exercises in application of meaningless mnemonic rules, then there is nothing to remember. That exam does not teach anything valuable.

Saying this, Vladimir Abramovich did not refer to anyone. He took it as a self-obvious common sense wisdom, but added that only the second function is commonly anticipated.

The second function is of prime value from the viewpoint of a student. Many people, including those responsible for educational systems, never overgrow the level of a student and never notice the other two functions.

The American tradition of mathematical exams does not motivate a student to learn any theory. Exams are composed of problems. Formally no knowledge of definitions or theorems is required.

Often, problems in an exam are overloaded with inessential difficulties like cumbersome calculations and irrelevant details in the statements.